Epsilon:
1,2
1,2
Lam:
1,2,3
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(3)(2)*x(1)(1)*x(1)(2)
Divisor:
Delta
1,2
1,2
Quotient:
-y(1)(2)*y(3)(1)
Lead Term of Product:
y(1)(2)*y(3)(1)*x(1)(2)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,2
Quotient:
y(1)(2)*y(2)(1)
Lead Term of Product:
-y(1)(2)*y(2)(1)*x(1)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
1,2
Quotient:
-y(1)(1)*y(1)(2)
Lead Term of Product:
y(1)(1)*y(1)(2)*x(2)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(1)(1)*x(3)(2)
Lead Term of Product:
-y(1)(1)*y(2)(2)*x(1)(1)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(2)(1)*x(1)(2)+y(1)(1)*x(2)(2)
Lead Term of Product:
-y(2)(1)*y(3)(2)*x(1)(1)*x(1)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(2)*y(3)(1)*x(1)(2)+y(2)(1)*y(3)(2)*x(1)(2)+y(1)(2)*y(3)(1)*x(2)(2)-y(1)(1)*y(3)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(3)(2)+y(1)(1)*y(2)(2)*x(3)(2)) - (-y(3)(1)*x(1)(2))*(y(2)(2)*x(1)(1)-y(2)(1)*x(1)(2)-y(1)(2)*x(2)(1)+y(1)(1)*x(2)(2))
-------
Rewrite:
-y(2)(1)*y(3)(2)*x(1)(1)*x(1)(2)+y(2)(1)*y(3)(1)*x(1)(2)^2+y(1)(2)*y(3)(1)*x(1)(2)*x(2)(1)-y(1)(2)*y(3)(1)*x(1)(1)*x(2)(2)+y(1)(1)*y(3)(2)*x(1)(1)*x(2)(2)-y(1)(1)*y(3)(1)*x(1)(2)*x(2)(2)+y(1)(2)*y(2)(1)*x(1)(1)*x(3)(2)-y(1)(1)*y(2)(2)*x(1)(1)*x(3)(2)
-----------
TeX output:
S(\eps{1}{2}{1}{2}, \lam{1}{2}{3}{1}{2}{2}) =
(-y_{1, 2} y_{3, 1})  \del{1}{2}{1}{2} +(y_{1, 2} y_{2, 1})  \del{1}{3}{1}{2} +(-y_{1, 1} y_{1, 2})  \del{2}{3}{1}{2} +(-y_{1, 1} x_{3, 2})  \eps{1}{2}{1}{2} +(-y_{2, 1} x_{1, 2}+y_{1, 1} x_{2, 2})  \eps{1}{3}{1}{2}
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,3
1,2,3
Lead Term of Spoly:
-y(2)(1)*y(3)(2)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,2
1,3
Quotient:
-y(1)(2)*y(3)(1)
Lead Term of Product:
y(1)(2)*y(3)(1)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,3
Quotient:
y(1)(1)*y(3)(1)
Lead Term of Product:
-y(1)(1)*y(3)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
1,3
Quotient:
y(1)(2)*y(2)(1)
Lead Term of Product:
-y(1)(2)*y(2)(1)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
-y(1)(1)*y(2)(1)
Lead Term of Product:
y(1)(1)*y(2)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,3
Quotient:
-y(1)(1)*y(1)(2)
Lead Term of Product:
y(1)(1)*y(1)(2)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
y(1)(1)^2
Lead Term of Product:
-y(1)(1)^2*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(1)(1)*x(3)(3)
Lead Term of Product:
-y(1)(1)*y(2)(2)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(2)(1)*x(1)(3)+y(1)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(3)(2)*x(1)(1)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(2)*y(3)(1)*x(1)(3)+y(2)(1)*y(3)(2)*x(1)(3)+y(1)(2)*y(3)(1)*x(2)(3)-y(1)(1)*y(3)(2)*x(2)(3)-y(1)(2)*y(2)(1)*x(3)(3)+y(1)(1)*y(2)(2)*x(3)(3)) - (-y(3)(1)*x(1)(3))*(y(2)(2)*x(1)(1)-y(2)(1)*x(1)(2)-y(1)(2)*x(2)(1)+y(1)(1)*x(2)(2))
-------
Rewrite:
-y(2)(1)*y(3)(2)*x(1)(1)*x(1)(3)+y(2)(1)*y(3)(1)*x(1)(2)*x(1)(3)+y(1)(2)*y(3)(1)*x(1)(3)*x(2)(1)-y(1)(1)*y(3)(1)*x(1)(3)*x(2)(2)-y(1)(2)*y(3)(1)*x(1)(1)*x(2)(3)+y(1)(1)*y(3)(2)*x(1)(1)*x(2)(3)+y(1)(2)*y(2)(1)*x(1)(1)*x(3)(3)-y(1)(1)*y(2)(2)*x(1)(1)*x(3)(3)
-----------
TeX output:
S(\eps{1}{2}{1}{2}, \lam{1}{2}{3}{1}{2}{3}) =
(-y_{1, 2} y_{3, 1})  \del{1}{2}{1}{3} +(y_{1, 1} y_{3, 1})  \del{1}{2}{2}{3} +(y_{1, 2} y_{2, 1})  \del{1}{3}{1}{3} +(-y_{1, 1} y_{2, 1})  \del{1}{3}{2}{3} +(-y_{1, 1} y_{1, 2})  \del{2}{3}{1}{3} +(y_{1, 1}^2)  \del{2}{3}{2}{3} +(-y_{1, 1} x_{3, 3})  \eps{1}{2}{1}{2} +(-y_{2, 1} x_{1, 3}+y_{1, 1} x_{2, 3})  \eps{1}{3}{1}{2}
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,3
1,2,4
Lead Term of Spoly:
-y(2)(1)*y(3)(2)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(2)*y(3)(1)
Lead Term of Product:
y(1)(2)*y(3)(1)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
y(1)(1)*y(3)(1)
Lead Term of Product:
-y(1)(1)*y(3)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
y(1)(2)*y(2)(1)
Lead Term of Product:
-y(1)(2)*y(2)(1)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(1)(1)*y(2)(1)
Lead Term of Product:
y(1)(1)*y(2)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
-y(1)(1)*y(1)(2)
Lead Term of Product:
y(1)(1)*y(1)(2)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
y(1)(1)^2
Lead Term of Product:
-y(1)(1)^2*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(1)(1)*x(3)(4)
Lead Term of Product:
-y(1)(1)*y(2)(2)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(2)*x(1)(1)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(2)*y(3)(1)*x(1)(4)+y(2)(1)*y(3)(2)*x(1)(4)+y(1)(2)*y(3)(1)*x(2)(4)-y(1)(1)*y(3)(2)*x(2)(4)-y(1)(2)*y(2)(1)*x(3)(4)+y(1)(1)*y(2)(2)*x(3)(4)) - (-y(3)(1)*x(1)(4))*(y(2)(2)*x(1)(1)-y(2)(1)*x(1)(2)-y(1)(2)*x(2)(1)+y(1)(1)*x(2)(2))
-------
Rewrite:
-y(2)(1)*y(3)(2)*x(1)(1)*x(1)(4)+y(2)(1)*y(3)(1)*x(1)(2)*x(1)(4)+y(1)(2)*y(3)(1)*x(1)(4)*x(2)(1)-y(1)(1)*y(3)(1)*x(1)(4)*x(2)(2)-y(1)(2)*y(3)(1)*x(1)(1)*x(2)(4)+y(1)(1)*y(3)(2)*x(1)(1)*x(2)(4)+y(1)(2)*y(2)(1)*x(1)(1)*x(3)(4)-y(1)(1)*y(2)(2)*x(1)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{2}, \lam{1}{2}{3}{1}{2}{4}) =
(-y_{1, 2} y_{3, 1})  \del{1}{2}{1}{4} +(y_{1, 1} y_{3, 1})  \del{1}{2}{2}{4} +(y_{1, 2} y_{2, 1})  \del{1}{3}{1}{4} +(-y_{1, 1} y_{2, 1})  \del{1}{3}{2}{4} +(-y_{1, 1} y_{1, 2})  \del{2}{3}{1}{4} +(y_{1, 1}^2)  \del{2}{3}{2}{4} +(-y_{1, 1} x_{3, 4})  \eps{1}{2}{1}{2} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{1}{2}
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,4
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(4)(2)*x(1)(1)*x(1)(2)
Divisor:
Delta
1,2
1,2
Quotient:
-y(1)(2)*y(4)(1)
Lead Term of Product:
y(1)(2)*y(4)(1)*x(1)(2)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,4
1,2
Quotient:
y(1)(2)*y(2)(1)
Lead Term of Product:
-y(1)(2)*y(2)(1)*x(1)(2)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,2
Quotient:
-y(1)(1)*y(1)(2)
Lead Term of Product:
y(1)(1)*y(1)(2)*x(2)(2)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(1)(1)*x(4)(2)
Lead Term of Product:
-y(1)(1)*y(2)(2)*x(1)(1)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(2)(1)*x(1)(2)+y(1)(1)*x(2)(2)
Lead Term of Product:
-y(2)(1)*y(4)(2)*x(1)(1)*x(1)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(2)*y(4)(1)*x(1)(2)+y(2)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(2)(2)-y(1)(1)*y(4)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(4)(2)+y(1)(1)*y(2)(2)*x(4)(2)) - (-y(4)(1)*x(1)(2))*(y(2)(2)*x(1)(1)-y(2)(1)*x(1)(2)-y(1)(2)*x(2)(1)+y(1)(1)*x(2)(2))
-------
Rewrite:
-y(2)(1)*y(4)(2)*x(1)(1)*x(1)(2)+y(2)(1)*y(4)(1)*x(1)(2)^2+y(1)(2)*y(4)(1)*x(1)(2)*x(2)(1)-y(1)(2)*y(4)(1)*x(1)(1)*x(2)(2)+y(1)(1)*y(4)(2)*x(1)(1)*x(2)(2)-y(1)(1)*y(4)(1)*x(1)(2)*x(2)(2)+y(1)(2)*y(2)(1)*x(1)(1)*x(4)(2)-y(1)(1)*y(2)(2)*x(1)(1)*x(4)(2)
-----------
TeX output:
S(\eps{1}{2}{1}{2}, \lam{1}{2}{4}{1}{2}{2}) =
(-y_{1, 2} y_{4, 1})  \del{1}{2}{1}{2} +(y_{1, 2} y_{2, 1})  \del{1}{4}{1}{2} +(-y_{1, 1} y_{1, 2})  \del{2}{4}{1}{2} +(-y_{1, 1} x_{4, 2})  \eps{1}{2}{1}{2} +(-y_{2, 1} x_{1, 2}+y_{1, 1} x_{2, 2})  \eps{1}{4}{1}{2}
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,4
1,2,3
Lead Term of Spoly:
-y(2)(1)*y(4)(2)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,2
1,3
Quotient:
-y(1)(2)*y(4)(1)
Lead Term of Product:
y(1)(2)*y(4)(1)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,3
Quotient:
y(1)(1)*y(4)(1)
Lead Term of Product:
-y(1)(1)*y(4)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,3
Quotient:
y(1)(2)*y(2)(1)
Lead Term of Product:
-y(1)(2)*y(2)(1)*x(1)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
-y(1)(1)*y(2)(1)
Lead Term of Product:
y(1)(1)*y(2)(1)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
-y(1)(1)*y(1)(2)
Lead Term of Product:
y(1)(1)*y(1)(2)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(1)(1)^2
Lead Term of Product:
-y(1)(1)^2*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(1)(1)*x(4)(3)
Lead Term of Product:
-y(1)(1)*y(2)(2)*x(1)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(2)(1)*x(1)(3)+y(1)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(4)(2)*x(1)(1)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(2)*y(4)(1)*x(1)(3)+y(2)(1)*y(4)(2)*x(1)(3)+y(1)(2)*y(4)(1)*x(2)(3)-y(1)(1)*y(4)(2)*x(2)(3)-y(1)(2)*y(2)(1)*x(4)(3)+y(1)(1)*y(2)(2)*x(4)(3)) - (-y(4)(1)*x(1)(3))*(y(2)(2)*x(1)(1)-y(2)(1)*x(1)(2)-y(1)(2)*x(2)(1)+y(1)(1)*x(2)(2))
-------
Rewrite:
-y(2)(1)*y(4)(2)*x(1)(1)*x(1)(3)+y(2)(1)*y(4)(1)*x(1)(2)*x(1)(3)+y(1)(2)*y(4)(1)*x(1)(3)*x(2)(1)-y(1)(1)*y(4)(1)*x(1)(3)*x(2)(2)-y(1)(2)*y(4)(1)*x(1)(1)*x(2)(3)+y(1)(1)*y(4)(2)*x(1)(1)*x(2)(3)+y(1)(2)*y(2)(1)*x(1)(1)*x(4)(3)-y(1)(1)*y(2)(2)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{2}{1}{2}, \lam{1}{2}{4}{1}{2}{3}) =
(-y_{1, 2} y_{4, 1})  \del{1}{2}{1}{3} +(y_{1, 1} y_{4, 1})  \del{1}{2}{2}{3} +(y_{1, 2} y_{2, 1})  \del{1}{4}{1}{3} +(-y_{1, 1} y_{2, 1})  \del{1}{4}{2}{3} +(-y_{1, 1} y_{1, 2})  \del{2}{4}{1}{3} +(y_{1, 1}^2)  \del{2}{4}{2}{3} +(-y_{1, 1} x_{4, 3})  \eps{1}{2}{1}{2} +(-y_{2, 1} x_{1, 3}+y_{1, 1} x_{2, 3})  \eps{1}{4}{1}{2}
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,4
1,2,4
Lead Term of Spoly:
-y(2)(1)*y(4)(2)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(2)*y(4)(1)
Lead Term of Product:
y(1)(2)*y(4)(1)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
y(1)(1)*y(4)(1)
Lead Term of Product:
-y(1)(1)*y(4)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
y(1)(2)*y(2)(1)
Lead Term of Product:
-y(1)(2)*y(2)(1)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
-y(1)(1)*y(2)(1)
Lead Term of Product:
y(1)(1)*y(2)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(1)(1)*y(1)(2)
Lead Term of Product:
y(1)(1)*y(1)(2)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(1)^2
Lead Term of Product:
-y(1)(1)^2*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(2)(2)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(2)*x(1)(1)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(2)*y(4)(1)*x(1)(4)+y(2)(1)*y(4)(2)*x(1)(4)+y(1)(2)*y(4)(1)*x(2)(4)-y(1)(1)*y(4)(2)*x(2)(4)-y(1)(2)*y(2)(1)*x(4)(4)+y(1)(1)*y(2)(2)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(2)(2)*x(1)(1)-y(2)(1)*x(1)(2)-y(1)(2)*x(2)(1)+y(1)(1)*x(2)(2))
-------
Rewrite:
-y(2)(1)*y(4)(2)*x(1)(1)*x(1)(4)+y(2)(1)*y(4)(1)*x(1)(2)*x(1)(4)+y(1)(2)*y(4)(1)*x(1)(4)*x(2)(1)-y(1)(1)*y(4)(1)*x(1)(4)*x(2)(2)-y(1)(2)*y(4)(1)*x(1)(1)*x(2)(4)+y(1)(1)*y(4)(2)*x(1)(1)*x(2)(4)+y(1)(2)*y(2)(1)*x(1)(1)*x(4)(4)-y(1)(1)*y(2)(2)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{2}, \lam{1}{2}{4}{1}{2}{4}) =
(-y_{1, 2} y_{4, 1})  \del{1}{2}{1}{4} +(y_{1, 1} y_{4, 1})  \del{1}{2}{2}{4} +(y_{1, 2} y_{2, 1})  \del{1}{4}{1}{4} +(-y_{1, 1} y_{2, 1})  \del{1}{4}{2}{4} +(-y_{1, 1} y_{1, 2})  \del{2}{4}{1}{4} +(y_{1, 1}^2)  \del{2}{4}{2}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{2}{1}{2} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{1}{2}
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,3
1,3,3
Lead Term of Spoly:
-y(2)(1)*y(3)(3)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,2
1,3
Quotient:
-y(1)(3)*y(3)(1)
Lead Term of Product:
y(1)(3)*y(3)(1)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,3
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
1,3
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(1)(1)*x(3)(3)
Lead Term of Product:
-y(1)(1)*y(2)(3)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(2)(1)*x(1)(3)+y(1)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(1)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(3)(1)*x(1)(3)+y(2)(1)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(1)*x(2)(3)-y(1)(1)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(1)*x(3)(3)+y(1)(1)*y(2)(3)*x(3)(3)) - (-y(3)(1)*x(1)(3))*(y(2)(3)*x(1)(1)-y(2)(1)*x(1)(3)-y(1)(3)*x(2)(1)+y(1)(1)*x(2)(3))
-------
Rewrite:
-y(2)(1)*y(3)(3)*x(1)(1)*x(1)(3)+y(2)(1)*y(3)(1)*x(1)(3)^2+y(1)(3)*y(3)(1)*x(1)(3)*x(2)(1)-y(1)(3)*y(3)(1)*x(1)(1)*x(2)(3)+y(1)(1)*y(3)(3)*x(1)(1)*x(2)(3)-y(1)(1)*y(3)(1)*x(1)(3)*x(2)(3)+y(1)(3)*y(2)(1)*x(1)(1)*x(3)(3)-y(1)(1)*y(2)(3)*x(1)(1)*x(3)(3)
-----------
TeX output:
S(\eps{1}{2}{1}{3}, \lam{1}{2}{3}{1}{3}{3}) =
(-y_{1, 3} y_{3, 1})  \del{1}{2}{1}{3} +(y_{1, 3} y_{2, 1})  \del{1}{3}{1}{3} +(-y_{1, 1} y_{1, 3})  \del{2}{3}{1}{3} +(-y_{1, 1} x_{3, 3})  \eps{1}{2}{1}{3} +(-y_{2, 1} x_{1, 3}+y_{1, 1} x_{2, 3})  \eps{1}{3}{1}{3}
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,3
1,3,4
Lead Term of Spoly:
-y(2)(1)*y(3)(3)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(3)*y(3)(1)
Lead Term of Product:
y(1)(3)*y(3)(1)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
y(1)(1)*y(3)(1)
Lead Term of Product:
-y(1)(1)*y(3)(1)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(1)*y(2)(1)
Lead Term of Product:
y(1)(1)*y(2)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(1)(1)^2
Lead Term of Product:
-y(1)(1)^2*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(1)(1)*x(3)(4)
Lead Term of Product:
-y(1)(1)*y(2)(3)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(1)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(3)(1)*x(1)(4)+y(2)(1)*y(3)(3)*x(1)(4)+y(1)(3)*y(3)(1)*x(2)(4)-y(1)(1)*y(3)(3)*x(2)(4)-y(1)(3)*y(2)(1)*x(3)(4)+y(1)(1)*y(2)(3)*x(3)(4)) - (-y(3)(1)*x(1)(4))*(y(2)(3)*x(1)(1)-y(2)(1)*x(1)(3)-y(1)(3)*x(2)(1)+y(1)(1)*x(2)(3))
-------
Rewrite:
-y(2)(1)*y(3)(3)*x(1)(1)*x(1)(4)+y(2)(1)*y(3)(1)*x(1)(3)*x(1)(4)+y(1)(3)*y(3)(1)*x(1)(4)*x(2)(1)-y(1)(1)*y(3)(1)*x(1)(4)*x(2)(3)-y(1)(3)*y(3)(1)*x(1)(1)*x(2)(4)+y(1)(1)*y(3)(3)*x(1)(1)*x(2)(4)+y(1)(3)*y(2)(1)*x(1)(1)*x(3)(4)-y(1)(1)*y(2)(3)*x(1)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{3}, \lam{1}{2}{3}{1}{3}{4}) =
(-y_{1, 3} y_{3, 1})  \del{1}{2}{1}{4} +(y_{1, 1} y_{3, 1})  \del{1}{2}{3}{4} +(y_{1, 3} y_{2, 1})  \del{1}{3}{1}{4} +(-y_{1, 1} y_{2, 1})  \del{1}{3}{3}{4} +(-y_{1, 1} y_{1, 3})  \del{2}{3}{1}{4} +(y_{1, 1}^2)  \del{2}{3}{3}{4} +(-y_{1, 1} x_{3, 4})  \eps{1}{2}{1}{3} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{1}{3}
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,3
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,2
1,3
Quotient:
-y(1)(3)*y(3)(2)+y(1)(2)*y(3)(3)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,3
Quotient:
-y(1)(1)*y(3)(3)
Lead Term of Product:
y(1)(1)*y(3)(3)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(3)(3)*x(1)(3)+y(1)(3)*x(3)(3)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(1)(2)*x(3)(3)
Lead Term of Product:
-y(1)(2)*y(2)(3)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(1)(3)+y(1)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(3)(2)*x(1)(3)+y(2)(2)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(2)*x(2)(3)-y(1)(2)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(3)(3)+y(1)(2)*y(2)(3)*x(3)(3)) - (-y(3)(2)*x(1)(3))*(y(2)(3)*x(1)(1)-y(2)(1)*x(1)(3)-y(1)(3)*x(2)(1)+y(1)(1)*x(2)(3))
-------
Rewrite:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(3)+y(2)(1)*y(3)(2)*x(1)(3)^2+y(1)(3)*y(3)(2)*x(1)(3)*x(2)(1)-y(1)(3)*y(3)(2)*x(1)(1)*x(2)(3)+y(1)(2)*y(3)(3)*x(1)(1)*x(2)(3)-y(1)(1)*y(3)(2)*x(1)(3)*x(2)(3)+y(1)(3)*y(2)(2)*x(1)(1)*x(3)(3)-y(1)(2)*y(2)(3)*x(1)(1)*x(3)(3)
-----------
TeX output:
S(\eps{1}{2}{1}{3}, \lam{1}{2}{3}{2}{3}{3}) =
(-y_{1, 3} y_{3, 2}+y_{1, 2} y_{3, 3})  \del{1}{2}{1}{3} +(-y_{1, 1} y_{3, 3})  \del{1}{2}{2}{3} +(y_{1, 3} y_{2, 1})  \del{1}{3}{2}{3} +(-y_{1, 1} y_{1, 3})  \del{2}{3}{2}{3} +(-y_{3, 3} x_{1, 3}+y_{1, 3} x_{3, 3})  \eps{1}{2}{1}{2} +(-y_{1, 2} x_{3, 3})  \eps{1}{2}{1}{3} +(-y_{2, 1} x_{1, 3}+y_{1, 1} x_{2, 3})  \eps{1}{3}{2}{3}
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,3
2,3,4
Lead Term of Spoly:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(3)*y(3)(2)+y(1)(2)*y(3)(3)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(1)*y(3)(3)
Lead Term of Product:
y(1)(1)*y(3)(3)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(1)*y(3)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(2)*y(2)(1)
Lead Term of Product:
y(1)(2)*y(2)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(1)(1)*y(1)(2)
Lead Term of Product:
-y(1)(1)*y(1)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(3)(3)*x(1)(4)+y(1)(3)*x(3)(4)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(1)(2)*x(3)(4)
Lead Term of Product:
-y(1)(2)*y(2)(3)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(3)(2)*x(1)(4)+y(2)(2)*y(3)(3)*x(1)(4)+y(1)(3)*y(3)(2)*x(2)(4)-y(1)(2)*y(3)(3)*x(2)(4)-y(1)(3)*y(2)(2)*x(3)(4)+y(1)(2)*y(2)(3)*x(3)(4)) - (-y(3)(2)*x(1)(4))*(y(2)(3)*x(1)(1)-y(2)(1)*x(1)(3)-y(1)(3)*x(2)(1)+y(1)(1)*x(2)(3))
-------
Rewrite:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(4)+y(2)(1)*y(3)(2)*x(1)(3)*x(1)(4)+y(1)(3)*y(3)(2)*x(1)(4)*x(2)(1)-y(1)(1)*y(3)(2)*x(1)(4)*x(2)(3)-y(1)(3)*y(3)(2)*x(1)(1)*x(2)(4)+y(1)(2)*y(3)(3)*x(1)(1)*x(2)(4)+y(1)(3)*y(2)(2)*x(1)(1)*x(3)(4)-y(1)(2)*y(2)(3)*x(1)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{3}, \lam{1}{2}{3}{2}{3}{4}) =
(-y_{1, 3} y_{3, 2}+y_{1, 2} y_{3, 3})  \del{1}{2}{1}{4} +(-y_{1, 1} y_{3, 3})  \del{1}{2}{2}{4} +(y_{1, 1} y_{3, 2})  \del{1}{2}{3}{4} +(y_{1, 3} y_{2, 1})  \del{1}{3}{2}{4} +(-y_{1, 2} y_{2, 1})  \del{1}{3}{3}{4} +(-y_{1, 1} y_{1, 3})  \del{2}{3}{2}{4} +(y_{1, 1} y_{1, 2})  \del{2}{3}{3}{4} +(-y_{3, 3} x_{1, 4}+y_{1, 3} x_{3, 4})  \eps{1}{2}{1}{2} +(-y_{1, 2} x_{3, 4})  \eps{1}{2}{1}{3} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{2}{3}
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,4
1,3,3
Lead Term of Spoly:
-y(2)(1)*y(4)(3)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,2
1,3
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,4
1,3
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(1)(1)*x(4)(3)
Lead Term of Product:
-y(1)(1)*y(2)(3)*x(1)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,3
Quotient:
-y(2)(1)*x(1)(3)+y(1)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(1)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(4)(1)*x(1)(3)+y(2)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(2)(3)-y(1)(1)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(1)*x(4)(3)+y(1)(1)*y(2)(3)*x(4)(3)) - (-y(4)(1)*x(1)(3))*(y(2)(3)*x(1)(1)-y(2)(1)*x(1)(3)-y(1)(3)*x(2)(1)+y(1)(1)*x(2)(3))
-------
Rewrite:
-y(2)(1)*y(4)(3)*x(1)(1)*x(1)(3)+y(2)(1)*y(4)(1)*x(1)(3)^2+y(1)(3)*y(4)(1)*x(1)(3)*x(2)(1)-y(1)(3)*y(4)(1)*x(1)(1)*x(2)(3)+y(1)(1)*y(4)(3)*x(1)(1)*x(2)(3)-y(1)(1)*y(4)(1)*x(1)(3)*x(2)(3)+y(1)(3)*y(2)(1)*x(1)(1)*x(4)(3)-y(1)(1)*y(2)(3)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{2}{1}{3}, \lam{1}{2}{4}{1}{3}{3}) =
(-y_{1, 3} y_{4, 1})  \del{1}{2}{1}{3} +(y_{1, 3} y_{2, 1})  \del{1}{4}{1}{3} +(-y_{1, 1} y_{1, 3})  \del{2}{4}{1}{3} +(-y_{1, 1} x_{4, 3})  \eps{1}{2}{1}{3} +(-y_{2, 1} x_{1, 3}+y_{1, 1} x_{2, 3})  \eps{1}{4}{1}{3}
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,4
1,3,4
Lead Term of Spoly:
-y(2)(1)*y(4)(3)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
y(1)(1)*y(4)(1)
Lead Term of Product:
-y(1)(1)*y(4)(1)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
-y(1)(1)*y(2)(1)
Lead Term of Product:
y(1)(1)*y(2)(1)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(1)^2
Lead Term of Product:
-y(1)(1)^2*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(2)(3)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,3
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(1)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(4)(1)*x(1)(4)+y(2)(1)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(1)*x(2)(4)-y(1)(1)*y(4)(3)*x(2)(4)-y(1)(3)*y(2)(1)*x(4)(4)+y(1)(1)*y(2)(3)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(2)(3)*x(1)(1)-y(2)(1)*x(1)(3)-y(1)(3)*x(2)(1)+y(1)(1)*x(2)(3))
-------
Rewrite:
-y(2)(1)*y(4)(3)*x(1)(1)*x(1)(4)+y(2)(1)*y(4)(1)*x(1)(3)*x(1)(4)+y(1)(3)*y(4)(1)*x(1)(4)*x(2)(1)-y(1)(1)*y(4)(1)*x(1)(4)*x(2)(3)-y(1)(3)*y(4)(1)*x(1)(1)*x(2)(4)+y(1)(1)*y(4)(3)*x(1)(1)*x(2)(4)+y(1)(3)*y(2)(1)*x(1)(1)*x(4)(4)-y(1)(1)*y(2)(3)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{3}, \lam{1}{2}{4}{1}{3}{4}) =
(-y_{1, 3} y_{4, 1})  \del{1}{2}{1}{4} +(y_{1, 1} y_{4, 1})  \del{1}{2}{3}{4} +(y_{1, 3} y_{2, 1})  \del{1}{4}{1}{4} +(-y_{1, 1} y_{2, 1})  \del{1}{4}{3}{4} +(-y_{1, 1} y_{1, 3})  \del{2}{4}{1}{4} +(y_{1, 1}^2)  \del{2}{4}{3}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{2}{1}{3} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{1}{3}
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,4
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,2
1,3
Quotient:
-y(1)(3)*y(4)(2)+y(1)(2)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,3
Quotient:
-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(3)*x(1)(3)+y(1)(3)*x(4)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(1)(2)*x(4)(3)
Lead Term of Product:
-y(1)(2)*y(2)(3)*x(1)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*x(1)(3)+y(1)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(4)(2)*x(1)(3)+y(2)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(2)(3)-y(1)(2)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(4)(3)+y(1)(2)*y(2)(3)*x(4)(3)) - (-y(4)(2)*x(1)(3))*(y(2)(3)*x(1)(1)-y(2)(1)*x(1)(3)-y(1)(3)*x(2)(1)+y(1)(1)*x(2)(3))
-------
Rewrite:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(3)+y(2)(1)*y(4)(2)*x(1)(3)^2+y(1)(3)*y(4)(2)*x(1)(3)*x(2)(1)-y(1)(3)*y(4)(2)*x(1)(1)*x(2)(3)+y(1)(2)*y(4)(3)*x(1)(1)*x(2)(3)-y(1)(1)*y(4)(2)*x(1)(3)*x(2)(3)+y(1)(3)*y(2)(2)*x(1)(1)*x(4)(3)-y(1)(2)*y(2)(3)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{2}{1}{3}, \lam{1}{2}{4}{2}{3}{3}) =
(-y_{1, 3} y_{4, 2}+y_{1, 2} y_{4, 3})  \del{1}{2}{1}{3} +(-y_{1, 1} y_{4, 3})  \del{1}{2}{2}{3} +(y_{1, 3} y_{2, 1})  \del{1}{4}{2}{3} +(-y_{1, 1} y_{1, 3})  \del{2}{4}{2}{3} +(-y_{4, 3} x_{1, 3}+y_{1, 3} x_{4, 3})  \eps{1}{2}{1}{2} +(-y_{1, 2} x_{4, 3})  \eps{1}{2}{1}{3} +(-y_{2, 1} x_{1, 3}+y_{1, 1} x_{2, 3})  \eps{1}{4}{2}{3}
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,4
2,3,4
Lead Term of Spoly:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(3)*y(4)(2)+y(1)(2)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(1)*y(4)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
-y(1)(2)*y(2)(1)
Lead Term of Product:
y(1)(2)*y(2)(1)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(1)*y(1)(2)
Lead Term of Product:
-y(1)(1)*y(1)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(3)*x(1)(4)+y(1)(3)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(2)(3)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(4)(2)*x(1)(4)+y(2)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(2)(4)-y(1)(2)*y(4)(3)*x(2)(4)-y(1)(3)*y(2)(2)*x(4)(4)+y(1)(2)*y(2)(3)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(2)(3)*x(1)(1)-y(2)(1)*x(1)(3)-y(1)(3)*x(2)(1)+y(1)(1)*x(2)(3))
-------
Rewrite:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(4)+y(2)(1)*y(4)(2)*x(1)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(1)(4)*x(2)(1)-y(1)(1)*y(4)(2)*x(1)(4)*x(2)(3)-y(1)(3)*y(4)(2)*x(1)(1)*x(2)(4)+y(1)(2)*y(4)(3)*x(1)(1)*x(2)(4)+y(1)(3)*y(2)(2)*x(1)(1)*x(4)(4)-y(1)(2)*y(2)(3)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{3}, \lam{1}{2}{4}{2}{3}{4}) =
(-y_{1, 3} y_{4, 2}+y_{1, 2} y_{4, 3})  \del{1}{2}{1}{4} +(-y_{1, 1} y_{4, 3})  \del{1}{2}{2}{4} +(y_{1, 1} y_{4, 2})  \del{1}{2}{3}{4} +(y_{1, 3} y_{2, 1})  \del{1}{4}{2}{4} +(-y_{1, 2} y_{2, 1})  \del{1}{4}{3}{4} +(-y_{1, 1} y_{1, 3})  \del{2}{4}{2}{4} +(y_{1, 1} y_{1, 2})  \del{2}{4}{3}{4} +(-y_{4, 3} x_{1, 4}+y_{1, 3} x_{4, 4})  \eps{1}{2}{1}{2} +(-y_{1, 2} x_{4, 4})  \eps{1}{2}{1}{3} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{2}{3}
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,3
1,4,4
Lead Term of Spoly:
-y(2)(1)*y(3)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(4)*y(3)(1)
Lead Term of Product:
y(1)(4)*y(3)(1)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
y(1)(4)*y(2)(1)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
-y(1)(1)*x(3)(4)
Lead Term of Product:
-y(1)(1)*y(2)(4)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(4)*y(3)(1)*x(1)(4)+y(2)(1)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(1)*x(2)(4)-y(1)(1)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(1)*x(3)(4)+y(1)(1)*y(2)(4)*x(3)(4)) - (-y(3)(1)*x(1)(4))*(y(2)(4)*x(1)(1)-y(2)(1)*x(1)(4)-y(1)(4)*x(2)(1)+y(1)(1)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(3)(4)*x(1)(1)*x(1)(4)+y(2)(1)*y(3)(1)*x(1)(4)^2+y(1)(4)*y(3)(1)*x(1)(4)*x(2)(1)-y(1)(4)*y(3)(1)*x(1)(1)*x(2)(4)+y(1)(1)*y(3)(4)*x(1)(1)*x(2)(4)-y(1)(1)*y(3)(1)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(1)*x(1)(1)*x(3)(4)-y(1)(1)*y(2)(4)*x(1)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{4}, \lam{1}{2}{3}{1}{4}{4}) =
(-y_{1, 4} y_{3, 1})  \del{1}{2}{1}{4} +(y_{1, 4} y_{2, 1})  \del{1}{3}{1}{4} +(-y_{1, 1} y_{1, 4})  \del{2}{3}{1}{4} +(-y_{1, 1} x_{3, 4})  \eps{1}{2}{1}{4} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{1}{4}
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,3
2,4,4
Lead Term of Spoly:
-y(2)(2)*y(3)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(4)*y(3)(2)+y(1)(2)*y(3)(4)
Lead Term of Product:
y(1)(4)*y(3)(2)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(1)*y(3)(4)
Lead Term of Product:
y(1)(1)*y(3)(4)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(1)(4)*y(2)(1)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(3)(4)*x(1)(4)+y(1)(4)*x(3)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
-y(1)(2)*x(3)(4)
Lead Term of Product:
-y(1)(2)*y(2)(4)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(4)*y(3)(2)*x(1)(4)+y(2)(2)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(2)*x(2)(4)-y(1)(2)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(2)*x(3)(4)+y(1)(2)*y(2)(4)*x(3)(4)) - (-y(3)(2)*x(1)(4))*(y(2)(4)*x(1)(1)-y(2)(1)*x(1)(4)-y(1)(4)*x(2)(1)+y(1)(1)*x(2)(4))
-------
Rewrite:
-y(2)(2)*y(3)(4)*x(1)(1)*x(1)(4)+y(2)(1)*y(3)(2)*x(1)(4)^2+y(1)(4)*y(3)(2)*x(1)(4)*x(2)(1)-y(1)(4)*y(3)(2)*x(1)(1)*x(2)(4)+y(1)(2)*y(3)(4)*x(1)(1)*x(2)(4)-y(1)(1)*y(3)(2)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(2)*x(1)(1)*x(3)(4)-y(1)(2)*y(2)(4)*x(1)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{4}, \lam{1}{2}{3}{2}{4}{4}) =
(-y_{1, 4} y_{3, 2}+y_{1, 2} y_{3, 4})  \del{1}{2}{1}{4} +(-y_{1, 1} y_{3, 4})  \del{1}{2}{2}{4} +(y_{1, 4} y_{2, 1})  \del{1}{3}{2}{4} +(-y_{1, 1} y_{1, 4})  \del{2}{3}{2}{4} +(-y_{3, 4} x_{1, 4}+y_{1, 4} x_{3, 4})  \eps{1}{2}{1}{2} +(-y_{1, 2} x_{3, 4})  \eps{1}{2}{1}{4} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{2}{4}
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,3
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(3)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(4)*y(3)(3)+y(1)(3)*y(3)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(1)*y(3)(4)
Lead Term of Product:
y(1)(1)*y(3)(4)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(4)*y(2)(1)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(3)(4)*x(1)(4)+y(1)(4)*x(3)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
-y(1)(3)*x(3)(4)
Lead Term of Product:
-y(1)(3)*y(2)(4)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(4)*y(3)(3)*x(1)(4)+y(2)(3)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(3)*x(2)(4)-y(1)(3)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(3)(4)+y(1)(3)*y(2)(4)*x(3)(4)) - (-y(3)(3)*x(1)(4))*(y(2)(4)*x(1)(1)-y(2)(1)*x(1)(4)-y(1)(4)*x(2)(1)+y(1)(1)*x(2)(4))
-------
Rewrite:
-y(2)(3)*y(3)(4)*x(1)(1)*x(1)(4)+y(2)(1)*y(3)(3)*x(1)(4)^2+y(1)(4)*y(3)(3)*x(1)(4)*x(2)(1)-y(1)(4)*y(3)(3)*x(1)(1)*x(2)(4)+y(1)(3)*y(3)(4)*x(1)(1)*x(2)(4)-y(1)(1)*y(3)(3)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(3)*x(1)(1)*x(3)(4)-y(1)(3)*y(2)(4)*x(1)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{4}, \lam{1}{2}{3}{3}{4}{4}) =
(-y_{1, 4} y_{3, 3}+y_{1, 3} y_{3, 4})  \del{1}{2}{1}{4} +(-y_{1, 1} y_{3, 4})  \del{1}{2}{3}{4} +(y_{1, 4} y_{2, 1})  \del{1}{3}{3}{4} +(-y_{1, 1} y_{1, 4})  \del{2}{3}{3}{4} +(-y_{3, 4} x_{1, 4}+y_{1, 4} x_{3, 4})  \eps{1}{2}{1}{3} +(-y_{1, 3} x_{3, 4})  \eps{1}{2}{1}{4} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{3}{4}
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,4
1,4,4
Lead Term of Spoly:
-y(2)(1)*y(4)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(4)*y(4)(1)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
y(1)(4)*y(2)(1)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(2)(4)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(4)*y(4)(1)*x(1)(4)+y(2)(1)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(1)*x(2)(4)-y(1)(1)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(1)*x(4)(4)+y(1)(1)*y(2)(4)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(2)(4)*x(1)(1)-y(2)(1)*x(1)(4)-y(1)(4)*x(2)(1)+y(1)(1)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(4)(4)*x(1)(1)*x(1)(4)+y(2)(1)*y(4)(1)*x(1)(4)^2+y(1)(4)*y(4)(1)*x(1)(4)*x(2)(1)-y(1)(4)*y(4)(1)*x(1)(1)*x(2)(4)+y(1)(1)*y(4)(4)*x(1)(1)*x(2)(4)-y(1)(1)*y(4)(1)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(1)*x(1)(1)*x(4)(4)-y(1)(1)*y(2)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{4}, \lam{1}{2}{4}{1}{4}{4}) =
(-y_{1, 4} y_{4, 1})  \del{1}{2}{1}{4} +(y_{1, 4} y_{2, 1})  \del{1}{4}{1}{4} +(-y_{1, 1} y_{1, 4})  \del{2}{4}{1}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{2}{1}{4} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{1}{4}
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,4
2,4,4
Lead Term of Spoly:
-y(2)(2)*y(4)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(4)*y(4)(2)+y(1)(2)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(4)*y(2)(1)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(2)(4)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(4)*y(4)(2)*x(1)(4)+y(2)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(2)(4)-y(1)(2)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(2)*x(4)(4)+y(1)(2)*y(2)(4)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(2)(4)*x(1)(1)-y(2)(1)*x(1)(4)-y(1)(4)*x(2)(1)+y(1)(1)*x(2)(4))
-------
Rewrite:
-y(2)(2)*y(4)(4)*x(1)(1)*x(1)(4)+y(2)(1)*y(4)(2)*x(1)(4)^2+y(1)(4)*y(4)(2)*x(1)(4)*x(2)(1)-y(1)(4)*y(4)(2)*x(1)(1)*x(2)(4)+y(1)(2)*y(4)(4)*x(1)(1)*x(2)(4)-y(1)(1)*y(4)(2)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(2)*x(1)(1)*x(4)(4)-y(1)(2)*y(2)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{4}, \lam{1}{2}{4}{2}{4}{4}) =
(-y_{1, 4} y_{4, 2}+y_{1, 2} y_{4, 4})  \del{1}{2}{1}{4} +(-y_{1, 1} y_{4, 4})  \del{1}{2}{2}{4} +(y_{1, 4} y_{2, 1})  \del{1}{4}{2}{4} +(-y_{1, 1} y_{1, 4})  \del{2}{4}{2}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{2}{1}{2} +(-y_{1, 2} x_{4, 4})  \eps{1}{2}{1}{4} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{2}{4}
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,2,4
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(4)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
-y(1)(4)*y(4)(3)+y(1)(3)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(3)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(2)(1)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
-y(1)(3)*x(4)(4)
Lead Term of Product:
-y(1)(3)*y(2)(4)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(4)*y(4)(3)*x(1)(4)+y(2)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(2)(4)-y(1)(3)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(4)(4)+y(1)(3)*y(2)(4)*x(4)(4)) - (-y(4)(3)*x(1)(4))*(y(2)(4)*x(1)(1)-y(2)(1)*x(1)(4)-y(1)(4)*x(2)(1)+y(1)(1)*x(2)(4))
-------
Rewrite:
-y(2)(3)*y(4)(4)*x(1)(1)*x(1)(4)+y(2)(1)*y(4)(3)*x(1)(4)^2+y(1)(4)*y(4)(3)*x(1)(4)*x(2)(1)-y(1)(4)*y(4)(3)*x(1)(1)*x(2)(4)+y(1)(3)*y(4)(4)*x(1)(1)*x(2)(4)-y(1)(1)*y(4)(3)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(3)*x(1)(1)*x(4)(4)-y(1)(3)*y(2)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{1}{4}, \lam{1}{2}{4}{3}{4}{4}) =
(-y_{1, 4} y_{4, 3}+y_{1, 3} y_{4, 4})  \del{1}{2}{1}{4} +(-y_{1, 1} y_{4, 4})  \del{1}{2}{3}{4} +(y_{1, 4} y_{2, 1})  \del{1}{4}{3}{4} +(-y_{1, 1} y_{1, 4})  \del{2}{4}{3}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{2}{1}{3} +(-y_{1, 3} x_{4, 4})  \eps{1}{2}{1}{4} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{3}{4}
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
1,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,3
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(2)(3)*y(3)(2)*x(1)(2)
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(1)*y(2)(3)*y(3)(2)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(3)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-y(2)(2)
Lead Term of Product:
y(2)(2)^2*y(3)(1)*x(1)(3)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,3
Quotient:
-x(2)(2)
Lead Term of Product:
y(1)(3)*y(2)(2)*y(3)(1)*x(2)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(3))*(-y(2)(2)*y(3)(1)*x(1)(2)+y(2)(1)*y(3)(2)*x(1)(2)+y(1)(2)*y(3)(1)*x(2)(2)-y(1)(1)*y(3)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(3)(2)+y(1)(1)*y(2)(2)*x(3)(2)) - (-y(2)(2)*y(3)(1))*(y(2)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3))
-------
Rewrite:
-y(2)(1)*y(2)(3)*y(3)(2)*x(1)(2)+y(2)(2)^2*y(3)(1)*x(1)(3)+y(1)(3)*y(2)(2)*y(3)(1)*x(2)(2)-y(1)(2)*y(2)(3)*y(3)(1)*x(2)(2)+y(1)(1)*y(2)(3)*y(3)(2)*x(2)(2)-y(1)(2)*y(2)(2)*y(3)(1)*x(2)(3)+y(1)(2)*y(2)(1)*y(2)(3)*x(3)(2)-y(1)(1)*y(2)(2)*y(2)(3)*x(3)(2)
-----------
TeX output: S(\eps{1}{2}{2}{3}, \lam{1}{2}{3}{1}{2}{2}) = (-y_{2,
1} y_{3, 2})  \eps{1}{2}{2}{3} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2,
2})  \eps{2}{3}{2}{3} +(-y_{2, 2})  \lam{1}{2}{3}{1}{2}{3}
+(-x_{2, 2})  \psi{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,3
1,3,3
Lead Term of Spoly:
-y(2)(1)*y(3)(3)*x(1)(2)*x(1)(3)
Divisor:
Delta
1,2
2,3
Quotient:
-y(1)(3)*y(3)(1)
Lead Term of Product:
y(1)(3)*y(3)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(1)(1)*x(3)(3)
Lead Term of Product:
-y(1)(1)*y(2)(3)*x(1)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(1)(3)+y(1)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-x(1)(3)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(3)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(3)*y(3)(1)*x(1)(3)+y(2)(1)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(1)*x(2)(3)-y(1)(1)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(1)*x(3)(3)+y(1)(1)*y(2)(3)*x(3)(3)) - (-y(3)(1)*x(1)(3))*(y(2)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3))
-------
Rewrite:
-y(2)(1)*y(3)(3)*x(1)(2)*x(1)(3)+y(2)(2)*y(3)(1)*x(1)(3)^2+y(1)(3)*y(3)(1)*x(1)(3)*x(2)(2)-y(1)(3)*y(3)(1)*x(1)(2)*x(2)(3)+y(1)(1)*y(3)(3)*x(1)(2)*x(2)(3)-y(1)(2)*y(3)(1)*x(1)(3)*x(2)(3)+y(1)(3)*y(2)(1)*x(1)(2)*x(3)(3)-y(1)(1)*y(2)(3)*x(1)(2)*x(3)(3)
-----------
TeX output:
S(\eps{1}{2}{2}{3}, \lam{1}{2}{3}{1}{3}{3}) =
(-y_{1, 3} y_{3, 1})  \del{1}{2}{2}{3} +(y_{1, 3} y_{2, 1})  \del{1}{3}{2}{3} +(-y_{1, 1} y_{1, 3})  \del{2}{3}{2}{3} +(-y_{1, 1} x_{3, 3})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{1, 3}+y_{1, 1} x_{2, 3})  \eps{1}{3}{2}{3} +(-x_{1, 3})  \lam{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,3
1,3,4
Lead Term of Spoly:
-y(2)(1)*y(3)(3)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(3)*y(3)(1)
Lead Term of Product:
y(1)(3)*y(3)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(1)*y(3)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(1)*y(2)(2)
Lead Term of Product:
y(1)(1)*y(2)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(1)(1)*y(1)(2)
Lead Term of Product:
-y(1)(1)*y(1)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(1)(1)*x(3)(4)
Lead Term of Product:
-y(1)(1)*y(2)(3)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(3)*y(3)(1)*x(1)(4)+y(2)(1)*y(3)(3)*x(1)(4)+y(1)(3)*y(3)(1)*x(2)(4)-y(1)(1)*y(3)(3)*x(2)(4)-y(1)(3)*y(2)(1)*x(3)(4)+y(1)(1)*y(2)(3)*x(3)(4)) - (-y(3)(1)*x(1)(4))*(y(2)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3))
-------
Rewrite:
-y(2)(1)*y(3)(3)*x(1)(2)*x(1)(4)+y(2)(2)*y(3)(1)*x(1)(3)*x(1)(4)+y(1)(3)*y(3)(1)*x(1)(4)*x(2)(2)-y(1)(2)*y(3)(1)*x(1)(4)*x(2)(3)-y(1)(3)*y(3)(1)*x(1)(2)*x(2)(4)+y(1)(1)*y(3)(3)*x(1)(2)*x(2)(4)+y(1)(3)*y(2)(1)*x(1)(2)*x(3)(4)-y(1)(1)*y(2)(3)*x(1)(2)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{2}{3}, \lam{1}{2}{3}{1}{3}{4}) =
(-y_{1, 3} y_{3, 1})  \del{1}{2}{2}{4} +(y_{1, 1} y_{3, 2})  \del{1}{2}{3}{4} +(y_{1, 3} y_{2, 1})  \del{1}{3}{2}{4} +(-y_{1, 1} y_{2, 2})  \del{1}{3}{3}{4} +(-y_{1, 1} y_{1, 3})  \del{2}{3}{2}{4} +(y_{1, 1} y_{1, 2})  \del{2}{3}{3}{4} +(-y_{1, 1} x_{3, 4})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{2}{3} +(-x_{1, 4})  \lam{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,3
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(3)(3)*x(1)(2)*x(1)(3)
Divisor:
Delta
1,2
2,3
Quotient:
-y(1)(3)*y(3)(2)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-y(1)(2)*y(1)(3)
Lead Term of Product:
y(1)(2)*y(1)(3)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(1)(2)*x(3)(3)
Lead Term of Product:
-y(1)(2)*y(2)(3)*x(1)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(2)*x(1)(3)+y(1)(2)*x(2)(3)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(3)*y(3)(2)*x(1)(3)+y(2)(2)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(2)*x(2)(3)-y(1)(2)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(3)(3)+y(1)(2)*y(2)(3)*x(3)(3)) - (-y(3)(2)*x(1)(3))*(y(2)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3))
-------
Rewrite:
-y(2)(2)*y(3)(3)*x(1)(2)*x(1)(3)+y(2)(2)*y(3)(2)*x(1)(3)^2+y(1)(3)*y(3)(2)*x(1)(3)*x(2)(2)-y(1)(3)*y(3)(2)*x(1)(2)*x(2)(3)+y(1)(2)*y(3)(3)*x(1)(2)*x(2)(3)-y(1)(2)*y(3)(2)*x(1)(3)*x(2)(3)+y(1)(3)*y(2)(2)*x(1)(2)*x(3)(3)-y(1)(2)*y(2)(3)*x(1)(2)*x(3)(3)
-----------
TeX output:
S(\eps{1}{2}{2}{3}, \lam{1}{2}{3}{2}{3}{3}) =
(-y_{1, 3} y_{3, 2})  \del{1}{2}{2}{3} +(y_{1, 3} y_{2, 2})  \del{1}{3}{2}{3} +(-y_{1, 2} y_{1, 3})  \del{2}{3}{2}{3} +(-y_{1, 2} x_{3, 3})  \eps{1}{2}{2}{3} +(-y_{2, 2} x_{1, 3}+y_{1, 2} x_{2, 3})  \eps{1}{3}{2}{3}
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,3
2,3,4
Lead Term of Spoly:
-y(2)(2)*y(3)(3)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(3)*y(3)(2)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
y(1)(2)*y(3)(2)
Lead Term of Product:
-y(1)(2)*y(3)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(2)*y(2)(2)
Lead Term of Product:
y(1)(2)*y(2)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(2)*y(1)(3)
Lead Term of Product:
y(1)(2)*y(1)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(1)(2)^2
Lead Term of Product:
-y(1)(2)^2*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(1)(2)*x(3)(4)
Lead Term of Product:
-y(1)(2)*y(2)(3)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(2)*x(1)(4)+y(1)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(3)*y(3)(2)*x(1)(4)+y(2)(2)*y(3)(3)*x(1)(4)+y(1)(3)*y(3)(2)*x(2)(4)-y(1)(2)*y(3)(3)*x(2)(4)-y(1)(3)*y(2)(2)*x(3)(4)+y(1)(2)*y(2)(3)*x(3)(4)) - (-y(3)(2)*x(1)(4))*(y(2)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3))
-------
Rewrite:
-y(2)(2)*y(3)(3)*x(1)(2)*x(1)(4)+y(2)(2)*y(3)(2)*x(1)(3)*x(1)(4)+y(1)(3)*y(3)(2)*x(1)(4)*x(2)(2)-y(1)(2)*y(3)(2)*x(1)(4)*x(2)(3)-y(1)(3)*y(3)(2)*x(1)(2)*x(2)(4)+y(1)(2)*y(3)(3)*x(1)(2)*x(2)(4)+y(1)(3)*y(2)(2)*x(1)(2)*x(3)(4)-y(1)(2)*y(2)(3)*x(1)(2)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{2}{3}, \lam{1}{2}{3}{2}{3}{4}) =
(-y_{1, 3} y_{3, 2})  \del{1}{2}{2}{4} +(y_{1, 2} y_{3, 2})  \del{1}{2}{3}{4} +(y_{1, 3} y_{2, 2})  \del{1}{3}{2}{4} +(-y_{1, 2} y_{2, 2})  \del{1}{3}{3}{4} +(-y_{1, 2} y_{1, 3})  \del{2}{3}{2}{4} +(y_{1, 2}^2)  \del{2}{3}{3}{4} +(-y_{1, 2} x_{3, 4})  \eps{1}{2}{2}{3} +(-y_{2, 2} x_{1, 4}+y_{1, 2} x_{2, 4})  \eps{1}{3}{2}{3}
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,4
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(2)(3)*y(4)(2)*x(1)(2)
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(2)(3)*y(4)(2)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(4)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-y(2)(2)
Lead Term of Product:
y(2)(2)^2*y(4)(1)*x(1)(3)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,3
Quotient:
-x(2)(2)
Lead Term of Product:
y(1)(3)*y(2)(2)*y(4)(1)*x(2)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(3))*(-y(2)(2)*y(4)(1)*x(1)(2)+y(2)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(2)(2)-y(1)(1)*y(4)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(4)(2)+y(1)(1)*y(2)(2)*x(4)(2)) - (-y(2)(2)*y(4)(1))*(y(2)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3))
-------
Rewrite:
-y(2)(1)*y(2)(3)*y(4)(2)*x(1)(2)+y(2)(2)^2*y(4)(1)*x(1)(3)+y(1)(3)*y(2)(2)*y(4)(1)*x(2)(2)-y(1)(2)*y(2)(3)*y(4)(1)*x(2)(2)+y(1)(1)*y(2)(3)*y(4)(2)*x(2)(2)-y(1)(2)*y(2)(2)*y(4)(1)*x(2)(3)+y(1)(2)*y(2)(1)*y(2)(3)*x(4)(2)-y(1)(1)*y(2)(2)*y(2)(3)*x(4)(2)
-----------
TeX output:
S(\eps{1}{2}{2}{3}, \lam{1}{2}{4}{1}{2}{2}) =
(-y_{2, 1} y_{4, 2})  \eps{1}{2}{2}{3} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2, 2})  \eps{2}{4}{2}{3} +(-y_{2, 2})  \lam{1}{2}{4}{1}{2}{3} +(-x_{2, 2})  \psi{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,4
1,3,3
Lead Term of Spoly:
-y(2)(1)*y(4)(3)*x(1)(2)*x(1)(3)
Divisor:
Delta
1,2
2,3
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(1)(1)*x(4)(3)
Lead Term of Product:
-y(1)(1)*y(2)(3)*x(1)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*x(1)(3)+y(1)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-x(1)(3)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(3)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(3)*y(4)(1)*x(1)(3)+y(2)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(2)(3)-y(1)(1)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(1)*x(4)(3)+y(1)(1)*y(2)(3)*x(4)(3)) - (-y(4)(1)*x(1)(3))*(y(2)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3))
-------
Rewrite:
-y(2)(1)*y(4)(3)*x(1)(2)*x(1)(3)+y(2)(2)*y(4)(1)*x(1)(3)^2+y(1)(3)*y(4)(1)*x(1)(3)*x(2)(2)-y(1)(3)*y(4)(1)*x(1)(2)*x(2)(3)+y(1)(1)*y(4)(3)*x(1)(2)*x(2)(3)-y(1)(2)*y(4)(1)*x(1)(3)*x(2)(3)+y(1)(3)*y(2)(1)*x(1)(2)*x(4)(3)-y(1)(1)*y(2)(3)*x(1)(2)*x(4)(3)
-----------
TeX output:
S(\eps{1}{2}{2}{3}, \lam{1}{2}{4}{1}{3}{3}) =
(-y_{1, 3} y_{4, 1})  \del{1}{2}{2}{3} +(y_{1, 3} y_{2, 1})  \del{1}{4}{2}{3} +(-y_{1, 1} y_{1, 3})  \del{2}{4}{2}{3} +(-y_{1, 1} x_{4, 3})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{1, 3}+y_{1, 1} x_{2, 3})  \eps{1}{4}{2}{3} +(-x_{1, 3})  \lam{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,4
1,3,4
Lead Term of Spoly:
-y(2)(1)*y(4)(3)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(1)*y(4)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(3)*y(2)(1)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
-y(1)(1)*y(2)(2)
Lead Term of Product:
y(1)(1)*y(2)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(1)*y(1)(2)
Lead Term of Product:
-y(1)(1)*y(1)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(2)(3)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(3)*y(4)(1)*x(1)(4)+y(2)(1)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(1)*x(2)(4)-y(1)(1)*y(4)(3)*x(2)(4)-y(1)(3)*y(2)(1)*x(4)(4)+y(1)(1)*y(2)(3)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(2)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3))
-------
Rewrite:
-y(2)(1)*y(4)(3)*x(1)(2)*x(1)(4)+y(2)(2)*y(4)(1)*x(1)(3)*x(1)(4)+y(1)(3)*y(4)(1)*x(1)(4)*x(2)(2)-y(1)(2)*y(4)(1)*x(1)(4)*x(2)(3)-y(1)(3)*y(4)(1)*x(1)(2)*x(2)(4)+y(1)(1)*y(4)(3)*x(1)(2)*x(2)(4)+y(1)(3)*y(2)(1)*x(1)(2)*x(4)(4)-y(1)(1)*y(2)(3)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{2}{3}, \lam{1}{2}{4}{1}{3}{4}) =
(-y_{1, 3} y_{4, 1})  \del{1}{2}{2}{4} +(y_{1, 1} y_{4, 2})  \del{1}{2}{3}{4} +(y_{1, 3} y_{2, 1})  \del{1}{4}{2}{4} +(-y_{1, 1} y_{2, 2})  \del{1}{4}{3}{4} +(-y_{1, 1} y_{1, 3})  \del{2}{4}{2}{4} +(y_{1, 1} y_{1, 2})  \del{2}{4}{3}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{2}{3} +(-x_{1, 4})  \lam{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,4
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(4)(3)*x(1)(2)*x(1)(3)
Divisor:
Delta
1,2
2,3
Quotient:
-y(1)(3)*y(4)(2)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
-y(1)(2)*y(1)(3)
Lead Term of Product:
y(1)(2)*y(1)(3)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(1)(2)*x(4)(3)
Lead Term of Product:
-y(1)(2)*y(2)(3)*x(1)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(2)*x(1)(3)+y(1)(2)*x(2)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(3)*y(4)(2)*x(1)(3)+y(2)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(2)(3)-y(1)(2)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(4)(3)+y(1)(2)*y(2)(3)*x(4)(3)) - (-y(4)(2)*x(1)(3))*(y(2)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3))
-------
Rewrite:
-y(2)(2)*y(4)(3)*x(1)(2)*x(1)(3)+y(2)(2)*y(4)(2)*x(1)(3)^2+y(1)(3)*y(4)(2)*x(1)(3)*x(2)(2)-y(1)(3)*y(4)(2)*x(1)(2)*x(2)(3)+y(1)(2)*y(4)(3)*x(1)(2)*x(2)(3)-y(1)(2)*y(4)(2)*x(1)(3)*x(2)(3)+y(1)(3)*y(2)(2)*x(1)(2)*x(4)(3)-y(1)(2)*y(2)(3)*x(1)(2)*x(4)(3)
-----------
TeX output:
S(\eps{1}{2}{2}{3}, \lam{1}{2}{4}{2}{3}{3}) =
(-y_{1, 3} y_{4, 2})  \del{1}{2}{2}{3} +(y_{1, 3} y_{2, 2})  \del{1}{4}{2}{3} +(-y_{1, 2} y_{1, 3})  \del{2}{4}{2}{3} +(-y_{1, 2} x_{4, 3})  \eps{1}{2}{2}{3} +(-y_{2, 2} x_{1, 3}+y_{1, 2} x_{2, 3})  \eps{1}{4}{2}{3}
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,4
2,3,4
Lead Term of Spoly:
-y(2)(2)*y(4)(3)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(3)*y(4)(2)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
y(1)(2)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(4)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
-y(1)(2)*y(2)(2)
Lead Term of Product:
y(1)(2)*y(2)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(1)(2)*y(1)(3)
Lead Term of Product:
y(1)(2)*y(1)(3)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(2)^2
Lead Term of Product:
-y(1)(2)^2*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(2)(3)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(2)*x(1)(4)+y(1)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(3)*y(4)(2)*x(1)(4)+y(2)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(2)(4)-y(1)(2)*y(4)(3)*x(2)(4)-y(1)(3)*y(2)(2)*x(4)(4)+y(1)(2)*y(2)(3)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(2)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3))
-------
Rewrite:
-y(2)(2)*y(4)(3)*x(1)(2)*x(1)(4)+y(2)(2)*y(4)(2)*x(1)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(1)(4)*x(2)(2)-y(1)(2)*y(4)(2)*x(1)(4)*x(2)(3)-y(1)(3)*y(4)(2)*x(1)(2)*x(2)(4)+y(1)(2)*y(4)(3)*x(1)(2)*x(2)(4)+y(1)(3)*y(2)(2)*x(1)(2)*x(4)(4)-y(1)(2)*y(2)(3)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{2}{3}, \lam{1}{2}{4}{2}{3}{4}) =
(-y_{1, 3} y_{4, 2})  \del{1}{2}{2}{4} +(y_{1, 2} y_{4, 2})  \del{1}{2}{3}{4} +(y_{1, 3} y_{2, 2})  \del{1}{4}{2}{4} +(-y_{1, 2} y_{2, 2})  \del{1}{4}{3}{4} +(-y_{1, 2} y_{1, 3})  \del{2}{4}{2}{4} +(y_{1, 2}^2)  \del{2}{4}{3}{4} +(-y_{1, 2} x_{4, 4})  \eps{1}{2}{2}{3} +(-y_{2, 2} x_{1, 4}+y_{1, 2} x_{2, 4})  \eps{1}{4}{2}{3}
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,3,4
1,2,2
Lead Term of Spoly:
-y(2)(3)*y(3)(1)*y(4)(2)*x(1)(2)
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(2)(3)*y(3)(1)*y(4)(2)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(4)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
y(4)(2)
Lead Term of Product:
-y(2)(2)*y(3)(1)*y(4)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-y(3)(2)
Lead Term of Product:
y(2)(2)*y(3)(2)*y(4)(1)*x(1)(3)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,2
Quotient:
-y(1)(3)
Lead Term of Product:
y(1)(3)*y(3)(2)*y(4)(1)*x(2)(2)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,3
Quotient:
x(4)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(3)(1)*x(4)(2)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,3
Quotient:
-x(3)(2)
Lead Term of Product:
y(1)(3)*y(2)(2)*y(4)(1)*x(3)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(3))*(-y(3)(2)*y(4)(1)*x(1)(2)+y(3)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(3)(2)-y(1)(1)*y(4)(2)*x(3)(2)-y(1)(2)*y(3)(1)*x(4)(2)+y(1)(1)*y(3)(2)*x(4)(2)) - (-y(3)(2)*y(4)(1))*(y(2)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3))
-------
Rewrite:
-y(2)(3)*y(3)(1)*y(4)(2)*x(1)(2)+y(2)(2)*y(3)(2)*y(4)(1)*x(1)(3)+y(1)(3)*y(3)(2)*y(4)(1)*x(2)(2)-y(1)(2)*y(3)(2)*y(4)(1)*x(2)(3)-y(1)(2)*y(2)(3)*y(4)(1)*x(3)(2)+y(1)(1)*y(2)(3)*y(4)(2)*x(3)(2)+y(1)(2)*y(2)(3)*y(3)(1)*x(4)(2)-y(1)(1)*y(2)(3)*y(3)(2)*x(4)(2)
-----------
TeX output:
S(\eps{1}{2}{2}{3}, \lam{1}{3}{4}{1}{2}{2}) =
(-y_{3, 1} y_{4, 2})  \eps{1}{2}{2}{3} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2, 2})  \eps{3}{4}{2}{3} +(y_{4, 2})  \lam{1}{2}{3}{1}{2}{3} +(-y_{3, 2})  \lam{1}{2}{4}{1}{2}{3} +(-y_{1, 3})  \lam{2}{3}{4}{1}{2}{2} +(x_{4, 2})  \psi{1}{2}{3}{1}{2}{3} +(-x_{3, 2})  \psi{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,3
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(2)(4)*y(3)(2)*x(1)(2)
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(1)*y(2)(4)*y(3)(2)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(3)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
-y(2)(2)
Lead Term of Product:
y(2)(2)^2*y(3)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,4
Quotient:
-x(2)(2)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(3)(1)*x(2)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(2)(2)*y(3)(1)*x(1)(2)+y(2)(1)*y(3)(2)*x(1)(2)+y(1)(2)*y(3)(1)*x(2)(2)-y(1)(1)*y(3)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(3)(2)+y(1)(1)*y(2)(2)*x(3)(2)) - (-y(2)(2)*y(3)(1))*(y(2)(4)*x(1)(2)-y(2)(2)*x(1)(4)-y(1)(4)*x(2)(2)+y(1)(2)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(2)(4)*y(3)(2)*x(1)(2)+y(2)(2)^2*y(3)(1)*x(1)(4)+y(1)(4)*y(2)(2)*y(3)(1)*x(2)(2)-y(1)(2)*y(2)(4)*y(3)(1)*x(2)(2)+y(1)(1)*y(2)(4)*y(3)(2)*x(2)(2)-y(1)(2)*y(2)(2)*y(3)(1)*x(2)(4)+y(1)(2)*y(2)(1)*y(2)(4)*x(3)(2)-y(1)(1)*y(2)(2)*y(2)(4)*x(3)(2)
-----------
TeX output:
S(\eps{1}{2}{2}{4}, \lam{1}{2}{3}{1}{2}{2}) =
(-y_{2, 1} y_{3, 2})  \eps{1}{2}{2}{4} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2, 2})  \eps{2}{3}{2}{4} +(-y_{2, 2})  \lam{1}{2}{3}{1}{2}{4} +(-x_{2, 2})  \psi{1}{2}{3}{1}{2}{4}
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,3
1,4,4
Lead Term of Spoly:
-y(2)(1)*y(3)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(4)*y(3)(1)
Lead Term of Product:
y(1)(4)*y(3)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(1)(4)*y(2)(1)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(1)(1)*x(3)(4)
Lead Term of Product:
-y(1)(1)*y(2)(4)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(4)*y(3)(1)*x(1)(4)+y(2)(1)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(1)*x(2)(4)-y(1)(1)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(1)*x(3)(4)+y(1)(1)*y(2)(4)*x(3)(4)) - (-y(3)(1)*x(1)(4))*(y(2)(4)*x(1)(2)-y(2)(2)*x(1)(4)-y(1)(4)*x(2)(2)+y(1)(2)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(3)(4)*x(1)(2)*x(1)(4)+y(2)(2)*y(3)(1)*x(1)(4)^2+y(1)(4)*y(3)(1)*x(1)(4)*x(2)(2)-y(1)(4)*y(3)(1)*x(1)(2)*x(2)(4)+y(1)(1)*y(3)(4)*x(1)(2)*x(2)(4)-y(1)(2)*y(3)(1)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(1)*x(1)(2)*x(3)(4)-y(1)(1)*y(2)(4)*x(1)(2)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{2}{4}, \lam{1}{2}{3}{1}{4}{4}) =
(-y_{1, 4} y_{3, 1})  \del{1}{2}{2}{4} +(y_{1, 4} y_{2, 1})  \del{1}{3}{2}{4} +(-y_{1, 1} y_{1, 4})  \del{2}{3}{2}{4} +(-y_{1, 1} x_{3, 4})  \eps{1}{2}{2}{4} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{2}{4} +(-x_{1, 4})  \lam{1}{2}{3}{1}{2}{4}
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,3
2,4,4
Lead Term of Spoly:
-y(2)(2)*y(3)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(4)*y(3)(2)
Lead Term of Product:
y(1)(4)*y(3)(2)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(1)(4)*y(2)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(2)*y(1)(4)
Lead Term of Product:
y(1)(2)*y(1)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(1)(2)*x(3)(4)
Lead Term of Product:
-y(1)(2)*y(2)(4)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(2)(2)*x(1)(4)+y(1)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(4)*y(3)(2)*x(1)(4)+y(2)(2)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(2)*x(2)(4)-y(1)(2)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(2)*x(3)(4)+y(1)(2)*y(2)(4)*x(3)(4)) - (-y(3)(2)*x(1)(4))*(y(2)(4)*x(1)(2)-y(2)(2)*x(1)(4)-y(1)(4)*x(2)(2)+y(1)(2)*x(2)(4))
-------
Rewrite:
-y(2)(2)*y(3)(4)*x(1)(2)*x(1)(4)+y(2)(2)*y(3)(2)*x(1)(4)^2+y(1)(4)*y(3)(2)*x(1)(4)*x(2)(2)-y(1)(4)*y(3)(2)*x(1)(2)*x(2)(4)+y(1)(2)*y(3)(4)*x(1)(2)*x(2)(4)-y(1)(2)*y(3)(2)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(2)*x(1)(2)*x(3)(4)-y(1)(2)*y(2)(4)*x(1)(2)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{2}{4}, \lam{1}{2}{3}{2}{4}{4}) =
(-y_{1, 4} y_{3, 2})  \del{1}{2}{2}{4} +(y_{1, 4} y_{2, 2})  \del{1}{3}{2}{4} +(-y_{1, 2} y_{1, 4})  \del{2}{3}{2}{4} +(-y_{1, 2} x_{3, 4})  \eps{1}{2}{2}{4} +(-y_{2, 2} x_{1, 4}+y_{1, 2} x_{2, 4})  \eps{1}{3}{2}{4}
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,3
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(3)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(4)*y(3)(3)+y(1)(3)*y(3)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(2)*y(3)(4)
Lead Term of Product:
y(1)(2)*y(3)(4)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(4)*y(2)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(2)*y(1)(4)
Lead Term of Product:
y(1)(2)*y(1)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(3)(4)*x(1)(4)+y(1)(4)*x(3)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(1)(3)*x(3)(4)
Lead Term of Product:
-y(1)(3)*y(2)(4)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(2)*x(1)(4)+y(1)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(4)*y(3)(3)*x(1)(4)+y(2)(3)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(3)*x(2)(4)-y(1)(3)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(3)(4)+y(1)(3)*y(2)(4)*x(3)(4)) - (-y(3)(3)*x(1)(4))*(y(2)(4)*x(1)(2)-y(2)(2)*x(1)(4)-y(1)(4)*x(2)(2)+y(1)(2)*x(2)(4))
-------
Rewrite:
-y(2)(3)*y(3)(4)*x(1)(2)*x(1)(4)+y(2)(2)*y(3)(3)*x(1)(4)^2+y(1)(4)*y(3)(3)*x(1)(4)*x(2)(2)-y(1)(4)*y(3)(3)*x(1)(2)*x(2)(4)+y(1)(3)*y(3)(4)*x(1)(2)*x(2)(4)-y(1)(2)*y(3)(3)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(3)*x(1)(2)*x(3)(4)-y(1)(3)*y(2)(4)*x(1)(2)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{2}{4}, \lam{1}{2}{3}{3}{4}{4}) =
(-y_{1, 4} y_{3, 3}+y_{1, 3} y_{3, 4})  \del{1}{2}{2}{4} +(-y_{1, 2} y_{3, 4})  \del{1}{2}{3}{4} +(y_{1, 4} y_{2, 2})  \del{1}{3}{3}{4} +(-y_{1, 2} y_{1, 4})  \del{2}{3}{3}{4} +(-y_{3, 4} x_{1, 4}+y_{1, 4} x_{3, 4})  \eps{1}{2}{2}{3} +(-y_{1, 3} x_{3, 4})  \eps{1}{2}{2}{4} +(-y_{2, 2} x_{1, 4}+y_{1, 2} x_{2, 4})  \eps{1}{3}{3}{4}
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,4
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(2)(4)*y(4)(2)*x(1)(2)
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(2)(4)*y(4)(2)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(4)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-y(2)(2)
Lead Term of Product:
y(2)(2)^2*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,4
Quotient:
-x(2)(2)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(4)(1)*x(2)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(2)(2)*y(4)(1)*x(1)(2)+y(2)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(2)(2)-y(1)(1)*y(4)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(4)(2)+y(1)(1)*y(2)(2)*x(4)(2)) - (-y(2)(2)*y(4)(1))*(y(2)(4)*x(1)(2)-y(2)(2)*x(1)(4)-y(1)(4)*x(2)(2)+y(1)(2)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(2)(4)*y(4)(2)*x(1)(2)+y(2)(2)^2*y(4)(1)*x(1)(4)+y(1)(4)*y(2)(2)*y(4)(1)*x(2)(2)-y(1)(2)*y(2)(4)*y(4)(1)*x(2)(2)+y(1)(1)*y(2)(4)*y(4)(2)*x(2)(2)-y(1)(2)*y(2)(2)*y(4)(1)*x(2)(4)+y(1)(2)*y(2)(1)*y(2)(4)*x(4)(2)-y(1)(1)*y(2)(2)*y(2)(4)*x(4)(2)
-----------
TeX output:
S(\eps{1}{2}{2}{4}, \lam{1}{2}{4}{1}{2}{2}) =
(-y_{2, 1} y_{4, 2})  \eps{1}{2}{2}{4} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2, 2})  \eps{2}{4}{2}{4} +(-y_{2, 2})  \lam{1}{2}{4}{1}{2}{4} +(-x_{2, 2})  \psi{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,4
1,4,4
Lead Term of Spoly:
-y(2)(1)*y(4)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(4)*y(4)(1)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(4)*y(2)(1)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(2)(4)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(4)*y(4)(1)*x(1)(4)+y(2)(1)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(1)*x(2)(4)-y(1)(1)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(1)*x(4)(4)+y(1)(1)*y(2)(4)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(2)(4)*x(1)(2)-y(2)(2)*x(1)(4)-y(1)(4)*x(2)(2)+y(1)(2)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(4)(4)*x(1)(2)*x(1)(4)+y(2)(2)*y(4)(1)*x(1)(4)^2+y(1)(4)*y(4)(1)*x(1)(4)*x(2)(2)-y(1)(4)*y(4)(1)*x(1)(2)*x(2)(4)+y(1)(1)*y(4)(4)*x(1)(2)*x(2)(4)-y(1)(2)*y(4)(1)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(1)*x(1)(2)*x(4)(4)-y(1)(1)*y(2)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{2}{4}, \lam{1}{2}{4}{1}{4}{4}) =
(-y_{1, 4} y_{4, 1})  \del{1}{2}{2}{4} +(y_{1, 4} y_{2, 1})  \del{1}{4}{2}{4} +(-y_{1, 1} y_{1, 4})  \del{2}{4}{2}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{2}{2}{4} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{2}{4} +(-x_{1, 4})  \lam{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,4
2,4,4
Lead Term of Spoly:
-y(2)(2)*y(4)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(4)*y(4)(2)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(4)*y(2)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(1)(2)*y(1)(4)
Lead Term of Product:
y(1)(2)*y(1)(4)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(2)(4)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(2)(2)*x(1)(4)+y(1)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(4)*y(4)(2)*x(1)(4)+y(2)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(2)(4)-y(1)(2)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(2)*x(4)(4)+y(1)(2)*y(2)(4)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(2)(4)*x(1)(2)-y(2)(2)*x(1)(4)-y(1)(4)*x(2)(2)+y(1)(2)*x(2)(4))
-------
Rewrite:
-y(2)(2)*y(4)(4)*x(1)(2)*x(1)(4)+y(2)(2)*y(4)(2)*x(1)(4)^2+y(1)(4)*y(4)(2)*x(1)(4)*x(2)(2)-y(1)(4)*y(4)(2)*x(1)(2)*x(2)(4)+y(1)(2)*y(4)(4)*x(1)(2)*x(2)(4)-y(1)(2)*y(4)(2)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(2)*x(1)(2)*x(4)(4)-y(1)(2)*y(2)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{2}{4}, \lam{1}{2}{4}{2}{4}{4}) =
(-y_{1, 4} y_{4, 2})  \del{1}{2}{2}{4} +(y_{1, 4} y_{2, 2})  \del{1}{4}{2}{4} +(-y_{1, 2} y_{1, 4})  \del{2}{4}{2}{4} +(-y_{1, 2} x_{4, 4})  \eps{1}{2}{2}{4} +(-y_{2, 2} x_{1, 4}+y_{1, 2} x_{2, 4})  \eps{1}{4}{2}{4}
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,2,4
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(4)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(4)*y(4)(3)+y(1)(3)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(3)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(2)*y(4)(4)
Lead Term of Product:
y(1)(2)*y(4)(4)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(2)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(2)*y(1)(4)
Lead Term of Product:
y(1)(2)*y(1)(4)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(1)(3)*x(4)(4)
Lead Term of Product:
-y(1)(3)*y(2)(4)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(2)*x(1)(4)+y(1)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(4)*y(4)(3)*x(1)(4)+y(2)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(2)(4)-y(1)(3)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(4)(4)+y(1)(3)*y(2)(4)*x(4)(4)) - (-y(4)(3)*x(1)(4))*(y(2)(4)*x(1)(2)-y(2)(2)*x(1)(4)-y(1)(4)*x(2)(2)+y(1)(2)*x(2)(4))
-------
Rewrite:
-y(2)(3)*y(4)(4)*x(1)(2)*x(1)(4)+y(2)(2)*y(4)(3)*x(1)(4)^2+y(1)(4)*y(4)(3)*x(1)(4)*x(2)(2)-y(1)(4)*y(4)(3)*x(1)(2)*x(2)(4)+y(1)(3)*y(4)(4)*x(1)(2)*x(2)(4)-y(1)(2)*y(4)(3)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(3)*x(1)(2)*x(4)(4)-y(1)(3)*y(2)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{2}{4}, \lam{1}{2}{4}{3}{4}{4}) =
(-y_{1, 4} y_{4, 3}+y_{1, 3} y_{4, 4})  \del{1}{2}{2}{4} +(-y_{1, 2} y_{4, 4})  \del{1}{2}{3}{4} +(y_{1, 4} y_{2, 2})  \del{1}{4}{3}{4} +(-y_{1, 2} y_{1, 4})  \del{2}{4}{3}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{2}{2}{3} +(-y_{1, 3} x_{4, 4})  \eps{1}{2}{2}{4} +(-y_{2, 2} x_{1, 4}+y_{1, 2} x_{2, 4})  \eps{1}{4}{3}{4}
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,3,4
1,2,2
Lead Term of Spoly:
-y(2)(4)*y(3)(1)*y(4)(2)*x(1)(2)
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(2)(4)*y(3)(1)*y(4)(2)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,4
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(4)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
y(4)(2)
Lead Term of Product:
-y(2)(2)*y(3)(1)*y(4)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-y(3)(2)
Lead Term of Product:
y(2)(2)*y(3)(2)*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,2
Quotient:
-y(1)(4)
Lead Term of Product:
y(1)(4)*y(3)(2)*y(4)(1)*x(2)(2)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,4
Quotient:
x(4)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*y(3)(1)*x(4)(2)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,4
Quotient:
-x(3)(2)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(4)(1)*x(3)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(3)(2)*y(4)(1)*x(1)(2)+y(3)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(3)(2)-y(1)(1)*y(4)(2)*x(3)(2)-y(1)(2)*y(3)(1)*x(4)(2)+y(1)(1)*y(3)(2)*x(4)(2)) - (-y(3)(2)*y(4)(1))*(y(2)(4)*x(1)(2)-y(2)(2)*x(1)(4)-y(1)(4)*x(2)(2)+y(1)(2)*x(2)(4))
-------
Rewrite:
-y(2)(4)*y(3)(1)*y(4)(2)*x(1)(2)+y(2)(2)*y(3)(2)*y(4)(1)*x(1)(4)+y(1)(4)*y(3)(2)*y(4)(1)*x(2)(2)-y(1)(2)*y(3)(2)*y(4)(1)*x(2)(4)-y(1)(2)*y(2)(4)*y(4)(1)*x(3)(2)+y(1)(1)*y(2)(4)*y(4)(2)*x(3)(2)+y(1)(2)*y(2)(4)*y(3)(1)*x(4)(2)-y(1)(1)*y(2)(4)*y(3)(2)*x(4)(2)
-----------
TeX output:
S(\eps{1}{2}{2}{4}, \lam{1}{3}{4}{1}{2}{2}) =
(-y_{3, 1} y_{4, 2})  \eps{1}{2}{2}{4} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2, 2})  \eps{3}{4}{2}{4} +(y_{4, 2})  \lam{1}{2}{3}{1}{2}{4} +(-y_{3, 2})  \lam{1}{2}{4}{1}{2}{4} +(-y_{1, 4})  \lam{2}{3}{4}{1}{2}{2} +(x_{4, 2})  \psi{1}{2}{3}{1}{2}{4} +(-x_{3, 2})  \psi{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
2,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,3
1,2,3
Lead Term of Spoly:
-y(2)(1)*y(2)(4)*y(3)(2)*x(1)(3)
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(1)*y(2)(4)*y(3)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(3)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
-y(2)(3)
Lead Term of Product:
y(2)(2)*y(2)(3)*y(3)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,3
Quotient:
x(2)(4)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(3)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,4
Quotient:
-x(2)(3)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(3)(1)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(2)(2)*y(3)(1)*x(1)(3)+y(2)(1)*y(3)(2)*x(1)(3)+y(1)(2)*y(3)(1)*x(2)(3)-y(1)(1)*y(3)(2)*x(2)(3)-y(1)(2)*y(2)(1)*x(3)(3)+y(1)(1)*y(2)(2)*x(3)(3)) - (-y(2)(2)*y(3)(1))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(2)(4)*y(3)(2)*x(1)(3)+y(2)(2)*y(2)(3)*y(3)(1)*x(1)(4)+y(1)(4)*y(2)(2)*y(3)(1)*x(2)(3)-y(1)(2)*y(2)(4)*y(3)(1)*x(2)(3)+y(1)(1)*y(2)(4)*y(3)(2)*x(2)(3)-y(1)(3)*y(2)(2)*y(3)(1)*x(2)(4)+y(1)(2)*y(2)(1)*y(2)(4)*x(3)(3)-y(1)(1)*y(2)(2)*y(2)(4)*x(3)(3)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{3}{1}{2}{3}) =
(-y_{2, 1} y_{3, 2})  \eps{1}{2}{3}{4} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2, 2})  \eps{2}{3}{3}{4} +(-y_{2, 3})  \lam{1}{2}{3}{1}{2}{4} +(x_{2, 4})  \psi{1}{2}{3}{1}{2}{3} +(-x_{2, 3})  \psi{1}{2}{3}{1}{2}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,3
1,3,3
Lead Term of Spoly:
-y(2)(1)*y(2)(4)*y(3)(3)*x(1)(3)
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(2)(1)*y(3)(3)
Lead Term of Product:
-y(2)(1)*y(2)(4)*y(3)(3)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(3)*y(2)(1)+y(1)(1)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(1)*y(3)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,3,4
Quotient:
-y(2)(3)
Lead Term of Product:
y(2)(3)^2*y(3)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,3,4
Quotient:
-x(2)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(3)(1)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(2)(3)*y(3)(1)*x(1)(3)+y(2)(1)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(1)*x(2)(3)-y(1)(1)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(1)*x(3)(3)+y(1)(1)*y(2)(3)*x(3)(3)) - (-y(2)(3)*y(3)(1))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(2)(4)*y(3)(3)*x(1)(3)+y(2)(3)^2*y(3)(1)*x(1)(4)+y(1)(4)*y(2)(3)*y(3)(1)*x(2)(3)-y(1)(3)*y(2)(4)*y(3)(1)*x(2)(3)+y(1)(1)*y(2)(4)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(3)*y(3)(1)*x(2)(4)+y(1)(3)*y(2)(1)*y(2)(4)*x(3)(3)-y(1)(1)*y(2)(3)*y(2)(4)*x(3)(3)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{3}{1}{3}{3}) =
(-y_{2, 1} y_{3, 3})  \eps{1}{2}{3}{4} +(-y_{1, 3} y_{2, 1}+y_{1, 1} y_{2, 3})  \eps{2}{3}{3}{4} +(-y_{2, 3})  \lam{1}{2}{3}{1}{3}{4} +(-x_{2, 3})  \psi{1}{2}{3}{1}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,3
1,4,4
Lead Term of Spoly:
-y(2)(1)*y(3)(4)*x(1)(3)*x(1)(4)
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(4)*y(3)(1)
Lead Term of Product:
y(1)(4)*y(3)(1)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(4)*y(2)(1)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(1)(1)*x(3)(4)
Lead Term of Product:
-y(1)(1)*y(2)(4)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(2)(4)*y(3)(1)*x(1)(4)+y(2)(1)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(1)*x(2)(4)-y(1)(1)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(1)*x(3)(4)+y(1)(1)*y(2)(4)*x(3)(4)) - (-y(3)(1)*x(1)(4))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(3)(4)*x(1)(3)*x(1)(4)+y(2)(3)*y(3)(1)*x(1)(4)^2+y(1)(4)*y(3)(1)*x(1)(4)*x(2)(3)-y(1)(4)*y(3)(1)*x(1)(3)*x(2)(4)+y(1)(1)*y(3)(4)*x(1)(3)*x(2)(4)-y(1)(3)*y(3)(1)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(1)*x(1)(3)*x(3)(4)-y(1)(1)*y(2)(4)*x(1)(3)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{3}{1}{4}{4}) =
(-y_{1, 4} y_{3, 1})  \del{1}{2}{3}{4} +(y_{1, 4} y_{2, 1})  \del{1}{3}{3}{4} +(-y_{1, 1} y_{1, 4})  \del{2}{3}{3}{4} +(-y_{1, 1} x_{3, 4})  \eps{1}{2}{3}{4} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{3}{4} +(-x_{1, 4})  \lam{1}{2}{3}{1}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,3
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(2)(4)*y(3)(3)*x(1)(3)
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(2)(2)*y(3)(3)
Lead Term of Product:
-y(2)(2)*y(2)(4)*y(3)(3)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(3)*y(2)(2)+y(1)(2)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(3)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
2,3,4
Quotient:
-y(2)(3)
Lead Term of Product:
y(2)(3)^2*y(3)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
2,3,4
Quotient:
-x(2)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(3)(2)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(2)(3)*y(3)(2)*x(1)(3)+y(2)(2)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(2)*x(2)(3)-y(1)(2)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(3)(3)+y(1)(2)*y(2)(3)*x(3)(3)) - (-y(2)(3)*y(3)(2))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(2)*y(2)(4)*y(3)(3)*x(1)(3)+y(2)(3)^2*y(3)(2)*x(1)(4)+y(1)(4)*y(2)(3)*y(3)(2)*x(2)(3)-y(1)(3)*y(2)(4)*y(3)(2)*x(2)(3)+y(1)(2)*y(2)(4)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(3)*y(3)(2)*x(2)(4)+y(1)(3)*y(2)(2)*y(2)(4)*x(3)(3)-y(1)(2)*y(2)(3)*y(2)(4)*x(3)(3)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{3}{2}{3}{3}) =
(-y_{2, 2} y_{3, 3})  \eps{1}{2}{3}{4} +(-y_{1, 3} y_{2, 2}+y_{1, 2} y_{2, 3})  \eps{2}{3}{3}{4} +(-y_{2, 3})  \lam{1}{2}{3}{2}{3}{4} +(-x_{2, 3})  \psi{1}{2}{3}{2}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,3
2,4,4
Lead Term of Spoly:
-y(2)(2)*y(3)(4)*x(1)(3)*x(1)(4)
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(4)*y(3)(2)
Lead Term of Product:
y(1)(4)*y(3)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(4)*y(2)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(2)*y(1)(4)
Lead Term of Product:
y(1)(2)*y(1)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(1)(2)*x(3)(4)
Lead Term of Product:
-y(1)(2)*y(2)(4)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(2)*x(1)(4)+y(1)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
2,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(3)*y(3)(2)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(2)(4)*y(3)(2)*x(1)(4)+y(2)(2)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(2)*x(2)(4)-y(1)(2)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(2)*x(3)(4)+y(1)(2)*y(2)(4)*x(3)(4)) - (-y(3)(2)*x(1)(4))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(2)*y(3)(4)*x(1)(3)*x(1)(4)+y(2)(3)*y(3)(2)*x(1)(4)^2+y(1)(4)*y(3)(2)*x(1)(4)*x(2)(3)-y(1)(4)*y(3)(2)*x(1)(3)*x(2)(4)+y(1)(2)*y(3)(4)*x(1)(3)*x(2)(4)-y(1)(3)*y(3)(2)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(2)*x(1)(3)*x(3)(4)-y(1)(2)*y(2)(4)*x(1)(3)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{3}{2}{4}{4}) =
(-y_{1, 4} y_{3, 2})  \del{1}{2}{3}{4} +(y_{1, 4} y_{2, 2})  \del{1}{3}{3}{4} +(-y_{1, 2} y_{1, 4})  \del{2}{3}{3}{4} +(-y_{1, 2} x_{3, 4})  \eps{1}{2}{3}{4} +(-y_{2, 2} x_{1, 4}+y_{1, 2} x_{2, 4})  \eps{1}{3}{3}{4} +(-x_{1, 4})  \lam{1}{2}{3}{2}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,3
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(3)(4)*x(1)(3)*x(1)(4)
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(4)*y(3)(3)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(3)*y(1)(4)
Lead Term of Product:
y(1)(3)*y(1)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(1)(3)*x(3)(4)
Lead Term of Product:
-y(1)(3)*y(2)(4)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(3)*x(1)(4)+y(1)(3)*x(2)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(2)(4)*y(3)(3)*x(1)(4)+y(2)(3)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(3)*x(2)(4)-y(1)(3)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(3)(4)+y(1)(3)*y(2)(4)*x(3)(4)) - (-y(3)(3)*x(1)(4))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(3)*y(3)(4)*x(1)(3)*x(1)(4)+y(2)(3)*y(3)(3)*x(1)(4)^2+y(1)(4)*y(3)(3)*x(1)(4)*x(2)(3)-y(1)(4)*y(3)(3)*x(1)(3)*x(2)(4)+y(1)(3)*y(3)(4)*x(1)(3)*x(2)(4)-y(1)(3)*y(3)(3)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(3)*x(1)(3)*x(3)(4)-y(1)(3)*y(2)(4)*x(1)(3)*x(3)(4)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{3}{3}{4}{4}) =
(-y_{1, 4} y_{3, 3})  \del{1}{2}{3}{4} +(y_{1, 4} y_{2, 3})  \del{1}{3}{3}{4} +(-y_{1, 3} y_{1, 4})  \del{2}{3}{3}{4} +(-y_{1, 3} x_{3, 4})  \eps{1}{2}{3}{4} +(-y_{2, 3} x_{1, 4}+y_{1, 3} x_{2, 4})  \eps{1}{3}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,4
1,2,3
Lead Term of Spoly:
-y(2)(1)*y(2)(4)*y(4)(2)*x(1)(3)
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(2)(4)*y(4)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-y(2)(3)
Lead Term of Product:
y(2)(2)*y(2)(3)*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,3
Quotient:
x(2)(4)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(4)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,4
Quotient:
-x(2)(3)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(4)(1)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(2)(2)*y(4)(1)*x(1)(3)+y(2)(1)*y(4)(2)*x(1)(3)+y(1)(2)*y(4)(1)*x(2)(3)-y(1)(1)*y(4)(2)*x(2)(3)-y(1)(2)*y(2)(1)*x(4)(3)+y(1)(1)*y(2)(2)*x(4)(3)) - (-y(2)(2)*y(4)(1))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(2)(4)*y(4)(2)*x(1)(3)+y(2)(2)*y(2)(3)*y(4)(1)*x(1)(4)+y(1)(4)*y(2)(2)*y(4)(1)*x(2)(3)-y(1)(2)*y(2)(4)*y(4)(1)*x(2)(3)+y(1)(1)*y(2)(4)*y(4)(2)*x(2)(3)-y(1)(3)*y(2)(2)*y(4)(1)*x(2)(4)+y(1)(2)*y(2)(1)*y(2)(4)*x(4)(3)-y(1)(1)*y(2)(2)*y(2)(4)*x(4)(3)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{4}{1}{2}{3}) =
(-y_{2, 1} y_{4, 2})  \eps{1}{2}{3}{4} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2, 2})  \eps{2}{4}{3}{4} +(-y_{2, 3})  \lam{1}{2}{4}{1}{2}{4} +(x_{2, 4})  \psi{1}{2}{4}{1}{2}{3} +(-x_{2, 3})  \psi{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,4
1,3,3
Lead Term of Spoly:
-y(2)(1)*y(2)(4)*y(4)(3)*x(1)(3)
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(2)(1)*y(4)(3)
Lead Term of Product:
-y(2)(1)*y(2)(4)*y(4)(3)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(1)(3)*y(2)(1)+y(1)(1)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(1)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,3,4
Quotient:
-y(2)(3)
Lead Term of Product:
y(2)(3)^2*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,3,4
Quotient:
-x(2)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(4)(1)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(2)(3)*y(4)(1)*x(1)(3)+y(2)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(2)(3)-y(1)(1)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(1)*x(4)(3)+y(1)(1)*y(2)(3)*x(4)(3)) - (-y(2)(3)*y(4)(1))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(2)(4)*y(4)(3)*x(1)(3)+y(2)(3)^2*y(4)(1)*x(1)(4)+y(1)(4)*y(2)(3)*y(4)(1)*x(2)(3)-y(1)(3)*y(2)(4)*y(4)(1)*x(2)(3)+y(1)(1)*y(2)(4)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(3)*y(4)(1)*x(2)(4)+y(1)(3)*y(2)(1)*y(2)(4)*x(4)(3)-y(1)(1)*y(2)(3)*y(2)(4)*x(4)(3)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{4}{1}{3}{3}) =
(-y_{2, 1} y_{4, 3})  \eps{1}{2}{3}{4} +(-y_{1, 3} y_{2, 1}+y_{1, 1} y_{2, 3})  \eps{2}{4}{3}{4} +(-y_{2, 3})  \lam{1}{2}{4}{1}{3}{4} +(-x_{2, 3})  \psi{1}{2}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,4
1,4,4
Lead Term of Spoly:
-y(2)(1)*y(4)(4)*x(1)(3)*x(1)(4)
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(4)*y(4)(1)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(2)(1)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(2)(4)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(2)(4)*y(4)(1)*x(1)(4)+y(2)(1)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(1)*x(2)(4)-y(1)(1)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(1)*x(4)(4)+y(1)(1)*y(2)(4)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(1)*y(4)(4)*x(1)(3)*x(1)(4)+y(2)(3)*y(4)(1)*x(1)(4)^2+y(1)(4)*y(4)(1)*x(1)(4)*x(2)(3)-y(1)(4)*y(4)(1)*x(1)(3)*x(2)(4)+y(1)(1)*y(4)(4)*x(1)(3)*x(2)(4)-y(1)(3)*y(4)(1)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(1)*x(1)(3)*x(4)(4)-y(1)(1)*y(2)(4)*x(1)(3)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{4}{1}{4}{4}) =
(-y_{1, 4} y_{4, 1})  \del{1}{2}{3}{4} +(y_{1, 4} y_{2, 1})  \del{1}{4}{3}{4} +(-y_{1, 1} y_{1, 4})  \del{2}{4}{3}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{2}{3}{4} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{3}{4} +(-x_{1, 4})  \lam{1}{2}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,4
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(2)(4)*y(4)(3)*x(1)(3)
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(2)(2)*y(4)(3)
Lead Term of Product:
-y(2)(2)*y(2)(4)*y(4)(3)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(1)(3)*y(2)(2)+y(1)(2)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
2,3,4
Quotient:
-y(2)(3)
Lead Term of Product:
y(2)(3)^2*y(4)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
2,3,4
Quotient:
-x(2)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(4)(2)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(2)(3)*y(4)(2)*x(1)(3)+y(2)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(2)(3)-y(1)(2)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(4)(3)+y(1)(2)*y(2)(3)*x(4)(3)) - (-y(2)(3)*y(4)(2))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(2)*y(2)(4)*y(4)(3)*x(1)(3)+y(2)(3)^2*y(4)(2)*x(1)(4)+y(1)(4)*y(2)(3)*y(4)(2)*x(2)(3)-y(1)(3)*y(2)(4)*y(4)(2)*x(2)(3)+y(1)(2)*y(2)(4)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(3)*y(4)(2)*x(2)(4)+y(1)(3)*y(2)(2)*y(2)(4)*x(4)(3)-y(1)(2)*y(2)(3)*y(2)(4)*x(4)(3)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{4}{2}{3}{3}) =
(-y_{2, 2} y_{4, 3})  \eps{1}{2}{3}{4} +(-y_{1, 3} y_{2, 2}+y_{1, 2} y_{2, 3})  \eps{2}{4}{3}{4} +(-y_{2, 3})  \lam{1}{2}{4}{2}{3}{4} +(-x_{2, 3})  \psi{1}{2}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,4
2,4,4
Lead Term of Spoly:
-y(2)(2)*y(4)(4)*x(1)(3)*x(1)(4)
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(4)*y(4)(2)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(2)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(2)*y(1)(4)
Lead Term of Product:
y(1)(2)*y(1)(4)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(2)(4)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(2)*x(1)(4)+y(1)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
2,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(2)(4)*y(4)(2)*x(1)(4)+y(2)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(2)(4)-y(1)(2)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(2)*x(4)(4)+y(1)(2)*y(2)(4)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(2)*y(4)(4)*x(1)(3)*x(1)(4)+y(2)(3)*y(4)(2)*x(1)(4)^2+y(1)(4)*y(4)(2)*x(1)(4)*x(2)(3)-y(1)(4)*y(4)(2)*x(1)(3)*x(2)(4)+y(1)(2)*y(4)(4)*x(1)(3)*x(2)(4)-y(1)(3)*y(4)(2)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(2)*x(1)(3)*x(4)(4)-y(1)(2)*y(2)(4)*x(1)(3)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{4}{2}{4}{4}) =
(-y_{1, 4} y_{4, 2})  \del{1}{2}{3}{4} +(y_{1, 4} y_{2, 2})  \del{1}{4}{3}{4} +(-y_{1, 2} y_{1, 4})  \del{2}{4}{3}{4} +(-y_{1, 2} x_{4, 4})  \eps{1}{2}{3}{4} +(-y_{2, 2} x_{1, 4}+y_{1, 2} x_{2, 4})  \eps{1}{4}{3}{4} +(-x_{1, 4})  \lam{1}{2}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,2,4
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(4)(4)*x(1)(3)*x(1)(4)
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(4)*y(4)(3)
Lead Term of Product:
y(1)(4)*y(4)(3)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(3)*y(1)(4)
Lead Term of Product:
y(1)(3)*y(1)(4)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(1)(3)*x(4)(4)
Lead Term of Product:
-y(1)(3)*y(2)(4)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(3)*x(1)(4)+y(1)(3)*x(2)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(2)(4)*y(4)(3)*x(1)(4)+y(2)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(2)(4)-y(1)(3)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(4)(4)+y(1)(3)*y(2)(4)*x(4)(4)) - (-y(4)(3)*x(1)(4))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(3)*y(4)(4)*x(1)(3)*x(1)(4)+y(2)(3)*y(4)(3)*x(1)(4)^2+y(1)(4)*y(4)(3)*x(1)(4)*x(2)(3)-y(1)(4)*y(4)(3)*x(1)(3)*x(2)(4)+y(1)(3)*y(4)(4)*x(1)(3)*x(2)(4)-y(1)(3)*y(4)(3)*x(1)(4)*x(2)(4)+y(1)(4)*y(2)(3)*x(1)(3)*x(4)(4)-y(1)(3)*y(2)(4)*x(1)(3)*x(4)(4)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{2}{4}{3}{4}{4}) =
(-y_{1, 4} y_{4, 3})  \del{1}{2}{3}{4} +(y_{1, 4} y_{2, 3})  \del{1}{4}{3}{4} +(-y_{1, 3} y_{1, 4})  \del{2}{4}{3}{4} +(-y_{1, 3} x_{4, 4})  \eps{1}{2}{3}{4} +(-y_{2, 3} x_{1, 4}+y_{1, 3} x_{2, 4})  \eps{1}{4}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,3,4
1,2,3
Lead Term of Spoly:
-y(2)(4)*y(3)(1)*y(4)(2)*x(1)(3)
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(2)(4)*y(3)(1)*y(4)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,3,4
Quotient:
y(4)(2)
Lead Term of Product:
-y(2)(3)*y(3)(1)*y(4)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
2,3,4
Quotient:
-y(4)(1)
Lead Term of Product:
y(2)(3)*y(3)(2)*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(2)(2)*y(3)(3)*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,3
Quotient:
-y(1)(4)
Lead Term of Product:
y(1)(4)*y(3)(2)*y(4)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,4
Quotient:
x(4)(3)
Lead Term of Product:
-y(1)(4)*y(2)(2)*y(3)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,3
Quotient:
x(3)(4)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(4)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(4)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(3)(2)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(2)*x(1)(3)+y(1)(2)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(2)*x(3)(3)-y(1)(2)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(2)*x(4)(3)) - (-y(3)(2)*y(4)(1))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(4)*y(3)(1)*y(4)(2)*x(1)(3)+y(2)(3)*y(3)(2)*y(4)(1)*x(1)(4)+y(1)(4)*y(3)(2)*y(4)(1)*x(2)(3)-y(1)(3)*y(3)(2)*y(4)(1)*x(2)(4)-y(1)(2)*y(2)(4)*y(4)(1)*x(3)(3)+y(1)(1)*y(2)(4)*y(4)(2)*x(3)(3)+y(1)(2)*y(2)(4)*y(3)(1)*x(4)(3)-y(1)(1)*y(2)(4)*y(3)(2)*x(4)(3)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{3}{4}{1}{2}{3}) =
(-y_{3, 1} y_{4, 2})  \eps{1}{2}{3}{4} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2, 2})  \eps{3}{4}{3}{4} +(y_{4, 2})  \lam{1}{2}{3}{1}{3}{4} +(-y_{4, 1})  \lam{1}{2}{3}{2}{3}{4} +(-y_{3, 3})  \lam{1}{2}{4}{1}{2}{4} +(-y_{1, 4})  \lam{2}{3}{4}{1}{2}{3} +(x_{4, 3})  \psi{1}{2}{3}{1}{2}{4} +(x_{3, 4})  \psi{1}{2}{4}{1}{2}{3} +(-x_{3, 3})  \psi{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,3,4
1,3,3
Lead Term of Spoly:
-y(2)(4)*y(3)(1)*y(4)(3)*x(1)(3)
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(3)(1)*y(4)(3)
Lead Term of Product:
-y(2)(4)*y(3)(1)*y(4)(3)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(3)*y(2)(1)+y(1)(1)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,3,4
Quotient:
y(4)(3)
Lead Term of Product:
-y(2)(3)*y(3)(1)*y(4)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,3,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(2)(3)*y(3)(3)*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,3,3
Quotient:
-y(1)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*y(4)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,3,4
Quotient:
x(4)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*y(3)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,3,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(4)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(3)(3)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(3)*x(4)(3)) - (-y(3)(3)*y(4)(1))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(4)*y(3)(1)*y(4)(3)*x(1)(3)+y(2)(3)*y(3)(3)*y(4)(1)*x(1)(4)+y(1)(4)*y(3)(3)*y(4)(1)*x(2)(3)-y(1)(3)*y(3)(3)*y(4)(1)*x(2)(4)-y(1)(3)*y(2)(4)*y(4)(1)*x(3)(3)+y(1)(1)*y(2)(4)*y(4)(3)*x(3)(3)+y(1)(3)*y(2)(4)*y(3)(1)*x(4)(3)-y(1)(1)*y(2)(4)*y(3)(3)*x(4)(3)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{3}{4}{1}{3}{3}) =
(-y_{3, 1} y_{4, 3})  \eps{1}{2}{3}{4} +(-y_{1, 3} y_{2, 1}+y_{1, 1} y_{2, 3})  \eps{3}{4}{3}{4} +(y_{4, 3})  \lam{1}{2}{3}{1}{3}{4} +(-y_{3, 3})  \lam{1}{2}{4}{1}{3}{4} +(-y_{1, 4})  \lam{2}{3}{4}{1}{3}{3} +(x_{4, 3})  \psi{1}{2}{3}{1}{3}{4} +(-x_{3, 3})  \psi{1}{2}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,3,4
2,3,3
Lead Term of Spoly:
-y(2)(4)*y(3)(2)*y(4)(3)*x(1)(3)
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(3)(2)*y(4)(3)
Lead Term of Product:
-y(2)(4)*y(3)(2)*y(4)(3)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(3)*y(2)(2)+y(1)(2)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
2,3,4
Quotient:
y(4)(3)
Lead Term of Product:
-y(2)(3)*y(3)(2)*y(4)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
2,3,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(2)(3)*y(3)(3)*y(4)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
2,3,3
Quotient:
-y(1)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*y(4)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Psi
1,2,3
2,3,4
Quotient:
x(4)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*y(3)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Psi
1,2,4
2,3,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(4)(2)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(4))*(-y(3)(3)*y(4)(2)*x(1)(3)+y(3)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(3)(3)-y(1)(2)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(2)*x(4)(3)+y(1)(2)*y(3)(3)*x(4)(3)) - (-y(3)(3)*y(4)(2))*(y(2)(4)*x(1)(3)-y(2)(3)*x(1)(4)-y(1)(4)*x(2)(3)+y(1)(3)*x(2)(4))
-------
Rewrite:
-y(2)(4)*y(3)(2)*y(4)(3)*x(1)(3)+y(2)(3)*y(3)(3)*y(4)(2)*x(1)(4)+y(1)(4)*y(3)(3)*y(4)(2)*x(2)(3)-y(1)(3)*y(3)(3)*y(4)(2)*x(2)(4)-y(1)(3)*y(2)(4)*y(4)(2)*x(3)(3)+y(1)(2)*y(2)(4)*y(4)(3)*x(3)(3)+y(1)(3)*y(2)(4)*y(3)(2)*x(4)(3)-y(1)(2)*y(2)(4)*y(3)(3)*x(4)(3)
-----------
TeX output:
S(\eps{1}{2}{3}{4}, \lam{1}{3}{4}{2}{3}{3}) =
(-y_{3, 2} y_{4, 3})  \eps{1}{2}{3}{4} +(-y_{1, 3} y_{2, 2}+y_{1, 2} y_{2, 3})  \eps{3}{4}{3}{4} +(y_{4, 3})  \lam{1}{2}{3}{2}{3}{4} +(-y_{3, 3})  \lam{1}{2}{4}{2}{3}{4} +(-y_{1, 4})  \lam{2}{3}{4}{2}{3}{3} +(x_{4, 3})  \psi{1}{2}{3}{2}{3}{4} +(-x_{3, 3})  \psi{1}{2}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,2
3,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,3
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,2
1,3
Quotient:
y(1)(2)*y(3)(3)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,3
Quotient:
-y(1)(3)*y(3)(1)-y(1)(1)*y(3)(3)
Lead Term of Product:
y(1)(3)*y(3)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
1,3
Quotient:
-y(1)(2)*y(2)(3)
Lead Term of Product:
y(1)(2)*y(2)(3)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
y(1)(3)*y(2)(1)+y(1)(1)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,3
Quotient:
y(1)(2)*y(1)(3)
Lead Term of Product:
-y(1)(2)*y(1)(3)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-2*y(1)(1)*y(1)(3)
Lead Term of Product:
2*y(1)(1)*y(1)(3)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(3)(3)*x(1)(3)+y(1)(3)*x(3)(3)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(3)(1)*x(1)(3)-y(1)(1)*x(3)(3)
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(1)(3)*x(2)(3)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(1)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(1)(3)+y(1)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-x(1)(3)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(3)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(3)(2)*x(1)(3)+y(2)(2)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(2)*x(2)(3)-y(1)(2)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(3)(3)+y(1)(2)*y(2)(3)*x(3)(3)) - (-y(2)(3)*x(1)(3))*(y(3)(2)*x(1)(1)-y(3)(1)*x(1)(2)-y(1)(2)*x(3)(1)+y(1)(1)*x(3)(2))
-------
Rewrite:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(3)+y(2)(3)*y(3)(1)*x(1)(2)*x(1)(3)-y(1)(3)*y(3)(2)*x(1)(1)*x(2)(3)+y(1)(2)*y(3)(3)*x(1)(1)*x(2)(3)+y(1)(2)*y(2)(3)*x(1)(3)*x(3)(1)-y(1)(1)*y(2)(3)*x(1)(3)*x(3)(2)+y(1)(3)*y(2)(2)*x(1)(1)*x(3)(3)-y(1)(2)*y(2)(3)*x(1)(1)*x(3)(3)
-----------
TeX output:
S(\eps{1}{3}{1}{2}, \lam{1}{2}{3}{2}{3}{3}) =
(y_{1, 2} y_{3, 3})  \del{1}{2}{1}{3} +(-y_{1, 3} y_{3, 1}-y_{1, 1} y_{3, 3})  \del{1}{2}{2}{3} +(-y_{1, 2} y_{2, 3})  \del{1}{3}{1}{3} +(y_{1, 3} y_{2, 1}+y_{1, 1} y_{2, 3})  \del{1}{3}{2}{3} +(y_{1, 2} y_{1, 3})  \del{2}{3}{1}{3} +(-2 y_{1, 1} y_{1, 3})  \del{2}{3}{2}{3} +(-y_{3, 3} x_{1, 3}+y_{1, 3} x_{3, 3})  \eps{1}{2}{1}{2} +(y_{3, 1} x_{1, 3}-y_{1, 1} x_{3, 3})  \eps{1}{2}{2}{3} +(-y_{1, 3} x_{2, 3})  \eps{1}{3}{1}{2} +(-y_{2, 1} x_{1, 3}+y_{1, 1} x_{2, 3})  \eps{1}{3}{2}{3} +(-x_{1, 3})  \lam{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,3
2,3,4
Lead Term of Spoly:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
y(1)(2)*y(3)(3)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(3)*y(3)(1)-y(1)(1)*y(3)(3)
Lead Term of Product:
y(1)(3)*y(3)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(1)*y(3)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(1)(2)*y(2)(3)
Lead Term of Product:
y(1)(2)*y(2)(3)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(1)(3)*y(2)(1)+y(1)(1)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(1)*y(2)(2)
Lead Term of Product:
y(1)(1)*y(2)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(2)*y(1)(3)
Lead Term of Product:
-y(1)(2)*y(1)(3)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-2*y(1)(1)*y(1)(3)
Lead Term of Product:
2*y(1)(1)*y(1)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(1)(1)*y(1)(2)
Lead Term of Product:
-y(1)(1)*y(1)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(3)(3)*x(1)(4)+y(1)(3)*x(3)(4)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(3)(1)*x(1)(4)-y(1)(1)*x(3)(4)
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(1)(3)*x(2)(4)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(3)(2)*x(1)(4)+y(2)(2)*y(3)(3)*x(1)(4)+y(1)(3)*y(3)(2)*x(2)(4)-y(1)(2)*y(3)(3)*x(2)(4)-y(1)(3)*y(2)(2)*x(3)(4)+y(1)(2)*y(2)(3)*x(3)(4)) - (-y(2)(3)*x(1)(4))*(y(3)(2)*x(1)(1)-y(3)(1)*x(1)(2)-y(1)(2)*x(3)(1)+y(1)(1)*x(3)(2))
-------
Rewrite:
-y(2)(2)*y(3)(3)*x(1)(1)*x(1)(4)+y(2)(3)*y(3)(1)*x(1)(2)*x(1)(4)-y(1)(3)*y(3)(2)*x(1)(1)*x(2)(4)+y(1)(2)*y(3)(3)*x(1)(1)*x(2)(4)+y(1)(2)*y(2)(3)*x(1)(4)*x(3)(1)-y(1)(1)*y(2)(3)*x(1)(4)*x(3)(2)+y(1)(3)*y(2)(2)*x(1)(1)*x(3)(4)-y(1)(2)*y(2)(3)*x(1)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{2}, \lam{1}{2}{3}{2}{3}{4}) =
(y_{1, 2} y_{3, 3})  \del{1}{2}{1}{4} +(-y_{1, 3} y_{3, 1}-y_{1, 1} y_{3, 3})  \del{1}{2}{2}{4} +(y_{1, 1} y_{3, 2})  \del{1}{2}{3}{4} +(-y_{1, 2} y_{2, 3})  \del{1}{3}{1}{4} +(y_{1, 3} y_{2, 1}+y_{1, 1} y_{2, 3})  \del{1}{3}{2}{4} +(-y_{1, 1} y_{2, 2})  \del{1}{3}{3}{4} +(y_{1, 2} y_{1, 3})  \del{2}{3}{1}{4} +(-2 y_{1, 1} y_{1, 3})  \del{2}{3}{2}{4} +(y_{1, 1} y_{1, 2})  \del{2}{3}{3}{4} +(-y_{3, 3} x_{1, 4}+y_{1, 3} x_{3, 4})  \eps{1}{2}{1}{2} +(y_{3, 1} x_{1, 4}-y_{1, 1} x_{3, 4})  \eps{1}{2}{2}{3} +(-y_{1, 3} x_{2, 4})  \eps{1}{3}{1}{2} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{2}{3} +(-x_{1, 4})  \lam{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,3
2,4,4
Lead Term of Spoly:
-y(2)(2)*y(3)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
y(1)(2)*y(3)(4)
Lead Term of Product:
-y(1)(2)*y(3)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(4)*y(3)(1)-y(1)(1)*y(3)(4)
Lead Term of Product:
y(1)(4)*y(3)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(1)(2)*y(2)(4)
Lead Term of Product:
y(1)(2)*y(2)(4)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(1)(4)*y(2)(1)+y(1)(1)*y(2)(4)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(2)*y(1)(4)
Lead Term of Product:
-y(1)(2)*y(1)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-2*y(1)(1)*y(1)(4)
Lead Term of Product:
2*y(1)(1)*y(1)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(3)(4)*x(1)(4)+y(1)(4)*x(3)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
y(3)(1)*x(1)(4)-y(1)(1)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(3)(1)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(4)*y(3)(2)*x(1)(4)+y(2)(2)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(2)*x(2)(4)-y(1)(2)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(2)*x(3)(4)+y(1)(2)*y(2)(4)*x(3)(4)) - (-y(2)(4)*x(1)(4))*(y(3)(2)*x(1)(1)-y(3)(1)*x(1)(2)-y(1)(2)*x(3)(1)+y(1)(1)*x(3)(2))
-------
Rewrite:
-y(2)(2)*y(3)(4)*x(1)(1)*x(1)(4)+y(2)(4)*y(3)(1)*x(1)(2)*x(1)(4)-y(1)(4)*y(3)(2)*x(1)(1)*x(2)(4)+y(1)(2)*y(3)(4)*x(1)(1)*x(2)(4)+y(1)(2)*y(2)(4)*x(1)(4)*x(3)(1)-y(1)(1)*y(2)(4)*x(1)(4)*x(3)(2)+y(1)(4)*y(2)(2)*x(1)(1)*x(3)(4)-y(1)(2)*y(2)(4)*x(1)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{2}, \lam{1}{2}{3}{2}{4}{4}) =
(y_{1, 2} y_{3, 4})  \del{1}{2}{1}{4} +(-y_{1, 4} y_{3, 1}-y_{1, 1} y_{3, 4})  \del{1}{2}{2}{4} +(-y_{1, 2} y_{2, 4})  \del{1}{3}{1}{4} +(y_{1, 4} y_{2, 1}+y_{1, 1} y_{2, 4})  \del{1}{3}{2}{4} +(y_{1, 2} y_{1, 4})  \del{2}{3}{1}{4} +(-2 y_{1, 1} y_{1, 4})  \del{2}{3}{2}{4} +(-y_{3, 4} x_{1, 4}+y_{1, 4} x_{3, 4})  \eps{1}{2}{1}{2} +(y_{3, 1} x_{1, 4}-y_{1, 1} x_{3, 4})  \eps{1}{2}{2}{4} +(-y_{1, 4} x_{2, 4})  \eps{1}{3}{1}{2} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{2}{4} +(-x_{1, 4})  \lam{1}{2}{3}{1}{2}{4}
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(1)(1)*x(1)(2)
Divisor:
Delta
1,3
1,2
Quotient:
-y(1)(2)*y(4)(1)
Lead Term of Product:
y(1)(2)*y(4)(1)*x(1)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,4
1,2
Quotient:
y(1)(2)*y(3)(1)
Lead Term of Product:
-y(1)(2)*y(3)(1)*x(1)(2)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,2
Quotient:
-y(1)(1)*y(1)(2)
Lead Term of Product:
y(1)(1)*y(1)(2)*x(3)(2)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(1)(1)*x(4)(2)
Lead Term of Product:
-y(1)(1)*y(3)(2)*x(1)(1)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(3)(1)*x(1)(2)+y(1)(1)*x(3)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(1)*x(1)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(2)*y(4)(1)*x(1)(2)+y(3)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(3)(2)-y(1)(1)*y(4)(2)*x(3)(2)-y(1)(2)*y(3)(1)*x(4)(2)+y(1)(1)*y(3)(2)*x(4)(2)) - (-y(4)(1)*x(1)(2))*(y(3)(2)*x(1)(1)-y(3)(1)*x(1)(2)-y(1)(2)*x(3)(1)+y(1)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(1)(1)*x(1)(2)+y(3)(1)*y(4)(1)*x(1)(2)^2+y(1)(2)*y(4)(1)*x(1)(2)*x(3)(1)-y(1)(2)*y(4)(1)*x(1)(1)*x(3)(2)+y(1)(1)*y(4)(2)*x(1)(1)*x(3)(2)-y(1)(1)*y(4)(1)*x(1)(2)*x(3)(2)+y(1)(2)*y(3)(1)*x(1)(1)*x(4)(2)-y(1)(1)*y(3)(2)*x(1)(1)*x(4)(2)
-----------
TeX output:
S(\eps{1}{3}{1}{2}, \lam{1}{3}{4}{1}{2}{2}) =
(-y_{1, 2} y_{4, 1})  \del{1}{3}{1}{2} +(y_{1, 2} y_{3, 1})  \del{1}{4}{1}{2} +(-y_{1, 1} y_{1, 2})  \del{3}{4}{1}{2} +(-y_{1, 1} x_{4, 2})  \eps{1}{3}{1}{2} +(-y_{3, 1} x_{1, 2}+y_{1, 1} x_{3, 2})  \eps{1}{4}{1}{2}
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,3,4
1,2,3
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,3
1,3
Quotient:
-y(1)(2)*y(4)(1)
Lead Term of Product:
y(1)(2)*y(4)(1)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
y(1)(1)*y(4)(1)
Lead Term of Product:
-y(1)(1)*y(4)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,3
Quotient:
y(1)(2)*y(3)(1)
Lead Term of Product:
-y(1)(2)*y(3)(1)*x(1)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
-y(1)(1)*y(3)(1)
Lead Term of Product:
y(1)(1)*y(3)(1)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
-y(1)(1)*y(1)(2)
Lead Term of Product:
y(1)(1)*y(1)(2)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
y(1)(1)^2
Lead Term of Product:
-y(1)(1)^2*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(1)(1)*x(4)(3)
Lead Term of Product:
-y(1)(1)*y(3)(2)*x(1)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(3)(1)*x(1)(3)+y(1)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(1)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(2)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(2)*x(1)(3)+y(1)(2)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(2)*x(3)(3)-y(1)(2)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(2)*x(4)(3)) - (-y(4)(1)*x(1)(3))*(y(3)(2)*x(1)(1)-y(3)(1)*x(1)(2)-y(1)(2)*x(3)(1)+y(1)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(1)(1)*x(1)(3)+y(3)(1)*y(4)(1)*x(1)(2)*x(1)(3)+y(1)(2)*y(4)(1)*x(1)(3)*x(3)(1)-y(1)(1)*y(4)(1)*x(1)(3)*x(3)(2)-y(1)(2)*y(4)(1)*x(1)(1)*x(3)(3)+y(1)(1)*y(4)(2)*x(1)(1)*x(3)(3)+y(1)(2)*y(3)(1)*x(1)(1)*x(4)(3)-y(1)(1)*y(3)(2)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{1}{2}, \lam{1}{3}{4}{1}{2}{3}) =
(-y_{1, 2} y_{4, 1})  \del{1}{3}{1}{3} +(y_{1, 1} y_{4, 1})  \del{1}{3}{2}{3} +(y_{1, 2} y_{3, 1})  \del{1}{4}{1}{3} +(-y_{1, 1} y_{3, 1})  \del{1}{4}{2}{3} +(-y_{1, 1} y_{1, 2})  \del{3}{4}{1}{3} +(y_{1, 1}^2)  \del{3}{4}{2}{3} +(-y_{1, 1} x_{4, 3})  \eps{1}{3}{1}{2} +(-y_{3, 1} x_{1, 3}+y_{1, 1} x_{3, 3})  \eps{1}{4}{1}{2}
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,3,4
1,2,4
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,3
1,4
Quotient:
-y(1)(2)*y(4)(1)
Lead Term of Product:
y(1)(2)*y(4)(1)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(1)(1)*y(4)(1)
Lead Term of Product:
-y(1)(1)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
y(1)(2)*y(3)(1)
Lead Term of Product:
-y(1)(2)*y(3)(1)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
-y(1)(1)*y(3)(1)
Lead Term of Product:
y(1)(1)*y(3)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(1)(1)*y(1)(2)
Lead Term of Product:
y(1)(1)*y(1)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
y(1)(1)^2
Lead Term of Product:
-y(1)(1)^2*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(2)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(1)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(2)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(2)*x(1)(4)+y(1)(2)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(2)*x(3)(4)-y(1)(2)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(2)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(2)*x(1)(1)-y(3)(1)*x(1)(2)-y(1)(2)*x(3)(1)+y(1)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(1)(1)*x(1)(4)+y(3)(1)*y(4)(1)*x(1)(2)*x(1)(4)+y(1)(2)*y(4)(1)*x(1)(4)*x(3)(1)-y(1)(1)*y(4)(1)*x(1)(4)*x(3)(2)-y(1)(2)*y(4)(1)*x(1)(1)*x(3)(4)+y(1)(1)*y(4)(2)*x(1)(1)*x(3)(4)+y(1)(2)*y(3)(1)*x(1)(1)*x(4)(4)-y(1)(1)*y(3)(2)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{2}, \lam{1}{3}{4}{1}{2}{4}) =
(-y_{1, 2} y_{4, 1})  \del{1}{3}{1}{4} +(y_{1, 1} y_{4, 1})  \del{1}{3}{2}{4} +(y_{1, 2} y_{3, 1})  \del{1}{4}{1}{4} +(-y_{1, 1} y_{3, 1})  \del{1}{4}{2}{4} +(-y_{1, 1} y_{1, 2})  \del{3}{4}{1}{4} +(y_{1, 1}^2)  \del{3}{4}{2}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{3}{1}{2} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{1}{2}
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
2,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(2)
Divisor:
Delta
2,3
1,2
Quotient:
-y(1)(2)*y(4)(1)
Lead Term of Product:
y(1)(2)*y(4)(1)*x(2)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,2
Quotient:
y(1)(2)*y(3)(1)
Lead Term of Product:
-y(1)(2)*y(3)(1)*x(2)(2)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,2
Quotient:
-y(1)(2)*y(2)(1)
Lead Term of Product:
y(1)(2)*y(2)(1)*x(3)(2)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(1)*x(3)(2)+y(3)(1)*x(4)(2)
Lead Term of Product:
-y(2)(2)*y(4)(1)*x(1)(1)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(2)(1)*x(4)(2)
Lead Term of Product:
-y(2)(1)*y(3)(2)*x(1)(1)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(3)(1)*x(2)(2)+y(2)(1)*x(3)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(2)*y(4)(1)*x(2)(2)+y(3)(1)*y(4)(2)*x(2)(2)+y(2)(2)*y(4)(1)*x(3)(2)-y(2)(1)*y(4)(2)*x(3)(2)-y(2)(2)*y(3)(1)*x(4)(2)+y(2)(1)*y(3)(2)*x(4)(2)) - (-y(4)(1)*x(2)(2))*(y(3)(2)*x(1)(1)-y(3)(1)*x(1)(2)-y(1)(2)*x(3)(1)+y(1)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(2)+y(3)(1)*y(4)(1)*x(1)(2)*x(2)(2)+y(1)(2)*y(4)(1)*x(2)(2)*x(3)(1)-y(2)(2)*y(4)(1)*x(1)(1)*x(3)(2)+y(2)(1)*y(4)(2)*x(1)(1)*x(3)(2)-y(1)(1)*y(4)(1)*x(2)(2)*x(3)(2)+y(2)(2)*y(3)(1)*x(1)(1)*x(4)(2)-y(2)(1)*y(3)(2)*x(1)(1)*x(4)(2)
-----------
TeX output:
S(\eps{1}{3}{1}{2}, \lam{2}{3}{4}{1}{2}{2}) =
(-y_{1, 2} y_{4, 1})  \del{2}{3}{1}{2} +(y_{1, 2} y_{3, 1})  \del{2}{4}{1}{2} +(-y_{1, 2} y_{2, 1})  \del{3}{4}{1}{2} +(-y_{4, 1} x_{3, 2}+y_{3, 1} x_{4, 2})  \eps{1}{2}{1}{2} +(-y_{2, 1} x_{4, 2})  \eps{1}{3}{1}{2} +(-y_{3, 1} x_{2, 2}+y_{2, 1} x_{3, 2})  \eps{1}{4}{1}{2}
----------------------------------
Epsilon:
1,3
1,2
Lam:
2,3,4
1,2,3
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(3)
Divisor:
Delta
2,3
1,3
Quotient:
-y(1)(2)*y(4)(1)
Lead Term of Product:
y(1)(2)*y(4)(1)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
y(1)(1)*y(4)(1)
Lead Term of Product:
-y(1)(1)*y(4)(1)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
y(1)(2)*y(3)(1)
Lead Term of Product:
-y(1)(2)*y(3)(1)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
-y(1)(1)*y(3)(1)
Lead Term of Product:
y(1)(1)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
-y(1)(2)*y(2)(1)
Lead Term of Product:
y(1)(2)*y(2)(1)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
y(1)(1)*y(2)(1)
Lead Term of Product:
-y(1)(1)*y(2)(1)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(1)*x(3)(3)+y(3)(1)*x(4)(3)
Lead Term of Product:
-y(2)(2)*y(4)(1)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(2)(1)*x(4)(3)
Lead Term of Product:
-y(2)(1)*y(3)(2)*x(1)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(3)(1)*x(2)(3)+y(2)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(2)*y(4)(1)*x(2)(3)+y(3)(1)*y(4)(2)*x(2)(3)+y(2)(2)*y(4)(1)*x(3)(3)-y(2)(1)*y(4)(2)*x(3)(3)-y(2)(2)*y(3)(1)*x(4)(3)+y(2)(1)*y(3)(2)*x(4)(3)) - (-y(4)(1)*x(2)(3))*(y(3)(2)*x(1)(1)-y(3)(1)*x(1)(2)-y(1)(2)*x(3)(1)+y(1)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(3)+y(3)(1)*y(4)(1)*x(1)(2)*x(2)(3)+y(1)(2)*y(4)(1)*x(2)(3)*x(3)(1)-y(1)(1)*y(4)(1)*x(2)(3)*x(3)(2)-y(2)(2)*y(4)(1)*x(1)(1)*x(3)(3)+y(2)(1)*y(4)(2)*x(1)(1)*x(3)(3)+y(2)(2)*y(3)(1)*x(1)(1)*x(4)(3)-y(2)(1)*y(3)(2)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{1}{2}, \lam{2}{3}{4}{1}{2}{3}) =
(-y_{1, 2} y_{4, 1})  \del{2}{3}{1}{3} +(y_{1, 1} y_{4, 1})  \del{2}{3}{2}{3} +(y_{1, 2} y_{3, 1})  \del{2}{4}{1}{3} +(-y_{1, 1} y_{3, 1})  \del{2}{4}{2}{3} +(-y_{1, 2} y_{2, 1})  \del{3}{4}{1}{3} +(y_{1, 1} y_{2, 1})  \del{3}{4}{2}{3} +(-y_{4, 1} x_{3, 3}+y_{3, 1} x_{4, 3})  \eps{1}{2}{1}{2} +(-y_{2, 1} x_{4, 3})  \eps{1}{3}{1}{2} +(-y_{3, 1} x_{2, 3}+y_{2, 1} x_{3, 3})  \eps{1}{4}{1}{2}
----------------------------------
Epsilon:
1,3
1,2
Lam:
2,3,4
1,2,4
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(1)(2)*y(4)(1)
Lead Term of Product:
y(1)(2)*y(4)(1)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
y(1)(1)*y(4)(1)
Lead Term of Product:
-y(1)(1)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(2)*y(3)(1)
Lead Term of Product:
-y(1)(2)*y(3)(1)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(1)(1)*y(3)(1)
Lead Term of Product:
y(1)(1)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(1)(2)*y(2)(1)
Lead Term of Product:
y(1)(2)*y(2)(1)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
y(1)(1)*y(2)(1)
Lead Term of Product:
-y(1)(1)*y(2)(1)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(1)*x(3)(4)+y(3)(1)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(4)(1)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(2)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(2)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(2)*x(2)(4)+y(2)(2)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(2)*x(3)(4)-y(2)(2)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(2)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(2)*x(1)(1)-y(3)(1)*x(1)(2)-y(1)(2)*x(3)(1)+y(1)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(4)+y(3)(1)*y(4)(1)*x(1)(2)*x(2)(4)+y(1)(2)*y(4)(1)*x(2)(4)*x(3)(1)-y(1)(1)*y(4)(1)*x(2)(4)*x(3)(2)-y(2)(2)*y(4)(1)*x(1)(1)*x(3)(4)+y(2)(1)*y(4)(2)*x(1)(1)*x(3)(4)+y(2)(2)*y(3)(1)*x(1)(1)*x(4)(4)-y(2)(1)*y(3)(2)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{2}, \lam{2}{3}{4}{1}{2}{4}) =
(-y_{1, 2} y_{4, 1})  \del{2}{3}{1}{4} +(y_{1, 1} y_{4, 1})  \del{2}{3}{2}{4} +(y_{1, 2} y_{3, 1})  \del{2}{4}{1}{4} +(-y_{1, 1} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{1, 2} y_{2, 1})  \del{3}{4}{1}{4} +(y_{1, 1} y_{2, 1})  \del{3}{4}{2}{4} +(-y_{4, 1} x_{3, 4}+y_{3, 1} x_{4, 4})  \eps{1}{2}{1}{2} +(-y_{2, 1} x_{4, 4})  \eps{1}{3}{1}{2} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{1}{2}
----------------------------------
Epsilon:
1,3
1,2
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,3
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(3)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
y(1)(3)*y(3)(4)
Lead Term of Product:
-y(1)(3)*y(3)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(4)*y(3)(1)-y(1)(1)*y(3)(4)
Lead Term of Product:
y(1)(4)*y(3)(1)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(1)(3)*y(2)(4)
Lead Term of Product:
y(1)(3)*y(2)(4)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(4)*y(2)(1)+y(1)(1)*y(2)(4)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(3)*y(1)(4)
Lead Term of Product:
-y(1)(3)*y(1)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-2*y(1)(1)*y(1)(4)
Lead Term of Product:
2*y(1)(1)*y(1)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(3)(4)*x(1)(4)+y(1)(4)*x(3)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(3)(1)*x(1)(4)-y(1)(1)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(3)(1)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(3)(3)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(4)*y(3)(3)*x(1)(4)+y(2)(3)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(3)*x(2)(4)-y(1)(3)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(3)(4)+y(1)(3)*y(2)(4)*x(3)(4)) - (-y(2)(4)*x(1)(4))*(y(3)(3)*x(1)(1)-y(3)(1)*x(1)(3)-y(1)(3)*x(3)(1)+y(1)(1)*x(3)(3))
-------
Rewrite:
-y(2)(3)*y(3)(4)*x(1)(1)*x(1)(4)+y(2)(4)*y(3)(1)*x(1)(3)*x(1)(4)-y(1)(4)*y(3)(3)*x(1)(1)*x(2)(4)+y(1)(3)*y(3)(4)*x(1)(1)*x(2)(4)+y(1)(3)*y(2)(4)*x(1)(4)*x(3)(1)-y(1)(1)*y(2)(4)*x(1)(4)*x(3)(3)+y(1)(4)*y(2)(3)*x(1)(1)*x(3)(4)-y(1)(3)*y(2)(4)*x(1)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \lam{1}{2}{3}{3}{4}{4}) =
(y_{1, 3} y_{3, 4})  \del{1}{2}{1}{4} +(-y_{1, 4} y_{3, 1}-y_{1, 1} y_{3, 4})  \del{1}{2}{3}{4} +(-y_{1, 3} y_{2, 4})  \del{1}{3}{1}{4} +(y_{1, 4} y_{2, 1}+y_{1, 1} y_{2, 4})  \del{1}{3}{3}{4} +(y_{1, 3} y_{1, 4})  \del{2}{3}{1}{4} +(-2 y_{1, 1} y_{1, 4})  \del{2}{3}{3}{4} +(-y_{3, 4} x_{1, 4}+y_{1, 4} x_{3, 4})  \eps{1}{2}{1}{3} +(y_{3, 1} x_{1, 4}-y_{1, 1} x_{3, 4})  \eps{1}{2}{3}{4} +(-y_{1, 4} x_{2, 4})  \eps{1}{3}{1}{3} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{3}{3}{4} +(-x_{1, 4})  \lam{1}{2}{3}{1}{3}{4}
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,3
1,3
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,4
1,3
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(1)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(1)(1)*x(4)(3)
Lead Term of Product:
-y(1)(1)*y(3)(3)*x(1)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,3
Quotient:
-y(3)(1)*x(1)(3)+y(1)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(1)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(3)*x(4)(3)) - (-y(4)(1)*x(1)(3))*(y(3)(3)*x(1)(1)-y(3)(1)*x(1)(3)-y(1)(3)*x(3)(1)+y(1)(1)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(1)*x(1)(3)+y(3)(1)*y(4)(1)*x(1)(3)^2+y(1)(3)*y(4)(1)*x(1)(3)*x(3)(1)-y(1)(3)*y(4)(1)*x(1)(1)*x(3)(3)+y(1)(1)*y(4)(3)*x(1)(1)*x(3)(3)-y(1)(1)*y(4)(1)*x(1)(3)*x(3)(3)+y(1)(3)*y(3)(1)*x(1)(1)*x(4)(3)-y(1)(1)*y(3)(3)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \lam{1}{3}{4}{1}{3}{3}) =
(-y_{1, 3} y_{4, 1})  \del{1}{3}{1}{3} +(y_{1, 3} y_{3, 1})  \del{1}{4}{1}{3} +(-y_{1, 1} y_{1, 3})  \del{3}{4}{1}{3} +(-y_{1, 1} x_{4, 3})  \eps{1}{3}{1}{3} +(-y_{3, 1} x_{1, 3}+y_{1, 1} x_{3, 3})  \eps{1}{4}{1}{3}
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,3,4
1,3,4
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,3
1,4
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(1)*y(4)(1)
Lead Term of Product:
-y(1)(1)*y(4)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
-y(1)(1)*y(3)(1)
Lead Term of Product:
y(1)(1)*y(3)(1)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(1)^2
Lead Term of Product:
-y(1)(1)^2*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(3)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,3
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(1)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(3)*x(3)(4)-y(1)(3)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(3)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(3)*x(1)(1)-y(3)(1)*x(1)(3)-y(1)(3)*x(3)(1)+y(1)(1)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(1)*x(1)(4)+y(3)(1)*y(4)(1)*x(1)(3)*x(1)(4)+y(1)(3)*y(4)(1)*x(1)(4)*x(3)(1)-y(1)(1)*y(4)(1)*x(1)(4)*x(3)(3)-y(1)(3)*y(4)(1)*x(1)(1)*x(3)(4)+y(1)(1)*y(4)(3)*x(1)(1)*x(3)(4)+y(1)(3)*y(3)(1)*x(1)(1)*x(4)(4)-y(1)(1)*y(3)(3)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \lam{1}{3}{4}{1}{3}{4}) =
(-y_{1, 3} y_{4, 1})  \del{1}{3}{1}{4} +(y_{1, 1} y_{4, 1})  \del{1}{3}{3}{4} +(y_{1, 3} y_{3, 1})  \del{1}{4}{1}{4} +(-y_{1, 1} y_{3, 1})  \del{1}{4}{3}{4} +(-y_{1, 1} y_{1, 3})  \del{3}{4}{1}{4} +(y_{1, 1}^2)  \del{3}{4}{3}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{3}{1}{3} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{1}{3}
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,3
1,3
Quotient:
-y(1)(3)*y(4)(2)+y(1)(2)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(1)(3)+y(1)(3)*x(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(1)(2)*x(4)(3)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(1)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(1)(3)+y(1)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(2)*x(1)(3)+y(3)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(3)(3)-y(1)(2)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(2)*x(4)(3)+y(1)(2)*y(3)(3)*x(4)(3)) - (-y(4)(2)*x(1)(3))*(y(3)(3)*x(1)(1)-y(3)(1)*x(1)(3)-y(1)(3)*x(3)(1)+y(1)(1)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(3)+y(3)(1)*y(4)(2)*x(1)(3)^2+y(1)(3)*y(4)(2)*x(1)(3)*x(3)(1)-y(1)(3)*y(4)(2)*x(1)(1)*x(3)(3)+y(1)(2)*y(4)(3)*x(1)(1)*x(3)(3)-y(1)(1)*y(4)(2)*x(1)(3)*x(3)(3)+y(1)(3)*y(3)(2)*x(1)(1)*x(4)(3)-y(1)(2)*y(3)(3)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \lam{1}{3}{4}{2}{3}{3}) =
(-y_{1, 3} y_{4, 2}+y_{1, 2} y_{4, 3})  \del{1}{3}{1}{3} +(-y_{1, 1} y_{4, 3})  \del{1}{3}{2}{3} +(y_{1, 3} y_{3, 1})  \del{1}{4}{2}{3} +(-y_{1, 1} y_{1, 3})  \del{3}{4}{2}{3} +(-y_{4, 3} x_{1, 3}+y_{1, 3} x_{4, 3})  \eps{1}{3}{1}{2} +(-y_{1, 2} x_{4, 3})  \eps{1}{3}{1}{3} +(-y_{3, 1} x_{1, 3}+y_{1, 1} x_{3, 3})  \eps{1}{4}{2}{3}
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,3
1,4
Quotient:
-y(1)(3)*y(4)(2)+y(1)(2)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(1)*y(4)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
-y(1)(2)*y(3)(1)
Lead Term of Product:
y(1)(2)*y(3)(1)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(1)*y(1)(2)
Lead Term of Product:
-y(1)(1)*y(1)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(1)(4)+y(1)(3)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(3)*x(3)(4)-y(1)(3)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(3)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(3)(3)*x(1)(1)-y(3)(1)*x(1)(3)-y(1)(3)*x(3)(1)+y(1)(1)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(4)+y(3)(1)*y(4)(2)*x(1)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(1)(4)*x(3)(1)-y(1)(1)*y(4)(2)*x(1)(4)*x(3)(3)-y(1)(3)*y(4)(2)*x(1)(1)*x(3)(4)+y(1)(2)*y(4)(3)*x(1)(1)*x(3)(4)+y(1)(3)*y(3)(2)*x(1)(1)*x(4)(4)-y(1)(2)*y(3)(3)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \lam{1}{3}{4}{2}{3}{4}) =
(-y_{1, 3} y_{4, 2}+y_{1, 2} y_{4, 3})  \del{1}{3}{1}{4} +(-y_{1, 1} y_{4, 3})  \del{1}{3}{2}{4} +(y_{1, 1} y_{4, 2})  \del{1}{3}{3}{4} +(y_{1, 3} y_{3, 1})  \del{1}{4}{2}{4} +(-y_{1, 2} y_{3, 1})  \del{1}{4}{3}{4} +(-y_{1, 1} y_{1, 3})  \del{3}{4}{2}{4} +(y_{1, 1} y_{1, 2})  \del{3}{4}{3}{4} +(-y_{4, 3} x_{1, 4}+y_{1, 3} x_{4, 4})  \eps{1}{3}{1}{2} +(-y_{1, 2} x_{4, 4})  \eps{1}{3}{1}{3} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{2}{3}
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
2,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(1)*x(2)(3)
Divisor:
Delta
2,3
1,3
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
-y(1)(3)*y(2)(1)
Lead Term of Product:
y(1)(3)*y(2)(1)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(4)(1)*x(3)(3)+y(3)(1)*x(4)(3)
Lead Term of Product:
-y(2)(3)*y(4)(1)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(2)(1)*x(4)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,3
Quotient:
-y(3)(1)*x(2)(3)+y(2)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(1)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(1)*x(2)(3)+y(3)(1)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(1)*x(3)(3)-y(2)(1)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(1)*x(4)(3)+y(2)(1)*y(3)(3)*x(4)(3)) - (-y(4)(1)*x(2)(3))*(y(3)(3)*x(1)(1)-y(3)(1)*x(1)(3)-y(1)(3)*x(3)(1)+y(1)(1)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(1)*x(2)(3)+y(3)(1)*y(4)(1)*x(1)(3)*x(2)(3)+y(1)(3)*y(4)(1)*x(2)(3)*x(3)(1)-y(2)(3)*y(4)(1)*x(1)(1)*x(3)(3)+y(2)(1)*y(4)(3)*x(1)(1)*x(3)(3)-y(1)(1)*y(4)(1)*x(2)(3)*x(3)(3)+y(2)(3)*y(3)(1)*x(1)(1)*x(4)(3)-y(2)(1)*y(3)(3)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \lam{2}{3}{4}{1}{3}{3}) =
(-y_{1, 3} y_{4, 1})  \del{2}{3}{1}{3} +(y_{1, 3} y_{3, 1})  \del{2}{4}{1}{3} +(-y_{1, 3} y_{2, 1})  \del{3}{4}{1}{3} +(-y_{4, 1} x_{3, 3}+y_{3, 1} x_{4, 3})  \eps{1}{2}{1}{3} +(-y_{2, 1} x_{4, 3})  \eps{1}{3}{1}{3} +(-y_{3, 1} x_{2, 3}+y_{2, 1} x_{3, 3})  \eps{1}{4}{1}{3}
----------------------------------
Epsilon:
1,3
1,3
Lam:
2,3,4
1,3,4
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(1)(1)*y(4)(1)
Lead Term of Product:
-y(1)(1)*y(4)(1)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(1)*y(3)(1)
Lead Term of Product:
y(1)(1)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(1)(3)*y(2)(1)
Lead Term of Product:
y(1)(3)*y(2)(1)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(1)*y(2)(1)
Lead Term of Product:
-y(1)(1)*y(2)(1)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(4)(1)*x(3)(4)+y(3)(1)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(1)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,3
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(1)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(3)*x(2)(4)+y(2)(3)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(3)*x(3)(4)-y(2)(3)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(3)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(3)*x(1)(1)-y(3)(1)*x(1)(3)-y(1)(3)*x(3)(1)+y(1)(1)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(1)*x(2)(4)+y(3)(1)*y(4)(1)*x(1)(3)*x(2)(4)+y(1)(3)*y(4)(1)*x(2)(4)*x(3)(1)-y(1)(1)*y(4)(1)*x(2)(4)*x(3)(3)-y(2)(3)*y(4)(1)*x(1)(1)*x(3)(4)+y(2)(1)*y(4)(3)*x(1)(1)*x(3)(4)+y(2)(3)*y(3)(1)*x(1)(1)*x(4)(4)-y(2)(1)*y(3)(3)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \lam{2}{3}{4}{1}{3}{4}) =
(-y_{1, 3} y_{4, 1})  \del{2}{3}{1}{4} +(y_{1, 1} y_{4, 1})  \del{2}{3}{3}{4} +(y_{1, 3} y_{3, 1})  \del{2}{4}{1}{4} +(-y_{1, 1} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{1, 3} y_{2, 1})  \del{3}{4}{1}{4} +(y_{1, 1} y_{2, 1})  \del{3}{4}{3}{4} +(-y_{4, 1} x_{3, 4}+y_{3, 1} x_{4, 4})  \eps{1}{2}{1}{3} +(-y_{2, 1} x_{4, 4})  \eps{1}{3}{1}{3} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{1}{3}
----------------------------------
Epsilon:
1,3
1,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
2,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(3)
Divisor:
Delta
2,3
1,3
Quotient:
-y(1)(3)*y(4)(2)+y(1)(2)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(3)*y(2)(1)
Lead Term of Product:
y(1)(3)*y(2)(1)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(4)(3)*x(3)(3)-y(3)(3)*x(4)(3)
Lead Term of Product:
y(2)(2)*y(4)(3)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(4)(2)*x(3)(3)+y(3)(2)*x(4)(3)
Lead Term of Product:
-y(2)(3)*y(4)(2)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(2)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(4)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(3)+y(2)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(3)*x(4)(3)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(1)(2)*x(4)(3)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(1)(1)*x(4)(3)
Lead Term of Product:
y(1)(1)*y(3)(3)*x(2)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,2,3
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(3)*y(2)(2)*x(3)(1)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(2)*x(2)(3)+y(3)(2)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(2)*x(3)(3)-y(2)(2)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(2)*x(4)(3)+y(2)(2)*y(3)(3)*x(4)(3)) - (-y(4)(2)*x(2)(3))*(y(3)(3)*x(1)(1)-y(3)(1)*x(1)(3)-y(1)(3)*x(3)(1)+y(1)(1)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(3)+y(3)(1)*y(4)(2)*x(1)(3)*x(2)(3)+y(1)(3)*y(4)(2)*x(2)(3)*x(3)(1)-y(2)(3)*y(4)(2)*x(1)(1)*x(3)(3)+y(2)(2)*y(4)(3)*x(1)(1)*x(3)(3)-y(1)(1)*y(4)(2)*x(2)(3)*x(3)(3)+y(2)(3)*y(3)(2)*x(1)(1)*x(4)(3)-y(2)(2)*y(3)(3)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \lam{2}{3}{4}{2}{3}{3}) =
(-y_{1, 3} y_{4, 2}+y_{1, 2} y_{4, 3})  \del{2}{3}{1}{3} +(-y_{1, 1} y_{4, 3})  \del{2}{3}{2}{3} +(y_{1, 3} y_{3, 1})  \del{2}{4}{2}{3} +(-y_{1, 3} y_{2, 1})  \del{3}{4}{2}{3} +(y_{4, 3} x_{3, 3}-y_{3, 3} x_{4, 3})  \eps{1}{2}{1}{2} +(-y_{4, 2} x_{3, 3}+y_{3, 2} x_{4, 3})  \eps{1}{2}{1}{3} +(-y_{4, 3} x_{2, 3})  \eps{1}{3}{1}{2} +(-y_{2, 1} x_{4, 3})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{2, 3}+y_{2, 1} x_{3, 3})  \eps{1}{4}{2}{3} +(y_{1, 3} x_{4, 3})  \eps{2}{3}{1}{2} +(-y_{1, 2} x_{4, 3})  \eps{2}{3}{1}{3} +(y_{1, 1} x_{4, 3})  \eps{2}{3}{2}{3} +(-x_{4, 3})  \pho{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,3
1,3
Lam:
2,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(1)(3)*y(4)(2)+y(1)(2)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(1)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(2)*y(3)(1)
Lead Term of Product:
y(1)(2)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(3)*y(2)(1)
Lead Term of Product:
y(1)(3)*y(2)(1)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(2)*y(2)(1)
Lead Term of Product:
-y(1)(2)*y(2)(1)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(4)(3)*x(3)(4)-y(3)(3)*x(4)(4)
Lead Term of Product:
y(2)(2)*y(4)(3)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(4)(2)*x(3)(4)+y(3)(2)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(2)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(3)*x(4)(4)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(1)(1)*x(4)(4)
Lead Term of Product:
y(1)(1)*y(3)(3)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,2,3
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(3)*y(2)(2)*x(3)(1)*x(4)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(3)*x(2)(4)+y(2)(3)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(3)*x(3)(4)-y(2)(3)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(3)*x(4)(4)) - (-y(4)(2)*x(2)(4))*(y(3)(3)*x(1)(1)-y(3)(1)*x(1)(3)-y(1)(3)*x(3)(1)+y(1)(1)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(4)+y(3)(1)*y(4)(2)*x(1)(3)*x(2)(4)+y(1)(3)*y(4)(2)*x(2)(4)*x(3)(1)-y(1)(1)*y(4)(2)*x(2)(4)*x(3)(3)-y(2)(3)*y(4)(2)*x(1)(1)*x(3)(4)+y(2)(2)*y(4)(3)*x(1)(1)*x(3)(4)+y(2)(3)*y(3)(2)*x(1)(1)*x(4)(4)-y(2)(2)*y(3)(3)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \lam{2}{3}{4}{2}{3}{4}) =
(-y_{1, 3} y_{4, 2}+y_{1, 2} y_{4, 3})  \del{2}{3}{1}{4} +(-y_{1, 1} y_{4, 3})  \del{2}{3}{2}{4} +(y_{1, 1} y_{4, 2})  \del{2}{3}{3}{4} +(y_{1, 3} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{1, 2} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{1, 3} y_{2, 1})  \del{3}{4}{2}{4} +(y_{1, 2} y_{2, 1})  \del{3}{4}{3}{4} +(y_{4, 3} x_{3, 4}-y_{3, 3} x_{4, 4})  \eps{1}{2}{1}{2} +(-y_{4, 2} x_{3, 4}+y_{3, 2} x_{4, 4})  \eps{1}{2}{1}{3} +(-y_{4, 3} x_{2, 4})  \eps{1}{3}{1}{2} +(-y_{2, 1} x_{4, 4})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{2}{3} +(y_{1, 3} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{1, 2} x_{4, 4})  \eps{2}{3}{1}{3} +(y_{1, 1} x_{4, 4})  \eps{2}{3}{2}{3} +(-x_{4, 4})  \pho{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,3
1,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,3
1,4
Quotient:
-y(1)(4)*y(4)(1)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,4
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(4)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,4
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(4)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(4)*x(1)(1)-y(3)(1)*x(1)(4)-y(1)(4)*x(3)(1)+y(1)(1)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(1)(1)*x(1)(4)+y(3)(1)*y(4)(1)*x(1)(4)^2+y(1)(4)*y(4)(1)*x(1)(4)*x(3)(1)-y(1)(4)*y(4)(1)*x(1)(1)*x(3)(4)+y(1)(1)*y(4)(4)*x(1)(1)*x(3)(4)-y(1)(1)*y(4)(1)*x(1)(4)*x(3)(4)+y(1)(4)*y(3)(1)*x(1)(1)*x(4)(4)-y(1)(1)*y(3)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{4}, \lam{1}{3}{4}{1}{4}{4}) =
(-y_{1, 4} y_{4, 1})  \del{1}{3}{1}{4} +(y_{1, 4} y_{3, 1})  \del{1}{4}{1}{4} +(-y_{1, 1} y_{1, 4})  \del{3}{4}{1}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{3}{1}{4} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{1}{4}
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,3
1,4
Quotient:
-y(1)(4)*y(4)(2)+y(1)(2)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,4
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(4)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(4)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(3)(4)*x(1)(1)-y(3)(1)*x(1)(4)-y(1)(4)*x(3)(1)+y(1)(1)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(1)*x(1)(4)+y(3)(1)*y(4)(2)*x(1)(4)^2+y(1)(4)*y(4)(2)*x(1)(4)*x(3)(1)-y(1)(4)*y(4)(2)*x(1)(1)*x(3)(4)+y(1)(2)*y(4)(4)*x(1)(1)*x(3)(4)-y(1)(1)*y(4)(2)*x(1)(4)*x(3)(4)+y(1)(4)*y(3)(2)*x(1)(1)*x(4)(4)-y(1)(2)*y(3)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{4}, \lam{1}{3}{4}{2}{4}{4}) =
(-y_{1, 4} y_{4, 2}+y_{1, 2} y_{4, 4})  \del{1}{3}{1}{4} +(-y_{1, 1} y_{4, 4})  \del{1}{3}{2}{4} +(y_{1, 4} y_{3, 1})  \del{1}{4}{2}{4} +(-y_{1, 1} y_{1, 4})  \del{3}{4}{2}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{3}{1}{2} +(-y_{1, 2} x_{4, 4})  \eps{1}{3}{1}{4} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{2}{4}
----------------------------------
Epsilon:
1,3
1,4
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,3
1,4
Quotient:
-y(1)(4)*y(4)(3)+y(1)(3)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(3)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,4
Quotient:
-y(1)(3)*x(4)(4)
Lead Term of Product:
-y(1)(3)*y(3)(4)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(1)(4))*(y(3)(4)*x(1)(1)-y(3)(1)*x(1)(4)-y(1)(4)*x(3)(1)+y(1)(1)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(1)*x(1)(4)+y(3)(1)*y(4)(3)*x(1)(4)^2+y(1)(4)*y(4)(3)*x(1)(4)*x(3)(1)-y(1)(4)*y(4)(3)*x(1)(1)*x(3)(4)+y(1)(3)*y(4)(4)*x(1)(1)*x(3)(4)-y(1)(1)*y(4)(3)*x(1)(4)*x(3)(4)+y(1)(4)*y(3)(3)*x(1)(1)*x(4)(4)-y(1)(3)*y(3)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{4}, \lam{1}{3}{4}{3}{4}{4}) =
(-y_{1, 4} y_{4, 3}+y_{1, 3} y_{4, 4})  \del{1}{3}{1}{4} +(-y_{1, 1} y_{4, 4})  \del{1}{3}{3}{4} +(y_{1, 4} y_{3, 1})  \del{1}{4}{3}{4} +(-y_{1, 1} y_{1, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{3}{1}{3} +(-y_{1, 3} x_{4, 4})  \eps{1}{3}{1}{4} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{3}{4}
----------------------------------
Epsilon:
1,3
1,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
2,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(1)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(1)(4)*y(4)(1)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(1)(4)*y(2)(1)
Lead Term of Product:
y(1)(4)*y(2)(1)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
-y(4)(1)*x(3)(4)+y(3)(1)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(1)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,4
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(4)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(4)*x(1)(1)-y(3)(1)*x(1)(4)-y(1)(4)*x(3)(1)+y(1)(1)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(1)(1)*x(2)(4)+y(3)(1)*y(4)(1)*x(1)(4)*x(2)(4)+y(1)(4)*y(4)(1)*x(2)(4)*x(3)(1)-y(2)(4)*y(4)(1)*x(1)(1)*x(3)(4)+y(2)(1)*y(4)(4)*x(1)(1)*x(3)(4)-y(1)(1)*y(4)(1)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(1)*x(1)(1)*x(4)(4)-y(2)(1)*y(3)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{4}, \lam{2}{3}{4}{1}{4}{4}) =
(-y_{1, 4} y_{4, 1})  \del{2}{3}{1}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{1}{4} +(-y_{1, 4} y_{2, 1})  \del{3}{4}{1}{4} +(-y_{4, 1} x_{3, 4}+y_{3, 1} x_{4, 4})  \eps{1}{2}{1}{4} +(-y_{2, 1} x_{4, 4})  \eps{1}{3}{1}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{1}{4}
----------------------------------
Epsilon:
1,3
1,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
1,4
Lam:
2,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(1)(4)*y(4)(2)+y(1)(2)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(4)*y(2)(1)
Lead Term of Product:
y(1)(4)*y(2)(1)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(4)(4)*x(3)(4)-y(3)(4)*x(4)(4)
Lead Term of Product:
y(2)(2)*y(4)(4)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
-y(4)(2)*x(3)(4)+y(3)(2)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(2)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,4
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(4)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
y(1)(1)*x(4)(4)
Lead Term of Product:
y(1)(1)*y(3)(4)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,2,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(4)*y(2)(2)*x(3)(1)*x(4)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(4)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(2)(4))*(y(3)(4)*x(1)(1)-y(3)(1)*x(1)(4)-y(1)(4)*x(3)(1)+y(1)(1)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(1)*x(2)(4)+y(3)(1)*y(4)(2)*x(1)(4)*x(2)(4)+y(1)(4)*y(4)(2)*x(2)(4)*x(3)(1)-y(2)(4)*y(4)(2)*x(1)(1)*x(3)(4)+y(2)(2)*y(4)(4)*x(1)(1)*x(3)(4)-y(1)(1)*y(4)(2)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(2)*x(1)(1)*x(4)(4)-y(2)(2)*y(3)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{4}, \lam{2}{3}{4}{2}{4}{4}) =
(-y_{1, 4} y_{4, 2}+y_{1, 2} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{1, 1} y_{4, 4})  \del{2}{3}{2}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{1, 4} y_{2, 1})  \del{3}{4}{2}{4} +(y_{4, 4} x_{3, 4}-y_{3, 4} x_{4, 4})  \eps{1}{2}{1}{2} +(-y_{4, 2} x_{3, 4}+y_{3, 2} x_{4, 4})  \eps{1}{2}{1}{4} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{1}{2} +(-y_{2, 1} x_{4, 4})  \eps{1}{3}{2}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{2}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{1, 2} x_{4, 4})  \eps{2}{3}{1}{4} +(y_{1, 1} x_{4, 4})  \eps{2}{3}{2}{4} +(-x_{4, 4})  \pho{1}{2}{3}{1}{2}{4}
----------------------------------
Epsilon:
1,3
1,4
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(1)(4)*y(4)(3)+y(1)(3)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(3)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(4)*y(2)(1)
Lead Term of Product:
y(1)(4)*y(2)(1)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
y(4)(4)*x(3)(4)-y(3)(4)*x(4)(4)
Lead Term of Product:
y(2)(3)*y(4)(4)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
-y(4)(3)*x(3)(4)+y(3)(3)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(3)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,4
Quotient:
-y(1)(3)*x(4)(4)
Lead Term of Product:
-y(1)(3)*y(3)(4)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
y(1)(1)*x(4)(4)
Lead Term of Product:
y(1)(1)*y(3)(4)*x(2)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,3,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(4)*y(2)(3)*x(3)(1)*x(4)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(2)(4))*(y(3)(4)*x(1)(1)-y(3)(1)*x(1)(4)-y(1)(4)*x(3)(1)+y(1)(1)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(1)*x(2)(4)+y(3)(1)*y(4)(3)*x(1)(4)*x(2)(4)+y(1)(4)*y(4)(3)*x(2)(4)*x(3)(1)-y(2)(4)*y(4)(3)*x(1)(1)*x(3)(4)+y(2)(3)*y(4)(4)*x(1)(1)*x(3)(4)-y(1)(1)*y(4)(3)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(3)*x(1)(1)*x(4)(4)-y(2)(3)*y(3)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{1}{4}, \lam{2}{3}{4}{3}{4}{4}) =
(-y_{1, 4} y_{4, 3}+y_{1, 3} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{1, 1} y_{4, 4})  \del{2}{3}{3}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{1, 4} y_{2, 1})  \del{3}{4}{3}{4} +(y_{4, 4} x_{3, 4}-y_{3, 4} x_{4, 4})  \eps{1}{2}{1}{3} +(-y_{4, 3} x_{3, 4}+y_{3, 3} x_{4, 4})  \eps{1}{2}{1}{4} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{1}{3} +(-y_{2, 1} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{3}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{1}{3} +(-y_{1, 3} x_{4, 4})  \eps{2}{3}{1}{4} +(y_{1, 1} x_{4, 4})  \eps{2}{3}{3}{4} +(-x_{4, 4})  \pho{1}{2}{3}{1}{3}{4}
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,3
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(3)(2)*y(3)(3)*x(1)(2)
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(1)*y(3)(2)*y(3)(3)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(1)(2)*y(3)(1)+y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(2)*y(3)(1)*y(3)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-y(3)(2)
Lead Term of Product:
y(2)(2)*y(3)(1)*y(3)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,3
Quotient:
-x(3)(2)
Lead Term of Product:
y(1)(3)*y(2)(2)*y(3)(1)*x(3)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(3))*(-y(2)(2)*y(3)(1)*x(1)(2)+y(2)(1)*y(3)(2)*x(1)(2)+y(1)(2)*y(3)(1)*x(2)(2)-y(1)(1)*y(3)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(3)(2)+y(1)(1)*y(2)(2)*x(3)(2)) - (-y(2)(2)*y(3)(1))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(2)(1)*y(3)(2)*y(3)(3)*x(1)(2)+y(2)(2)*y(3)(1)*y(3)(2)*x(1)(3)-y(1)(2)*y(3)(1)*y(3)(3)*x(2)(2)+y(1)(1)*y(3)(2)*y(3)(3)*x(2)(2)+y(1)(3)*y(2)(2)*y(3)(1)*x(3)(2)+y(1)(2)*y(2)(1)*y(3)(3)*x(3)(2)-y(1)(1)*y(2)(2)*y(3)(3)*x(3)(2)-y(1)(2)*y(2)(2)*y(3)(1)*x(3)(3)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{1}{2}{3}{1}{2}{2}) =
(-y_{2, 1} y_{3, 2})  \eps{1}{3}{2}{3} +(-y_{1, 2} y_{3, 1}+y_{1, 1} y_{3, 2})  \eps{2}{3}{2}{3} +(-y_{3, 2})  \lam{1}{2}{3}{1}{2}{3} +(-x_{3, 2})  \psi{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,3
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(3)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
y(1)(3)*y(3)(4)
Lead Term of Product:
-y(1)(3)*y(3)(4)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(4)*y(3)(2)-y(1)(2)*y(3)(4)
Lead Term of Product:
y(1)(4)*y(3)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(1)(3)*y(2)(4)
Lead Term of Product:
y(1)(3)*y(2)(4)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(4)*y(2)(2)+y(1)(2)*y(2)(4)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
y(1)(3)*y(1)(4)
Lead Term of Product:
-y(1)(3)*y(1)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-2*y(1)(2)*y(1)(4)
Lead Term of Product:
2*y(1)(2)*y(1)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(3)(4)*x(1)(4)+y(1)(4)*x(3)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(3)(2)*x(1)(4)-y(1)(2)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(3)(2)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(3)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(2)*x(1)(4)+y(1)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
2,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(3)*y(3)(2)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(4)*y(3)(3)*x(1)(4)+y(2)(3)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(3)*x(2)(4)-y(1)(3)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(3)(4)+y(1)(3)*y(2)(4)*x(3)(4)) - (-y(2)(4)*x(1)(4))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(2)(3)*y(3)(4)*x(1)(2)*x(1)(4)+y(2)(4)*y(3)(2)*x(1)(3)*x(1)(4)-y(1)(4)*y(3)(3)*x(1)(2)*x(2)(4)+y(1)(3)*y(3)(4)*x(1)(2)*x(2)(4)+y(1)(3)*y(2)(4)*x(1)(4)*x(3)(2)-y(1)(2)*y(2)(4)*x(1)(4)*x(3)(3)+y(1)(4)*y(2)(3)*x(1)(2)*x(3)(4)-y(1)(3)*y(2)(4)*x(1)(2)*x(3)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{1}{2}{3}{3}{4}{4}) =
(y_{1, 3} y_{3, 4})  \del{1}{2}{2}{4} +(-y_{1, 4} y_{3, 2}-y_{1, 2} y_{3, 4})  \del{1}{2}{3}{4} +(-y_{1, 3} y_{2, 4})  \del{1}{3}{2}{4} +(y_{1, 4} y_{2, 2}+y_{1, 2} y_{2, 4})  \del{1}{3}{3}{4} +(y_{1, 3} y_{1, 4})  \del{2}{3}{2}{4} +(-2 y_{1, 2} y_{1, 4})  \del{2}{3}{3}{4} +(-y_{3, 4} x_{1, 4}+y_{1, 4} x_{3, 4})  \eps{1}{2}{2}{3} +(y_{3, 2} x_{1, 4}-y_{1, 2} x_{3, 4})  \eps{1}{2}{3}{4} +(-y_{1, 4} x_{2, 4})  \eps{1}{3}{2}{3} +(-y_{2, 2} x_{1, 4}+y_{1, 2} x_{2, 4})  \eps{1}{3}{3}{4} +(-x_{1, 4})  \lam{1}{2}{3}{2}{3}{4}
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,4
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(3)(3)*y(4)(2)*x(1)(2)
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(3)(3)*y(4)(2)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(1)(2)*y(4)(1)+y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(3)(3)*y(4)(1)*x(2)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(4)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-y(3)(2)
Lead Term of Product:
y(2)(2)*y(3)(2)*y(4)(1)*x(1)(3)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,3
Quotient:
-x(3)(2)
Lead Term of Product:
y(1)(3)*y(2)(2)*y(4)(1)*x(3)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(3))*(-y(2)(2)*y(4)(1)*x(1)(2)+y(2)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(2)(2)-y(1)(1)*y(4)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(4)(2)+y(1)(1)*y(2)(2)*x(4)(2)) - (-y(2)(2)*y(4)(1))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(2)(1)*y(3)(3)*y(4)(2)*x(1)(2)+y(2)(2)*y(3)(2)*y(4)(1)*x(1)(3)-y(1)(2)*y(3)(3)*y(4)(1)*x(2)(2)+y(1)(1)*y(3)(3)*y(4)(2)*x(2)(2)+y(1)(3)*y(2)(2)*y(4)(1)*x(3)(2)-y(1)(2)*y(2)(2)*y(4)(1)*x(3)(3)+y(1)(2)*y(2)(1)*y(3)(3)*x(4)(2)-y(1)(1)*y(2)(2)*y(3)(3)*x(4)(2)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{1}{2}{4}{1}{2}{2}) =
(-y_{2, 1} y_{4, 2})  \eps{1}{3}{2}{3} +(-y_{1, 2} y_{4, 1}+y_{1, 1} y_{4, 2})  \eps{2}{3}{2}{3} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2, 2})  \eps{3}{4}{2}{3} +(-y_{3, 2})  \lam{1}{2}{4}{1}{2}{3} +(-x_{3, 2})  \psi{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(3)(3)*y(4)(2)*x(1)(2)
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(3)(3)*y(4)(2)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
-y(1)(2)*y(3)(1)+y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(2)*y(3)(1)*y(4)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-y(3)(2)
Lead Term of Product:
y(3)(2)^2*y(4)(1)*x(1)(3)
Lead term is well behaved
Divisor:
Psi
1,3,4
1,2,3
Quotient:
-x(3)(2)
Lead Term of Product:
y(1)(3)*y(3)(2)*y(4)(1)*x(3)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(3))*(-y(3)(2)*y(4)(1)*x(1)(2)+y(3)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(3)(2)-y(1)(1)*y(4)(2)*x(3)(2)-y(1)(2)*y(3)(1)*x(4)(2)+y(1)(1)*y(3)(2)*x(4)(2)) - (-y(3)(2)*y(4)(1))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(3)(3)*y(4)(2)*x(1)(2)+y(3)(2)^2*y(4)(1)*x(1)(3)+y(1)(3)*y(3)(2)*y(4)(1)*x(3)(2)-y(1)(2)*y(3)(3)*y(4)(1)*x(3)(2)+y(1)(1)*y(3)(3)*y(4)(2)*x(3)(2)-y(1)(2)*y(3)(2)*y(4)(1)*x(3)(3)+y(1)(2)*y(3)(1)*y(3)(3)*x(4)(2)-y(1)(1)*y(3)(2)*y(3)(3)*x(4)(2)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{1}{3}{4}{1}{2}{2}) =
(-y_{3, 1} y_{4, 2})  \eps{1}{3}{2}{3} +(-y_{1, 2} y_{3, 1}+y_{1, 1} y_{3, 2})  \eps{3}{4}{2}{3} +(-y_{3, 2})  \lam{1}{3}{4}{1}{2}{3} +(-x_{3, 2})  \psi{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(2)*x(1)(3)
Divisor:
Delta
1,3
2,3
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(1)(1)*x(4)(3)
Lead Term of Product:
-y(1)(1)*y(3)(3)*x(1)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(1)(3)+y(1)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(1)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(3)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(3)*x(4)(3)) - (-y(4)(1)*x(1)(3))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(2)*x(1)(3)+y(3)(2)*y(4)(1)*x(1)(3)^2+y(1)(3)*y(4)(1)*x(1)(3)*x(3)(2)-y(1)(3)*y(4)(1)*x(1)(2)*x(3)(3)+y(1)(1)*y(4)(3)*x(1)(2)*x(3)(3)-y(1)(2)*y(4)(1)*x(1)(3)*x(3)(3)+y(1)(3)*y(3)(1)*x(1)(2)*x(4)(3)-y(1)(1)*y(3)(3)*x(1)(2)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{1}{3}{4}{1}{3}{3}) =
(-y_{1, 3} y_{4, 1})  \del{1}{3}{2}{3} +(y_{1, 3} y_{3, 1})  \del{1}{4}{2}{3} +(-y_{1, 1} y_{1, 3})  \del{3}{4}{2}{3} +(-y_{1, 1} x_{4, 3})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{1, 3}+y_{1, 1} x_{3, 3})  \eps{1}{4}{2}{3} +(-x_{1, 3})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,3,4
1,3,4
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,3
2,4
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(1)*y(4)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
-y(1)(1)*y(3)(2)
Lead Term of Product:
y(1)(1)*y(3)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(1)(3)
Lead Term of Product:
y(1)(1)*y(1)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(1)*y(1)(2)
Lead Term of Product:
-y(1)(1)*y(1)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(3)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(1)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(3)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(3)*x(3)(4)-y(1)(3)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(3)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(2)*x(1)(4)+y(3)(2)*y(4)(1)*x(1)(3)*x(1)(4)+y(1)(3)*y(4)(1)*x(1)(4)*x(3)(2)-y(1)(2)*y(4)(1)*x(1)(4)*x(3)(3)-y(1)(3)*y(4)(1)*x(1)(2)*x(3)(4)+y(1)(1)*y(4)(3)*x(1)(2)*x(3)(4)+y(1)(3)*y(3)(1)*x(1)(2)*x(4)(4)-y(1)(1)*y(3)(3)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{1}{3}{4}{1}{3}{4}) =
(-y_{1, 3} y_{4, 1})  \del{1}{3}{2}{4} +(y_{1, 1} y_{4, 2})  \del{1}{3}{3}{4} +(y_{1, 3} y_{3, 1})  \del{1}{4}{2}{4} +(-y_{1, 1} y_{3, 2})  \del{1}{4}{3}{4} +(-y_{1, 1} y_{1, 3})  \del{3}{4}{2}{4} +(y_{1, 1} y_{1, 2})  \del{3}{4}{3}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{2}{3} +(-x_{1, 4})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(2)*x(1)(3)
Divisor:
Delta
1,3
2,3
Quotient:
-y(1)(3)*y(4)(2)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(1)(3)*y(3)(2)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(2)*y(1)(3)
Lead Term of Product:
y(1)(2)*y(1)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(1)(2)*x(4)(3)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(1)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(2)*x(1)(3)+y(1)(2)*x(3)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(3)*y(4)(2)*x(1)(3)+y(3)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(3)(3)-y(1)(2)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(2)*x(4)(3)+y(1)(2)*y(3)(3)*x(4)(3)) - (-y(4)(2)*x(1)(3))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(2)*x(1)(3)+y(3)(2)*y(4)(2)*x(1)(3)^2+y(1)(3)*y(4)(2)*x(1)(3)*x(3)(2)-y(1)(3)*y(4)(2)*x(1)(2)*x(3)(3)+y(1)(2)*y(4)(3)*x(1)(2)*x(3)(3)-y(1)(2)*y(4)(2)*x(1)(3)*x(3)(3)+y(1)(3)*y(3)(2)*x(1)(2)*x(4)(3)-y(1)(2)*y(3)(3)*x(1)(2)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{1}{3}{4}{2}{3}{3}) =
(-y_{1, 3} y_{4, 2})  \del{1}{3}{2}{3} +(y_{1, 3} y_{3, 2})  \del{1}{4}{2}{3} +(-y_{1, 2} y_{1, 3})  \del{3}{4}{2}{3} +(-y_{1, 2} x_{4, 3})  \eps{1}{3}{2}{3} +(-y_{3, 2} x_{1, 3}+y_{1, 2} x_{3, 3})  \eps{1}{4}{2}{3}
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,3
2,4
Quotient:
-y(1)(3)*y(4)(2)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(2)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(4)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(3)*y(3)(2)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
-y(1)(2)*y(3)(2)
Lead Term of Product:
y(1)(2)*y(3)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(2)*y(1)(3)
Lead Term of Product:
y(1)(2)*y(1)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(2)^2
Lead Term of Product:
-y(1)(2)^2*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(2)*x(1)(4)+y(1)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(3)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(3)*x(3)(4)-y(1)(3)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(3)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(2)*x(1)(4)+y(3)(2)*y(4)(2)*x(1)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(1)(4)*x(3)(2)-y(1)(2)*y(4)(2)*x(1)(4)*x(3)(3)-y(1)(3)*y(4)(2)*x(1)(2)*x(3)(4)+y(1)(2)*y(4)(3)*x(1)(2)*x(3)(4)+y(1)(3)*y(3)(2)*x(1)(2)*x(4)(4)-y(1)(2)*y(3)(3)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{1}{3}{4}{2}{3}{4}) =
(-y_{1, 3} y_{4, 2})  \del{1}{3}{2}{4} +(y_{1, 2} y_{4, 2})  \del{1}{3}{3}{4} +(y_{1, 3} y_{3, 2})  \del{1}{4}{2}{4} +(-y_{1, 2} y_{3, 2})  \del{1}{4}{3}{4} +(-y_{1, 2} y_{1, 3})  \del{3}{4}{2}{4} +(y_{1, 2}^2)  \del{3}{4}{3}{4} +(-y_{1, 2} x_{4, 4})  \eps{1}{3}{2}{3} +(-y_{3, 2} x_{1, 4}+y_{1, 2} x_{3, 4})  \eps{1}{4}{2}{3}
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
2,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(3)
Divisor:
Delta
2,3
2,3
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(3)*y(2)(1)
Lead Term of Product:
y(1)(3)*y(2)(1)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(4)(1)*x(3)(3)+y(3)(1)*x(4)(3)
Lead Term of Product:
-y(2)(3)*y(4)(1)*x(1)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(4)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(3)+y(2)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-x(4)(3)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(3)*x(4)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
x(3)(3)
Lead Term of Product:
-y(2)(2)*y(4)(1)*x(1)(3)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(2)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(3)*y(4)(1)*x(2)(3)+y(3)(1)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(1)*x(3)(3)-y(2)(1)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(1)*x(4)(3)+y(2)(1)*y(3)(3)*x(4)(3)) - (-y(4)(1)*x(2)(3))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(3)+y(3)(2)*y(4)(1)*x(1)(3)*x(2)(3)+y(1)(3)*y(4)(1)*x(2)(3)*x(3)(2)-y(2)(3)*y(4)(1)*x(1)(2)*x(3)(3)+y(2)(1)*y(4)(3)*x(1)(2)*x(3)(3)-y(1)(2)*y(4)(1)*x(2)(3)*x(3)(3)+y(2)(3)*y(3)(1)*x(1)(2)*x(4)(3)-y(2)(1)*y(3)(3)*x(1)(2)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{2}{3}{4}{1}{3}{3}) =
(-y_{1, 3} y_{4, 1})  \del{2}{3}{2}{3} +(y_{1, 3} y_{3, 1})  \del{2}{4}{2}{3} +(-y_{1, 3} y_{2, 1})  \del{3}{4}{2}{3} +(-y_{4, 1} x_{3, 3}+y_{3, 1} x_{4, 3})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{4, 3})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{2, 3}+y_{2, 1} x_{3, 3})  \eps{1}{4}{2}{3} +(-x_{4, 3})  \lam{1}{2}{3}{1}{2}{3} +(x_{3, 3})  \lam{1}{2}{4}{1}{2}{3} +(-x_{2, 3})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,3
2,3
Lam:
2,3,4
1,3,4
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(3)*y(4)(1)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(1)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(1)*y(3)(2)
Lead Term of Product:
y(1)(1)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(3)*y(2)(1)
Lead Term of Product:
y(1)(3)*y(2)(1)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(1)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(4)(1)*x(3)(4)+y(3)(1)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(1)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-x(4)(4)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
x(3)(4)
Lead Term of Product:
-y(2)(2)*y(4)(1)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(3)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(3)*x(2)(4)+y(2)(3)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(3)*x(3)(4)-y(2)(3)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(3)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(4)+y(3)(2)*y(4)(1)*x(1)(3)*x(2)(4)+y(1)(3)*y(4)(1)*x(2)(4)*x(3)(2)-y(1)(2)*y(4)(1)*x(2)(4)*x(3)(3)-y(2)(3)*y(4)(1)*x(1)(2)*x(3)(4)+y(2)(1)*y(4)(3)*x(1)(2)*x(3)(4)+y(2)(3)*y(3)(1)*x(1)(2)*x(4)(4)-y(2)(1)*y(3)(3)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{2}{3}{4}{1}{3}{4}) =
(-y_{1, 3} y_{4, 1})  \del{2}{3}{2}{4} +(y_{1, 1} y_{4, 2})  \del{2}{3}{3}{4} +(y_{1, 3} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{1, 1} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{1, 3} y_{2, 1})  \del{3}{4}{2}{4} +(y_{1, 1} y_{2, 2})  \del{3}{4}{3}{4} +(-y_{4, 1} x_{3, 4}+y_{3, 1} x_{4, 4})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{4, 4})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{2}{3} +(-x_{4, 4})  \lam{1}{2}{3}{1}{2}{3} +(x_{3, 4})  \lam{1}{2}{4}{1}{2}{3} +(-x_{2, 4})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,3
2,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
2,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(2)*x(2)(3)
Divisor:
Delta
2,3
2,3
Quotient:
-y(1)(3)*y(4)(2)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(1)(3)*y(3)(2)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(3)*y(2)(2)
Lead Term of Product:
y(1)(3)*y(2)(2)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(4)(2)*x(3)(3)+y(3)(2)*x(4)(3)
Lead Term of Product:
-y(2)(3)*y(4)(2)*x(1)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(2)*x(4)(3)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(2)*x(2)(3)+y(2)(2)*x(3)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(2)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(3)*y(4)(2)*x(2)(3)+y(3)(2)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(2)*x(3)(3)-y(2)(2)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(2)*x(4)(3)+y(2)(2)*y(3)(3)*x(4)(3)) - (-y(4)(2)*x(2)(3))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(2)*x(2)(3)+y(3)(2)*y(4)(2)*x(1)(3)*x(2)(3)+y(1)(3)*y(4)(2)*x(2)(3)*x(3)(2)-y(2)(3)*y(4)(2)*x(1)(2)*x(3)(3)+y(2)(2)*y(4)(3)*x(1)(2)*x(3)(3)-y(1)(2)*y(4)(2)*x(2)(3)*x(3)(3)+y(2)(3)*y(3)(2)*x(1)(2)*x(4)(3)-y(2)(2)*y(3)(3)*x(1)(2)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{2}{3}{4}{2}{3}{3}) =
(-y_{1, 3} y_{4, 2})  \del{2}{3}{2}{3} +(y_{1, 3} y_{3, 2})  \del{2}{4}{2}{3} +(-y_{1, 3} y_{2, 2})  \del{3}{4}{2}{3} +(-y_{4, 2} x_{3, 3}+y_{3, 2} x_{4, 3})  \eps{1}{2}{2}{3} +(-y_{2, 2} x_{4, 3})  \eps{1}{3}{2}{3} +(-y_{3, 2} x_{2, 3}+y_{2, 2} x_{3, 3})  \eps{1}{4}{2}{3}
----------------------------------
Epsilon:
1,3
2,3
Lam:
2,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(3)*y(4)(2)
Lead Term of Product:
y(1)(3)*y(4)(2)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(1)(2)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(3)*y(3)(2)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(2)*y(3)(2)
Lead Term of Product:
y(1)(2)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(3)*y(2)(2)
Lead Term of Product:
y(1)(3)*y(2)(2)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(2)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(4)(2)*x(3)(4)+y(3)(2)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(2)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(2)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(2)*x(2)(4)+y(2)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(3)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(3)*x(2)(4)+y(2)(3)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(3)*x(3)(4)-y(2)(3)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(3)*x(4)(4)) - (-y(4)(2)*x(2)(4))*(y(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(2)*x(2)(4)+y(3)(2)*y(4)(2)*x(1)(3)*x(2)(4)+y(1)(3)*y(4)(2)*x(2)(4)*x(3)(2)-y(1)(2)*y(4)(2)*x(2)(4)*x(3)(3)-y(2)(3)*y(4)(2)*x(1)(2)*x(3)(4)+y(2)(2)*y(4)(3)*x(1)(2)*x(3)(4)+y(2)(3)*y(3)(2)*x(1)(2)*x(4)(4)-y(2)(2)*y(3)(3)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \lam{2}{3}{4}{2}{3}{4}) =
(-y_{1, 3} y_{4, 2})  \del{2}{3}{2}{4} +(y_{1, 2} y_{4, 2})  \del{2}{3}{3}{4} +(y_{1, 3} y_{3, 2})  \del{2}{4}{2}{4} +(-y_{1, 2} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{1, 3} y_{2, 2})  \del{3}{4}{2}{4} +(y_{1, 2} y_{2, 2})  \del{3}{4}{3}{4} +(-y_{4, 2} x_{3, 4}+y_{3, 2} x_{4, 4})  \eps{1}{2}{2}{3} +(-y_{2, 2} x_{4, 4})  \eps{1}{3}{2}{3} +(-y_{3, 2} x_{2, 4}+y_{2, 2} x_{3, 4})  \eps{1}{4}{2}{3}
----------------------------------
Epsilon:
1,3
2,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,3
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(3)(2)*y(3)(4)*x(1)(2)
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(1)*y(3)(2)*y(3)(4)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(1)(2)*y(3)(1)+y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(2)*y(3)(1)*y(3)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
-y(3)(2)
Lead Term of Product:
y(2)(2)*y(3)(1)*y(3)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,4
Quotient:
-x(3)(2)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(3)(1)*x(3)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(2)(2)*y(3)(1)*x(1)(2)+y(2)(1)*y(3)(2)*x(1)(2)+y(1)(2)*y(3)(1)*x(2)(2)-y(1)(1)*y(3)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(3)(2)+y(1)(1)*y(2)(2)*x(3)(2)) - (-y(2)(2)*y(3)(1))*(y(3)(4)*x(1)(2)-y(3)(2)*x(1)(4)-y(1)(4)*x(3)(2)+y(1)(2)*x(3)(4))
-------
Rewrite:
-y(2)(1)*y(3)(2)*y(3)(4)*x(1)(2)+y(2)(2)*y(3)(1)*y(3)(2)*x(1)(4)-y(1)(2)*y(3)(1)*y(3)(4)*x(2)(2)+y(1)(1)*y(3)(2)*y(3)(4)*x(2)(2)+y(1)(4)*y(2)(2)*y(3)(1)*x(3)(2)+y(1)(2)*y(2)(1)*y(3)(4)*x(3)(2)-y(1)(1)*y(2)(2)*y(3)(4)*x(3)(2)-y(1)(2)*y(2)(2)*y(3)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{4}, \lam{1}{2}{3}{1}{2}{2}) =
(-y_{2, 1} y_{3, 2})  \eps{1}{3}{2}{4} +(-y_{1, 2} y_{3, 1}+y_{1, 1} y_{3, 2})  \eps{2}{3}{2}{4} +(-y_{3, 2})  \lam{1}{2}{3}{1}{2}{4} +(-x_{3, 2})  \psi{1}{2}{3}{1}{2}{4}
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,4
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(3)(4)*y(4)(2)*x(1)(2)
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(3)(4)*y(4)(2)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(1)(2)*y(4)(1)+y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(3)(4)*y(4)(1)*x(2)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,4
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(4)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-y(3)(2)
Lead Term of Product:
y(2)(2)*y(3)(2)*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,4
Quotient:
-x(3)(2)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(4)(1)*x(3)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(2)(2)*y(4)(1)*x(1)(2)+y(2)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(2)(2)-y(1)(1)*y(4)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(4)(2)+y(1)(1)*y(2)(2)*x(4)(2)) - (-y(2)(2)*y(4)(1))*(y(3)(4)*x(1)(2)-y(3)(2)*x(1)(4)-y(1)(4)*x(3)(2)+y(1)(2)*x(3)(4))
-------
Rewrite:
-y(2)(1)*y(3)(4)*y(4)(2)*x(1)(2)+y(2)(2)*y(3)(2)*y(4)(1)*x(1)(4)-y(1)(2)*y(3)(4)*y(4)(1)*x(2)(2)+y(1)(1)*y(3)(4)*y(4)(2)*x(2)(2)+y(1)(4)*y(2)(2)*y(4)(1)*x(3)(2)-y(1)(2)*y(2)(2)*y(4)(1)*x(3)(4)+y(1)(2)*y(2)(1)*y(3)(4)*x(4)(2)-y(1)(1)*y(2)(2)*y(3)(4)*x(4)(2)
-----------
TeX output:
S(\eps{1}{3}{2}{4}, \lam{1}{2}{4}{1}{2}{2}) =
(-y_{2, 1} y_{4, 2})  \eps{1}{3}{2}{4} +(-y_{1, 2} y_{4, 1}+y_{1, 1} y_{4, 2})  \eps{2}{3}{2}{4} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2, 2})  \eps{3}{4}{2}{4} +(-y_{3, 2})  \lam{1}{2}{4}{1}{2}{4} +(-x_{3, 2})  \psi{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(3)(4)*y(4)(2)*x(1)(2)
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(3)(4)*y(4)(2)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,4
Quotient:
-y(1)(2)*y(3)(1)+y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(2)*y(3)(1)*y(4)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,4
Quotient:
-y(3)(2)
Lead Term of Product:
y(3)(2)^2*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,3,4
1,2,4
Quotient:
-x(3)(2)
Lead Term of Product:
y(1)(4)*y(3)(2)*y(4)(1)*x(3)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(3)(2)*y(4)(1)*x(1)(2)+y(3)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(3)(2)-y(1)(1)*y(4)(2)*x(3)(2)-y(1)(2)*y(3)(1)*x(4)(2)+y(1)(1)*y(3)(2)*x(4)(2)) - (-y(3)(2)*y(4)(1))*(y(3)(4)*x(1)(2)-y(3)(2)*x(1)(4)-y(1)(4)*x(3)(2)+y(1)(2)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(3)(4)*y(4)(2)*x(1)(2)+y(3)(2)^2*y(4)(1)*x(1)(4)+y(1)(4)*y(3)(2)*y(4)(1)*x(3)(2)-y(1)(2)*y(3)(4)*y(4)(1)*x(3)(2)+y(1)(1)*y(3)(4)*y(4)(2)*x(3)(2)-y(1)(2)*y(3)(2)*y(4)(1)*x(3)(4)+y(1)(2)*y(3)(1)*y(3)(4)*x(4)(2)-y(1)(1)*y(3)(2)*y(3)(4)*x(4)(2)
-----------
TeX output:
S(\eps{1}{3}{2}{4}, \lam{1}{3}{4}{1}{2}{2}) =
(-y_{3, 1} y_{4, 2})  \eps{1}{3}{2}{4} +(-y_{1, 2} y_{3, 1}+y_{1, 1} y_{3, 2})  \eps{3}{4}{2}{4} +(-y_{3, 2})  \lam{1}{3}{4}{1}{2}{4} +(-x_{3, 2})  \psi{1}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,3
2,4
Quotient:
-y(1)(4)*y(4)(1)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(4)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(4)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(4)*x(1)(2)-y(3)(2)*x(1)(4)-y(1)(4)*x(3)(2)+y(1)(2)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(1)(2)*x(1)(4)+y(3)(2)*y(4)(1)*x(1)(4)^2+y(1)(4)*y(4)(1)*x(1)(4)*x(3)(2)-y(1)(4)*y(4)(1)*x(1)(2)*x(3)(4)+y(1)(1)*y(4)(4)*x(1)(2)*x(3)(4)-y(1)(2)*y(4)(1)*x(1)(4)*x(3)(4)+y(1)(4)*y(3)(1)*x(1)(2)*x(4)(4)-y(1)(1)*y(3)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{4}, \lam{1}{3}{4}{1}{4}{4}) =
(-y_{1, 4} y_{4, 1})  \del{1}{3}{2}{4} +(y_{1, 4} y_{3, 1})  \del{1}{4}{2}{4} +(-y_{1, 1} y_{1, 4})  \del{3}{4}{2}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{3}{2}{4} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{2}{4} +(-x_{1, 4})  \lam{1}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,3
2,4
Quotient:
-y(1)(4)*y(4)(2)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(4)*y(3)(2)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(2)*y(1)(4)
Lead Term of Product:
y(1)(2)*y(1)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(4)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(2)*x(1)(4)+y(1)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(4)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(3)(4)*x(1)(2)-y(3)(2)*x(1)(4)-y(1)(4)*x(3)(2)+y(1)(2)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(2)*x(1)(4)+y(3)(2)*y(4)(2)*x(1)(4)^2+y(1)(4)*y(4)(2)*x(1)(4)*x(3)(2)-y(1)(4)*y(4)(2)*x(1)(2)*x(3)(4)+y(1)(2)*y(4)(4)*x(1)(2)*x(3)(4)-y(1)(2)*y(4)(2)*x(1)(4)*x(3)(4)+y(1)(4)*y(3)(2)*x(1)(2)*x(4)(4)-y(1)(2)*y(3)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{4}, \lam{1}{3}{4}{2}{4}{4}) =
(-y_{1, 4} y_{4, 2})  \del{1}{3}{2}{4} +(y_{1, 4} y_{3, 2})  \del{1}{4}{2}{4} +(-y_{1, 2} y_{1, 4})  \del{3}{4}{2}{4} +(-y_{1, 2} x_{4, 4})  \eps{1}{3}{2}{4} +(-y_{3, 2} x_{1, 4}+y_{1, 2} x_{3, 4})  \eps{1}{4}{2}{4}
----------------------------------
Epsilon:
1,3
2,4
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,3
2,4
Quotient:
-y(1)(4)*y(4)(3)+y(1)(3)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(3)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(2)*y(4)(4)
Lead Term of Product:
y(1)(2)*y(4)(4)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(3)(2)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(2)*y(1)(4)
Lead Term of Product:
y(1)(2)*y(1)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(1)(3)*x(4)(4)
Lead Term of Product:
-y(1)(3)*y(3)(4)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(2)*x(1)(4)+y(1)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(1)(4))*(y(3)(4)*x(1)(2)-y(3)(2)*x(1)(4)-y(1)(4)*x(3)(2)+y(1)(2)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(2)*x(1)(4)+y(3)(2)*y(4)(3)*x(1)(4)^2+y(1)(4)*y(4)(3)*x(1)(4)*x(3)(2)-y(1)(4)*y(4)(3)*x(1)(2)*x(3)(4)+y(1)(3)*y(4)(4)*x(1)(2)*x(3)(4)-y(1)(2)*y(4)(3)*x(1)(4)*x(3)(4)+y(1)(4)*y(3)(3)*x(1)(2)*x(4)(4)-y(1)(3)*y(3)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{4}, \lam{1}{3}{4}{3}{4}{4}) =
(-y_{1, 4} y_{4, 3}+y_{1, 3} y_{4, 4})  \del{1}{3}{2}{4} +(-y_{1, 2} y_{4, 4})  \del{1}{3}{3}{4} +(y_{1, 4} y_{3, 2})  \del{1}{4}{3}{4} +(-y_{1, 2} y_{1, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{3}{2}{3} +(-y_{1, 3} x_{4, 4})  \eps{1}{3}{2}{4} +(-y_{3, 2} x_{1, 4}+y_{1, 2} x_{3, 4})  \eps{1}{4}{3}{4}
----------------------------------
Epsilon:
1,3
2,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
2,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(1)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(4)*y(4)(1)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(4)*y(2)(1)
Lead Term of Product:
y(1)(4)*y(2)(1)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(4)(1)*x(3)(4)+y(3)(1)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(1)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(4)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
x(3)(4)
Lead Term of Product:
-y(2)(2)*y(4)(1)*x(1)(4)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(4)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(4)*x(1)(2)-y(3)(2)*x(1)(4)-y(1)(4)*x(3)(2)+y(1)(2)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(1)(2)*x(2)(4)+y(3)(2)*y(4)(1)*x(1)(4)*x(2)(4)+y(1)(4)*y(4)(1)*x(2)(4)*x(3)(2)-y(2)(4)*y(4)(1)*x(1)(2)*x(3)(4)+y(2)(1)*y(4)(4)*x(1)(2)*x(3)(4)-y(1)(2)*y(4)(1)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(1)*x(1)(2)*x(4)(4)-y(2)(1)*y(3)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{4}, \lam{2}{3}{4}{1}{4}{4}) =
(-y_{1, 4} y_{4, 1})  \del{2}{3}{2}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{1, 4} y_{2, 1})  \del{3}{4}{2}{4} +(-y_{4, 1} x_{3, 4}+y_{3, 1} x_{4, 4})  \eps{1}{2}{2}{4} +(-y_{2, 1} x_{4, 4})  \eps{1}{3}{2}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{2}{4} +(-x_{4, 4})  \lam{1}{2}{3}{1}{2}{4} +(x_{3, 4})  \lam{1}{2}{4}{1}{2}{4} +(-x_{2, 4})  \lam{1}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,3
2,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
2,4
Lam:
2,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(4)*y(4)(2)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(4)*y(3)(2)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(4)*y(2)(2)
Lead Term of Product:
y(1)(4)*y(2)(2)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(4)(2)*x(3)(4)+y(3)(2)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(2)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(2)(2)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(2)*x(2)(4)+y(2)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(4)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(2)(4))*(y(3)(4)*x(1)(2)-y(3)(2)*x(1)(4)-y(1)(4)*x(3)(2)+y(1)(2)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(2)*x(2)(4)+y(3)(2)*y(4)(2)*x(1)(4)*x(2)(4)+y(1)(4)*y(4)(2)*x(2)(4)*x(3)(2)-y(2)(4)*y(4)(2)*x(1)(2)*x(3)(4)+y(2)(2)*y(4)(4)*x(1)(2)*x(3)(4)-y(1)(2)*y(4)(2)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(2)*x(1)(2)*x(4)(4)-y(2)(2)*y(3)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{4}, \lam{2}{3}{4}{2}{4}{4}) =
(-y_{1, 4} y_{4, 2})  \del{2}{3}{2}{4} +(y_{1, 4} y_{3, 2})  \del{2}{4}{2}{4} +(-y_{1, 4} y_{2, 2})  \del{3}{4}{2}{4} +(-y_{4, 2} x_{3, 4}+y_{3, 2} x_{4, 4})  \eps{1}{2}{2}{4} +(-y_{2, 2} x_{4, 4})  \eps{1}{3}{2}{4} +(-y_{3, 2} x_{2, 4}+y_{2, 2} x_{3, 4})  \eps{1}{4}{2}{4}
----------------------------------
Epsilon:
1,3
2,4
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(4)*y(4)(3)+y(1)(3)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(2)*y(4)(4)
Lead Term of Product:
y(1)(2)*y(4)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(2)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(4)*y(2)(2)
Lead Term of Product:
y(1)(4)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(4)*x(3)(4)-y(3)(4)*x(4)(4)
Lead Term of Product:
y(2)(3)*y(4)(4)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(4)(3)*x(3)(4)+y(3)(3)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(3)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(2)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(2)*x(2)(4)+y(2)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(1)(3)*x(4)(4)
Lead Term of Product:
-y(1)(3)*y(3)(4)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
y(1)(2)*x(4)(4)
Lead Term of Product:
y(1)(2)*y(3)(4)*x(2)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
2,3,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(4)*y(2)(3)*x(3)(2)*x(4)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(2)(4))*(y(3)(4)*x(1)(2)-y(3)(2)*x(1)(4)-y(1)(4)*x(3)(2)+y(1)(2)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(2)*x(2)(4)+y(3)(2)*y(4)(3)*x(1)(4)*x(2)(4)+y(1)(4)*y(4)(3)*x(2)(4)*x(3)(2)-y(2)(4)*y(4)(3)*x(1)(2)*x(3)(4)+y(2)(3)*y(4)(4)*x(1)(2)*x(3)(4)-y(1)(2)*y(4)(3)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(3)*x(1)(2)*x(4)(4)-y(2)(3)*y(3)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{2}{4}, \lam{2}{3}{4}{3}{4}{4}) =
(-y_{1, 4} y_{4, 3}+y_{1, 3} y_{4, 4})  \del{2}{3}{2}{4} +(-y_{1, 2} y_{4, 4})  \del{2}{3}{3}{4} +(y_{1, 4} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{1, 4} y_{2, 2})  \del{3}{4}{3}{4} +(y_{4, 4} x_{3, 4}-y_{3, 4} x_{4, 4})  \eps{1}{2}{2}{3} +(-y_{4, 3} x_{3, 4}+y_{3, 3} x_{4, 4})  \eps{1}{2}{2}{4} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{2}{3} +(-y_{2, 2} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{3, 2} x_{2, 4}+y_{2, 2} x_{3, 4})  \eps{1}{4}{3}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{2}{3} +(-y_{1, 3} x_{4, 4})  \eps{2}{3}{2}{4} +(y_{1, 2} x_{4, 4})  \eps{2}{3}{3}{4} +(-x_{4, 4})  \pho{1}{2}{3}{2}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,3
1,2,3
Lead Term of Spoly:
-y(2)(1)*y(3)(2)*y(3)(4)*x(1)(3)
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(1)*y(3)(2)*y(3)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(2)*y(3)(1)+y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(2)*y(3)(1)*y(3)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(2)(2)*y(3)(1)*y(3)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,3
Quotient:
x(3)(4)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(3)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(3)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(2)(2)*y(3)(1)*x(1)(3)+y(2)(1)*y(3)(2)*x(1)(3)+y(1)(2)*y(3)(1)*x(2)(3)-y(1)(1)*y(3)(2)*x(2)(3)-y(1)(2)*y(2)(1)*x(3)(3)+y(1)(1)*y(2)(2)*x(3)(3)) - (-y(2)(2)*y(3)(1))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(2)(1)*y(3)(2)*y(3)(4)*x(1)(3)+y(2)(2)*y(3)(1)*y(3)(3)*x(1)(4)-y(1)(2)*y(3)(1)*y(3)(4)*x(2)(3)+y(1)(1)*y(3)(2)*y(3)(4)*x(2)(3)+y(1)(4)*y(2)(2)*y(3)(1)*x(3)(3)+y(1)(2)*y(2)(1)*y(3)(4)*x(3)(3)-y(1)(1)*y(2)(2)*y(3)(4)*x(3)(3)-y(1)(3)*y(2)(2)*y(3)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{2}{3}{1}{2}{3}) =
(-y_{2, 1} y_{3, 2})  \eps{1}{3}{3}{4} +(-y_{1, 2} y_{3, 1}+y_{1, 1} y_{3, 2})  \eps{2}{3}{3}{4} +(-y_{3, 3})  \lam{1}{2}{3}{1}{2}{4} +(x_{3, 4})  \psi{1}{2}{3}{1}{2}{3} +(-x_{3, 3})  \psi{1}{2}{3}{1}{2}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,3
1,3,3
Lead Term of Spoly:
-y(2)(1)*y(3)(3)*y(3)(4)*x(1)(3)
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(1)*y(3)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*y(3)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(3)*y(3)(1)+y(1)(1)*y(3)(3)
Lead Term of Product:
-y(1)(3)*y(3)(1)*y(3)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,3,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(2)(3)*y(3)(1)*y(3)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,3,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(3)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(2)(3)*y(3)(1)*x(1)(3)+y(2)(1)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(1)*x(2)(3)-y(1)(1)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(1)*x(3)(3)+y(1)(1)*y(2)(3)*x(3)(3)) - (-y(2)(3)*y(3)(1))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(2)(1)*y(3)(3)*y(3)(4)*x(1)(3)+y(2)(3)*y(3)(1)*y(3)(3)*x(1)(4)-y(1)(3)*y(3)(1)*y(3)(4)*x(2)(3)+y(1)(1)*y(3)(3)*y(3)(4)*x(2)(3)+y(1)(4)*y(2)(3)*y(3)(1)*x(3)(3)+y(1)(3)*y(2)(1)*y(3)(4)*x(3)(3)-y(1)(1)*y(2)(3)*y(3)(4)*x(3)(3)-y(1)(3)*y(2)(3)*y(3)(1)*x(3)(4)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{2}{3}{1}{3}{3}) =
(-y_{2, 1} y_{3, 3})  \eps{1}{3}{3}{4} +(-y_{1, 3} y_{3, 1}+y_{1, 1} y_{3, 3})  \eps{2}{3}{3}{4} +(-y_{3, 3})  \lam{1}{2}{3}{1}{3}{4} +(-x_{3, 3})  \psi{1}{2}{3}{1}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,3
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(3)(3)*y(3)(4)*x(1)(3)
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(2)*y(3)(3)
Lead Term of Product:
-y(2)(2)*y(3)(3)*y(3)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(3)*y(3)(2)+y(1)(2)*y(3)(3)
Lead Term of Product:
-y(1)(3)*y(3)(2)*y(3)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
2,3,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(2)(3)*y(3)(2)*y(3)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
2,3,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(3)(2)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(2)(3)*y(3)(2)*x(1)(3)+y(2)(2)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(2)*x(2)(3)-y(1)(2)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(3)(3)+y(1)(2)*y(2)(3)*x(3)(3)) - (-y(2)(3)*y(3)(2))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(2)(2)*y(3)(3)*y(3)(4)*x(1)(3)+y(2)(3)*y(3)(2)*y(3)(3)*x(1)(4)-y(1)(3)*y(3)(2)*y(3)(4)*x(2)(3)+y(1)(2)*y(3)(3)*y(3)(4)*x(2)(3)+y(1)(4)*y(2)(3)*y(3)(2)*x(3)(3)+y(1)(3)*y(2)(2)*y(3)(4)*x(3)(3)-y(1)(2)*y(2)(3)*y(3)(4)*x(3)(3)-y(1)(3)*y(2)(3)*y(3)(2)*x(3)(4)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{2}{3}{2}{3}{3}) =
(-y_{2, 2} y_{3, 3})  \eps{1}{3}{3}{4} +(-y_{1, 3} y_{3, 2}+y_{1, 2} y_{3, 3})  \eps{2}{3}{3}{4} +(-y_{3, 3})  \lam{1}{2}{3}{2}{3}{4} +(-x_{3, 3})  \psi{1}{2}{3}{2}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,4
1,2,3
Lead Term of Spoly:
-y(2)(1)*y(3)(4)*y(4)(2)*x(1)(3)
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(3)(4)*y(4)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(2)*y(4)(1)+y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(3)(4)*y(4)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(2)*y(2)(1)+y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(2)(2)*y(3)(3)*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,3
Quotient:
x(3)(4)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(4)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(4)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(2)(2)*y(4)(1)*x(1)(3)+y(2)(1)*y(4)(2)*x(1)(3)+y(1)(2)*y(4)(1)*x(2)(3)-y(1)(1)*y(4)(2)*x(2)(3)-y(1)(2)*y(2)(1)*x(4)(3)+y(1)(1)*y(2)(2)*x(4)(3)) - (-y(2)(2)*y(4)(1))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(2)(1)*y(3)(4)*y(4)(2)*x(1)(3)+y(2)(2)*y(3)(3)*y(4)(1)*x(1)(4)-y(1)(2)*y(3)(4)*y(4)(1)*x(2)(3)+y(1)(1)*y(3)(4)*y(4)(2)*x(2)(3)+y(1)(4)*y(2)(2)*y(4)(1)*x(3)(3)-y(1)(3)*y(2)(2)*y(4)(1)*x(3)(4)+y(1)(2)*y(2)(1)*y(3)(4)*x(4)(3)-y(1)(1)*y(2)(2)*y(3)(4)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{2}{4}{1}{2}{3}) =
(-y_{2, 1} y_{4, 2})  \eps{1}{3}{3}{4} +(-y_{1, 2} y_{4, 1}+y_{1, 1} y_{4, 2})  \eps{2}{3}{3}{4} +(-y_{1, 2} y_{2, 1}+y_{1, 1} y_{2, 2})  \eps{3}{4}{3}{4} +(-y_{3, 3})  \lam{1}{2}{4}{1}{2}{4} +(x_{3, 4})  \psi{1}{2}{4}{1}{2}{3} +(-x_{3, 3})  \psi{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,4
1,3,3
Lead Term of Spoly:
-y(2)(1)*y(3)(4)*y(4)(3)*x(1)(3)
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(1)*y(4)(3)
Lead Term of Product:
-y(2)(1)*y(3)(4)*y(4)(3)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(3)*y(4)(1)+y(1)(1)*y(4)(3)
Lead Term of Product:
-y(1)(3)*y(3)(4)*y(4)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(3)*y(2)(1)+y(1)(1)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,3,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(2)(3)*y(3)(3)*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,3,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(4)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(2)(3)*y(4)(1)*x(1)(3)+y(2)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(2)(3)-y(1)(1)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(1)*x(4)(3)+y(1)(1)*y(2)(3)*x(4)(3)) - (-y(2)(3)*y(4)(1))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(2)(1)*y(3)(4)*y(4)(3)*x(1)(3)+y(2)(3)*y(3)(3)*y(4)(1)*x(1)(4)-y(1)(3)*y(3)(4)*y(4)(1)*x(2)(3)+y(1)(1)*y(3)(4)*y(4)(3)*x(2)(3)+y(1)(4)*y(2)(3)*y(4)(1)*x(3)(3)-y(1)(3)*y(2)(3)*y(4)(1)*x(3)(4)+y(1)(3)*y(2)(1)*y(3)(4)*x(4)(3)-y(1)(1)*y(2)(3)*y(3)(4)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{2}{4}{1}{3}{3}) =
(-y_{2, 1} y_{4, 3})  \eps{1}{3}{3}{4} +(-y_{1, 3} y_{4, 1}+y_{1, 1} y_{4, 3})  \eps{2}{3}{3}{4} +(-y_{1, 3} y_{2, 1}+y_{1, 1} y_{2, 3})  \eps{3}{4}{3}{4} +(-y_{3, 3})  \lam{1}{2}{4}{1}{3}{4} +(-x_{3, 3})  \psi{1}{2}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,4
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(3)(4)*y(4)(3)*x(1)(3)
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(2)*y(4)(3)
Lead Term of Product:
-y(2)(2)*y(3)(4)*y(4)(3)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(3)*y(4)(2)+y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(3)*y(3)(4)*y(4)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(3)*y(2)(2)+y(1)(2)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
2,3,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(2)(3)*y(3)(3)*y(4)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
2,3,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(4)(2)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(2)(3)*y(4)(2)*x(1)(3)+y(2)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(2)(3)-y(1)(2)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(4)(3)+y(1)(2)*y(2)(3)*x(4)(3)) - (-y(2)(3)*y(4)(2))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(2)(2)*y(3)(4)*y(4)(3)*x(1)(3)+y(2)(3)*y(3)(3)*y(4)(2)*x(1)(4)-y(1)(3)*y(3)(4)*y(4)(2)*x(2)(3)+y(1)(2)*y(3)(4)*y(4)(3)*x(2)(3)+y(1)(4)*y(2)(3)*y(4)(2)*x(3)(3)-y(1)(3)*y(2)(3)*y(4)(2)*x(3)(4)+y(1)(3)*y(2)(2)*y(3)(4)*x(4)(3)-y(1)(2)*y(2)(3)*y(3)(4)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{2}{4}{2}{3}{3}) =
(-y_{2, 2} y_{4, 3})  \eps{1}{3}{3}{4} +(-y_{1, 3} y_{4, 2}+y_{1, 2} y_{4, 3})  \eps{2}{3}{3}{4} +(-y_{1, 3} y_{2, 2}+y_{1, 2} y_{2, 3})  \eps{3}{4}{3}{4} +(-y_{3, 3})  \lam{1}{2}{4}{2}{3}{4} +(-x_{3, 3})  \psi{1}{2}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,3,4
1,2,3
Lead Term of Spoly:
-y(3)(1)*y(3)(4)*y(4)(2)*x(1)(3)
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(3)(4)*y(4)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(2)*y(3)(1)+y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(2)*y(3)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(3)(2)*y(3)(3)*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,3,4
1,2,3
Quotient:
x(3)(4)
Lead Term of Product:
-y(1)(3)*y(3)(2)*y(4)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Psi
1,3,4
1,2,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(3)(2)*y(4)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(3)(2)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(2)*x(1)(3)+y(1)(2)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(2)*x(3)(3)-y(1)(2)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(2)*x(4)(3)) - (-y(3)(2)*y(4)(1))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(3)(4)*y(4)(2)*x(1)(3)+y(3)(2)*y(3)(3)*y(4)(1)*x(1)(4)+y(1)(4)*y(3)(2)*y(4)(1)*x(3)(3)-y(1)(2)*y(3)(4)*y(4)(1)*x(3)(3)+y(1)(1)*y(3)(4)*y(4)(2)*x(3)(3)-y(1)(3)*y(3)(2)*y(4)(1)*x(3)(4)+y(1)(2)*y(3)(1)*y(3)(4)*x(4)(3)-y(1)(1)*y(3)(2)*y(3)(4)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{3}{4}{1}{2}{3}) =
(-y_{3, 1} y_{4, 2})  \eps{1}{3}{3}{4} +(-y_{1, 2} y_{3, 1}+y_{1, 1} y_{3, 2})  \eps{3}{4}{3}{4} +(-y_{3, 3})  \lam{1}{3}{4}{1}{2}{4} +(x_{3, 4})  \psi{1}{3}{4}{1}{2}{3} +(-x_{3, 3})  \psi{1}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(3)(4)*y(4)(3)*x(1)(3)
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(3)(1)*y(4)(3)
Lead Term of Product:
-y(3)(1)*y(3)(4)*y(4)(3)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(3)*y(3)(1)+y(1)(1)*y(3)(3)
Lead Term of Product:
-y(1)(3)*y(3)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,3,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(3)(3)^2*y(4)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,3,4
1,3,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(3)(3)*y(4)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(3)(3)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(3)*x(4)(3)) - (-y(3)(3)*y(4)(1))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(3)(4)*y(4)(3)*x(1)(3)+y(3)(3)^2*y(4)(1)*x(1)(4)+y(1)(4)*y(3)(3)*y(4)(1)*x(3)(3)-y(1)(3)*y(3)(4)*y(4)(1)*x(3)(3)+y(1)(1)*y(3)(4)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(3)*y(4)(1)*x(3)(4)+y(1)(3)*y(3)(1)*y(3)(4)*x(4)(3)-y(1)(1)*y(3)(3)*y(3)(4)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{3}{4}{1}{3}{3}) =
(-y_{3, 1} y_{4, 3})  \eps{1}{3}{3}{4} +(-y_{1, 3} y_{3, 1}+y_{1, 1} y_{3, 3})  \eps{3}{4}{3}{4} +(-y_{3, 3})  \lam{1}{3}{4}{1}{3}{4} +(-x_{3, 3})  \psi{1}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(1)(3)*x(1)(4)
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(4)*y(4)(1)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(1)*y(1)(4)
Lead Term of Product:
y(1)(1)*y(1)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(4)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(3)(4)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(1)(3)*x(1)(4)+y(3)(3)*y(4)(1)*x(1)(4)^2+y(1)(4)*y(4)(1)*x(1)(4)*x(3)(3)-y(1)(4)*y(4)(1)*x(1)(3)*x(3)(4)+y(1)(1)*y(4)(4)*x(1)(3)*x(3)(4)-y(1)(3)*y(4)(1)*x(1)(4)*x(3)(4)+y(1)(4)*y(3)(1)*x(1)(3)*x(4)(4)-y(1)(1)*y(3)(4)*x(1)(3)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{3}{4}{1}{4}{4}) =
(-y_{1, 4} y_{4, 1})  \del{1}{3}{3}{4} +(y_{1, 4} y_{3, 1})  \del{1}{4}{3}{4} +(-y_{1, 1} y_{1, 4})  \del{3}{4}{3}{4} +(-y_{1, 1} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{3}{4} +(-x_{1, 4})  \lam{1}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(3)(4)*y(4)(3)*x(1)(3)
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(3)(4)*y(4)(3)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(3)*y(3)(2)+y(1)(2)*y(3)(3)
Lead Term of Product:
-y(1)(3)*y(3)(2)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
2,3,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(3)(3)^2*y(4)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,3,4
2,3,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(1)(4)*y(3)(3)*y(4)(2)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(3)(3)*y(4)(2)*x(1)(3)+y(3)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(3)(3)-y(1)(2)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(2)*x(4)(3)+y(1)(2)*y(3)(3)*x(4)(3)) - (-y(3)(3)*y(4)(2))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(3)(4)*y(4)(3)*x(1)(3)+y(3)(3)^2*y(4)(2)*x(1)(4)+y(1)(4)*y(3)(3)*y(4)(2)*x(3)(3)-y(1)(3)*y(3)(4)*y(4)(2)*x(3)(3)+y(1)(2)*y(3)(4)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(3)*y(4)(2)*x(3)(4)+y(1)(3)*y(3)(2)*y(3)(4)*x(4)(3)-y(1)(2)*y(3)(3)*y(3)(4)*x(4)(3)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{3}{4}{2}{3}{3}) =
(-y_{3, 2} y_{4, 3})  \eps{1}{3}{3}{4} +(-y_{1, 3} y_{3, 2}+y_{1, 2} y_{3, 3})  \eps{3}{4}{3}{4} +(-y_{3, 3})  \lam{1}{3}{4}{2}{3}{4} +(-x_{3, 3})  \psi{1}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(3)*x(1)(4)
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(4)*y(4)(2)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(3)(2)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(2)*y(1)(4)
Lead Term of Product:
y(1)(2)*y(1)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(4)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(2)*x(1)(4)+y(1)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
2,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(3)(3)*y(4)(2)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(3)(4)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(3)*x(1)(4)+y(3)(3)*y(4)(2)*x(1)(4)^2+y(1)(4)*y(4)(2)*x(1)(4)*x(3)(3)-y(1)(4)*y(4)(2)*x(1)(3)*x(3)(4)+y(1)(2)*y(4)(4)*x(1)(3)*x(3)(4)-y(1)(3)*y(4)(2)*x(1)(4)*x(3)(4)+y(1)(4)*y(3)(2)*x(1)(3)*x(4)(4)-y(1)(2)*y(3)(4)*x(1)(3)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{3}{4}{2}{4}{4}) =
(-y_{1, 4} y_{4, 2})  \del{1}{3}{3}{4} +(y_{1, 4} y_{3, 2})  \del{1}{4}{3}{4} +(-y_{1, 2} y_{1, 4})  \del{3}{4}{3}{4} +(-y_{1, 2} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{3, 2} x_{1, 4}+y_{1, 2} x_{3, 4})  \eps{1}{4}{3}{4} +(-x_{1, 4})  \lam{1}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(3)*x(1)(4)
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(4)*y(4)(3)
Lead Term of Product:
y(1)(4)*y(4)(3)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(3)(3)
Lead Term of Product:
-y(1)(4)*y(3)(3)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(3)*y(1)(4)
Lead Term of Product:
y(1)(3)*y(1)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(1)(3)*x(4)(4)
Lead Term of Product:
-y(1)(3)*y(3)(4)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(3)*x(1)(4)+y(1)(3)*x(3)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(1)(4))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(3)*x(1)(4)+y(3)(3)*y(4)(3)*x(1)(4)^2+y(1)(4)*y(4)(3)*x(1)(4)*x(3)(3)-y(1)(4)*y(4)(3)*x(1)(3)*x(3)(4)+y(1)(3)*y(4)(4)*x(1)(3)*x(3)(4)-y(1)(3)*y(4)(3)*x(1)(4)*x(3)(4)+y(1)(4)*y(3)(3)*x(1)(3)*x(4)(4)-y(1)(3)*y(3)(4)*x(1)(3)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{1}{3}{4}{3}{4}{4}) =
(-y_{1, 4} y_{4, 3})  \del{1}{3}{3}{4} +(y_{1, 4} y_{3, 3})  \del{1}{4}{3}{4} +(-y_{1, 3} y_{1, 4})  \del{3}{4}{3}{4} +(-y_{1, 3} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{3, 3} x_{1, 4}+y_{1, 3} x_{3, 4})  \eps{1}{4}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
2,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(1)(3)*x(2)(4)
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(4)*y(4)(1)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(4)*y(2)(1)
Lead Term of Product:
y(1)(4)*y(2)(1)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(4)(1)*x(3)(4)+y(3)(1)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(1)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,3,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(4)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,3,4
Quotient:
x(3)(4)
Lead Term of Product:
-y(2)(3)*y(4)(1)*x(1)(4)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(3)(4)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(1)(3)*x(2)(4)+y(3)(3)*y(4)(1)*x(1)(4)*x(2)(4)+y(1)(4)*y(4)(1)*x(2)(4)*x(3)(3)-y(2)(4)*y(4)(1)*x(1)(3)*x(3)(4)+y(2)(1)*y(4)(4)*x(1)(3)*x(3)(4)-y(1)(3)*y(4)(1)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(1)*x(1)(3)*x(4)(4)-y(2)(1)*y(3)(4)*x(1)(3)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{2}{3}{4}{1}{4}{4}) =
(-y_{1, 4} y_{4, 1})  \del{2}{3}{3}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{1, 4} y_{2, 1})  \del{3}{4}{3}{4} +(-y_{4, 1} x_{3, 4}+y_{3, 1} x_{4, 4})  \eps{1}{2}{3}{4} +(-y_{2, 1} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{3}{4} +(-x_{4, 4})  \lam{1}{2}{3}{1}{3}{4} +(x_{3, 4})  \lam{1}{2}{4}{1}{3}{4} +(-x_{2, 4})  \lam{1}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,3
3,4
Lam:
2,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(3)*x(2)(4)
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(4)*y(4)(2)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(2)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(4)*y(2)(2)
Lead Term of Product:
y(1)(4)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(4)(2)*x(3)(4)+y(3)(2)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(2)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(2)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(2)*x(2)(4)+y(2)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
2,3,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(2)(3)*y(3)(2)*x(1)(4)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
2,3,4
Quotient:
x(3)(4)
Lead Term of Product:
-y(2)(3)*y(4)(2)*x(1)(4)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
2,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(2)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(3)(4)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(2)(4))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(3)*x(2)(4)+y(3)(3)*y(4)(2)*x(1)(4)*x(2)(4)+y(1)(4)*y(4)(2)*x(2)(4)*x(3)(3)-y(2)(4)*y(4)(2)*x(1)(3)*x(3)(4)+y(2)(2)*y(4)(4)*x(1)(3)*x(3)(4)-y(1)(3)*y(4)(2)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(2)*x(1)(3)*x(4)(4)-y(2)(2)*y(3)(4)*x(1)(3)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{2}{3}{4}{2}{4}{4}) =
(-y_{1, 4} y_{4, 2})  \del{2}{3}{3}{4} +(y_{1, 4} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{1, 4} y_{2, 2})  \del{3}{4}{3}{4} +(-y_{4, 2} x_{3, 4}+y_{3, 2} x_{4, 4})  \eps{1}{2}{3}{4} +(-y_{2, 2} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{3, 2} x_{2, 4}+y_{2, 2} x_{3, 4})  \eps{1}{4}{3}{4} +(-x_{4, 4})  \lam{1}{2}{3}{2}{3}{4} +(x_{3, 4})  \lam{1}{2}{4}{2}{3}{4} +(-x_{2, 4})  \lam{1}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,3
3,4
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(3)*x(2)(4)
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(4)*y(4)(3)
Lead Term of Product:
y(1)(4)*y(4)(3)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(3)
Lead Term of Product:
-y(1)(4)*y(3)(3)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(4)*y(2)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
-y(4)(3)*x(3)(4)+y(3)(3)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(3)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(3)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(3)*x(2)(4)+y(2)(3)*x(3)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(3))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(2)(4))*(y(3)(4)*x(1)(3)-y(3)(3)*x(1)(4)-y(1)(4)*x(3)(3)+y(1)(3)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(3)*x(2)(4)+y(3)(3)*y(4)(3)*x(1)(4)*x(2)(4)+y(1)(4)*y(4)(3)*x(2)(4)*x(3)(3)-y(2)(4)*y(4)(3)*x(1)(3)*x(3)(4)+y(2)(3)*y(4)(4)*x(1)(3)*x(3)(4)-y(1)(3)*y(4)(3)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(3)*x(1)(3)*x(4)(4)-y(2)(3)*y(3)(4)*x(1)(3)*x(4)(4)
-----------
TeX output:
S(\eps{1}{3}{3}{4}, \lam{2}{3}{4}{3}{4}{4}) =
(-y_{1, 4} y_{4, 3})  \del{2}{3}{3}{4} +(y_{1, 4} y_{3, 3})  \del{2}{4}{3}{4} +(-y_{1, 4} y_{2, 3})  \del{3}{4}{3}{4} +(-y_{4, 3} x_{3, 4}+y_{3, 3} x_{4, 4})  \eps{1}{2}{3}{4} +(-y_{2, 3} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{3, 3} x_{2, 4}+y_{2, 3} x_{3, 4})  \eps{1}{4}{3}{4}
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,4
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,2
1,3
Quotient:
y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(2)*y(4)(3)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,3
Quotient:
-y(1)(3)*y(4)(1)-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,3
Quotient:
-y(1)(2)*y(2)(3)
Lead Term of Product:
y(1)(2)*y(2)(3)*x(1)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(1)(3)*y(2)(1)+y(1)(1)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
y(1)(2)*y(1)(3)
Lead Term of Product:
-y(1)(2)*y(1)(3)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
-2*y(1)(1)*y(1)(3)
Lead Term of Product:
2*y(1)(1)*y(1)(3)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(3)*x(1)(3)+y(1)(3)*x(4)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(1)*x(1)(3)-y(1)(1)*x(4)(3)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(1)(3)*x(2)(3)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(1)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*x(1)(3)+y(1)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-x(1)(3)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(3)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(4)(2)*x(1)(3)+y(2)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(2)(3)-y(1)(2)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(4)(3)+y(1)(2)*y(2)(3)*x(4)(3)) - (-y(2)(3)*x(1)(3))*(y(4)(2)*x(1)(1)-y(4)(1)*x(1)(2)-y(1)(2)*x(4)(1)+y(1)(1)*x(4)(2))
-------
Rewrite:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(3)+y(2)(3)*y(4)(1)*x(1)(2)*x(1)(3)-y(1)(3)*y(4)(2)*x(1)(1)*x(2)(3)+y(1)(2)*y(4)(3)*x(1)(1)*x(2)(3)+y(1)(2)*y(2)(3)*x(1)(3)*x(4)(1)-y(1)(1)*y(2)(3)*x(1)(3)*x(4)(2)+y(1)(3)*y(2)(2)*x(1)(1)*x(4)(3)-y(1)(2)*y(2)(3)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{4}{1}{2}, \lam{1}{2}{4}{2}{3}{3}) =
(y_{1, 2} y_{4, 3})  \del{1}{2}{1}{3} +(-y_{1, 3} y_{4, 1}-y_{1, 1} y_{4, 3})  \del{1}{2}{2}{3} +(-y_{1, 2} y_{2, 3})  \del{1}{4}{1}{3} +(y_{1, 3} y_{2, 1}+y_{1, 1} y_{2, 3})  \del{1}{4}{2}{3} +(y_{1, 2} y_{1, 3})  \del{2}{4}{1}{3} +(-2 y_{1, 1} y_{1, 3})  \del{2}{4}{2}{3} +(-y_{4, 3} x_{1, 3}+y_{1, 3} x_{4, 3})  \eps{1}{2}{1}{2} +(y_{4, 1} x_{1, 3}-y_{1, 1} x_{4, 3})  \eps{1}{2}{2}{3} +(-y_{1, 3} x_{2, 3})  \eps{1}{4}{1}{2} +(-y_{2, 1} x_{1, 3}+y_{1, 1} x_{2, 3})  \eps{1}{4}{2}{3} +(-x_{1, 3})  \lam{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,4
2,3,4
Lead Term of Spoly:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(2)*y(4)(3)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(3)*y(4)(1)-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(1)*y(4)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(1)(2)*y(2)(3)
Lead Term of Product:
y(1)(2)*y(2)(3)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(3)*y(2)(1)+y(1)(1)*y(2)(3)
Lead Term of Product:
-y(1)(3)*y(2)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
-y(1)(1)*y(2)(2)
Lead Term of Product:
y(1)(1)*y(2)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(2)*y(1)(3)
Lead Term of Product:
-y(1)(2)*y(1)(3)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-2*y(1)(1)*y(1)(3)
Lead Term of Product:
2*y(1)(1)*y(1)(3)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(1)*y(1)(2)
Lead Term of Product:
-y(1)(1)*y(1)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(3)*x(1)(4)+y(1)(3)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(1)*x(1)(4)-y(1)(1)*x(4)(4)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(1)(3)*x(2)(4)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(3)*y(4)(2)*x(1)(4)+y(2)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(2)(4)-y(1)(2)*y(4)(3)*x(2)(4)-y(1)(3)*y(2)(2)*x(4)(4)+y(1)(2)*y(2)(3)*x(4)(4)) - (-y(2)(3)*x(1)(4))*(y(4)(2)*x(1)(1)-y(4)(1)*x(1)(2)-y(1)(2)*x(4)(1)+y(1)(1)*x(4)(2))
-------
Rewrite:
-y(2)(2)*y(4)(3)*x(1)(1)*x(1)(4)+y(2)(3)*y(4)(1)*x(1)(2)*x(1)(4)-y(1)(3)*y(4)(2)*x(1)(1)*x(2)(4)+y(1)(2)*y(4)(3)*x(1)(1)*x(2)(4)+y(1)(2)*y(2)(3)*x(1)(4)*x(4)(1)-y(1)(1)*y(2)(3)*x(1)(4)*x(4)(2)+y(1)(3)*y(2)(2)*x(1)(1)*x(4)(4)-y(1)(2)*y(2)(3)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{1}{2}, \lam{1}{2}{4}{2}{3}{4}) =
(y_{1, 2} y_{4, 3})  \del{1}{2}{1}{4} +(-y_{1, 3} y_{4, 1}-y_{1, 1} y_{4, 3})  \del{1}{2}{2}{4} +(y_{1, 1} y_{4, 2})  \del{1}{2}{3}{4} +(-y_{1, 2} y_{2, 3})  \del{1}{4}{1}{4} +(y_{1, 3} y_{2, 1}+y_{1, 1} y_{2, 3})  \del{1}{4}{2}{4} +(-y_{1, 1} y_{2, 2})  \del{1}{4}{3}{4} +(y_{1, 2} y_{1, 3})  \del{2}{4}{1}{4} +(-2 y_{1, 1} y_{1, 3})  \del{2}{4}{2}{4} +(y_{1, 1} y_{1, 2})  \del{2}{4}{3}{4} +(-y_{4, 3} x_{1, 4}+y_{1, 3} x_{4, 4})  \eps{1}{2}{1}{2} +(y_{4, 1} x_{1, 4}-y_{1, 1} x_{4, 4})  \eps{1}{2}{2}{3} +(-y_{1, 3} x_{2, 4})  \eps{1}{4}{1}{2} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{2}{3} +(-x_{1, 4})  \lam{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,4
2,4,4
Lead Term of Spoly:
-y(2)(2)*y(4)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
y(1)(2)*y(4)(4)
Lead Term of Product:
-y(1)(2)*y(4)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(1)(4)*y(4)(1)-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(1)(2)*y(2)(4)
Lead Term of Product:
y(1)(2)*y(2)(4)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(4)*y(2)(1)+y(1)(1)*y(2)(4)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(2)*y(1)(4)
Lead Term of Product:
-y(1)(2)*y(1)(4)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-2*y(1)(1)*y(1)(4)
Lead Term of Product:
2*y(1)(1)*y(1)(4)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
y(4)(1)*x(1)(4)-y(1)(1)*x(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(4)(2)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(4)*y(4)(2)*x(1)(4)+y(2)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(2)(4)-y(1)(2)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(2)*x(4)(4)+y(1)(2)*y(2)(4)*x(4)(4)) - (-y(2)(4)*x(1)(4))*(y(4)(2)*x(1)(1)-y(4)(1)*x(1)(2)-y(1)(2)*x(4)(1)+y(1)(1)*x(4)(2))
-------
Rewrite:
-y(2)(2)*y(4)(4)*x(1)(1)*x(1)(4)+y(2)(4)*y(4)(1)*x(1)(2)*x(1)(4)-y(1)(4)*y(4)(2)*x(1)(1)*x(2)(4)+y(1)(2)*y(4)(4)*x(1)(1)*x(2)(4)+y(1)(2)*y(2)(4)*x(1)(4)*x(4)(1)-y(1)(1)*y(2)(4)*x(1)(4)*x(4)(2)+y(1)(4)*y(2)(2)*x(1)(1)*x(4)(4)-y(1)(2)*y(2)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{1}{2}, \lam{1}{2}{4}{2}{4}{4}) =
(y_{1, 2} y_{4, 4})  \del{1}{2}{1}{4} +(-y_{1, 4} y_{4, 1}-y_{1, 1} y_{4, 4})  \del{1}{2}{2}{4} +(-y_{1, 2} y_{2, 4})  \del{1}{4}{1}{4} +(y_{1, 4} y_{2, 1}+y_{1, 1} y_{2, 4})  \del{1}{4}{2}{4} +(y_{1, 2} y_{1, 4})  \del{2}{4}{1}{4} +(-2 y_{1, 1} y_{1, 4})  \del{2}{4}{2}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{2}{1}{2} +(y_{4, 1} x_{1, 4}-y_{1, 1} x_{4, 4})  \eps{1}{2}{2}{4} +(-y_{1, 4} x_{2, 4})  \eps{1}{4}{1}{2} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{2}{4} +(-x_{1, 4})  \lam{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,3
1,3
Quotient:
y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(2)*y(4)(3)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
-y(1)(3)*y(4)(1)-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,3
Quotient:
-y(1)(2)*y(3)(3)
Lead Term of Product:
y(1)(2)*y(3)(3)*x(1)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(1)(3)*y(3)(1)+y(1)(1)*y(3)(3)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
y(1)(2)*y(1)(3)
Lead Term of Product:
-y(1)(2)*y(1)(3)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-2*y(1)(1)*y(1)(3)
Lead Term of Product:
2*y(1)(1)*y(1)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(1)(3)+y(1)(3)*x(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
y(4)(1)*x(1)(3)-y(1)(1)*x(4)(3)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(1)(3)*x(3)(3)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(1)(3)+y(1)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(1)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(2)*x(1)(3)+y(3)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(3)(3)-y(1)(2)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(2)*x(4)(3)+y(1)(2)*y(3)(3)*x(4)(3)) - (-y(3)(3)*x(1)(3))*(y(4)(2)*x(1)(1)-y(4)(1)*x(1)(2)-y(1)(2)*x(4)(1)+y(1)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(3)+y(3)(3)*y(4)(1)*x(1)(2)*x(1)(3)-y(1)(3)*y(4)(2)*x(1)(1)*x(3)(3)+y(1)(2)*y(4)(3)*x(1)(1)*x(3)(3)+y(1)(2)*y(3)(3)*x(1)(3)*x(4)(1)-y(1)(1)*y(3)(3)*x(1)(3)*x(4)(2)+y(1)(3)*y(3)(2)*x(1)(1)*x(4)(3)-y(1)(2)*y(3)(3)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{4}{1}{2}, \lam{1}{3}{4}{2}{3}{3}) =
(y_{1, 2} y_{4, 3})  \del{1}{3}{1}{3} +(-y_{1, 3} y_{4, 1}-y_{1, 1} y_{4, 3})  \del{1}{3}{2}{3} +(-y_{1, 2} y_{3, 3})  \del{1}{4}{1}{3} +(y_{1, 3} y_{3, 1}+y_{1, 1} y_{3, 3})  \del{1}{4}{2}{3} +(y_{1, 2} y_{1, 3})  \del{3}{4}{1}{3} +(-2 y_{1, 1} y_{1, 3})  \del{3}{4}{2}{3} +(-y_{4, 3} x_{1, 3}+y_{1, 3} x_{4, 3})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{1, 3}-y_{1, 1} x_{4, 3})  \eps{1}{3}{2}{3} +(-y_{1, 3} x_{3, 3})  \eps{1}{4}{1}{2} +(-y_{3, 1} x_{1, 3}+y_{1, 1} x_{3, 3})  \eps{1}{4}{2}{3} +(-x_{1, 3})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,3
1,4
Quotient:
y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(2)*y(4)(3)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(1)(3)*y(4)(1)-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(1)*y(4)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(1)(2)*y(3)(3)
Lead Term of Product:
y(1)(2)*y(3)(3)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(3)*y(3)(1)+y(1)(1)*y(3)(3)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
-y(1)(1)*y(3)(2)
Lead Term of Product:
y(1)(1)*y(3)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(2)*y(1)(3)
Lead Term of Product:
-y(1)(2)*y(1)(3)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-2*y(1)(1)*y(1)(3)
Lead Term of Product:
2*y(1)(1)*y(1)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(1)*y(1)(2)
Lead Term of Product:
-y(1)(1)*y(1)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(1)(4)+y(1)(3)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
y(4)(1)*x(1)(4)-y(1)(1)*x(4)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(1)(3)*x(3)(4)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(1)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(1)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(3)*x(3)(4)-y(1)(3)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(3)*x(4)(4)) - (-y(3)(3)*x(1)(4))*(y(4)(2)*x(1)(1)-y(4)(1)*x(1)(2)-y(1)(2)*x(4)(1)+y(1)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(1)*x(1)(4)+y(3)(3)*y(4)(1)*x(1)(2)*x(1)(4)-y(1)(3)*y(4)(2)*x(1)(1)*x(3)(4)+y(1)(2)*y(4)(3)*x(1)(1)*x(3)(4)+y(1)(2)*y(3)(3)*x(1)(4)*x(4)(1)-y(1)(1)*y(3)(3)*x(1)(4)*x(4)(2)+y(1)(3)*y(3)(2)*x(1)(1)*x(4)(4)-y(1)(2)*y(3)(3)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{1}{2}, \lam{1}{3}{4}{2}{3}{4}) =
(y_{1, 2} y_{4, 3})  \del{1}{3}{1}{4} +(-y_{1, 3} y_{4, 1}-y_{1, 1} y_{4, 3})  \del{1}{3}{2}{4} +(y_{1, 1} y_{4, 2})  \del{1}{3}{3}{4} +(-y_{1, 2} y_{3, 3})  \del{1}{4}{1}{4} +(y_{1, 3} y_{3, 1}+y_{1, 1} y_{3, 3})  \del{1}{4}{2}{4} +(-y_{1, 1} y_{3, 2})  \del{1}{4}{3}{4} +(y_{1, 2} y_{1, 3})  \del{3}{4}{1}{4} +(-2 y_{1, 1} y_{1, 3})  \del{3}{4}{2}{4} +(y_{1, 1} y_{1, 2})  \del{3}{4}{3}{4} +(-y_{4, 3} x_{1, 4}+y_{1, 3} x_{4, 4})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{1, 4}-y_{1, 1} x_{4, 4})  \eps{1}{3}{2}{3} +(-y_{1, 3} x_{3, 4})  \eps{1}{4}{1}{2} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{2}{3} +(-x_{1, 4})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,3
1,4
Quotient:
y(1)(2)*y(4)(4)
Lead Term of Product:
-y(1)(2)*y(4)(4)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(1)(4)*y(4)(1)-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(1)(2)*y(3)(4)
Lead Term of Product:
y(1)(2)*y(3)(4)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(1)(4)*y(3)(1)+y(1)(1)*y(3)(4)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(2)*y(1)(4)
Lead Term of Product:
-y(1)(2)*y(1)(4)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-2*y(1)(1)*y(1)(4)
Lead Term of Product:
2*y(1)(1)*y(1)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
y(4)(1)*x(1)(4)-y(1)(1)*x(4)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(2)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(4)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(1)(4))*(y(4)(2)*x(1)(1)-y(4)(1)*x(1)(2)-y(1)(2)*x(4)(1)+y(1)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(1)*x(1)(4)+y(3)(4)*y(4)(1)*x(1)(2)*x(1)(4)-y(1)(4)*y(4)(2)*x(1)(1)*x(3)(4)+y(1)(2)*y(4)(4)*x(1)(1)*x(3)(4)+y(1)(2)*y(3)(4)*x(1)(4)*x(4)(1)-y(1)(1)*y(3)(4)*x(1)(4)*x(4)(2)+y(1)(4)*y(3)(2)*x(1)(1)*x(4)(4)-y(1)(2)*y(3)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{1}{2}, \lam{1}{3}{4}{2}{4}{4}) =
(y_{1, 2} y_{4, 4})  \del{1}{3}{1}{4} +(-y_{1, 4} y_{4, 1}-y_{1, 1} y_{4, 4})  \del{1}{3}{2}{4} +(-y_{1, 2} y_{3, 4})  \del{1}{4}{1}{4} +(y_{1, 4} y_{3, 1}+y_{1, 1} y_{3, 4})  \del{1}{4}{2}{4} +(y_{1, 2} y_{1, 4})  \del{3}{4}{1}{4} +(-2 y_{1, 1} y_{1, 4})  \del{3}{4}{2}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{1, 4}-y_{1, 1} x_{4, 4})  \eps{1}{3}{2}{4} +(-y_{1, 4} x_{3, 4})  \eps{1}{4}{1}{2} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{2}{4} +(-x_{1, 4})  \lam{1}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,4
1,2
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,2
Lam:
2,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(3)
Divisor:
Delta
2,3
1,3
Quotient:
y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(2)*y(4)(3)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-y(1)(3)*y(4)(1)-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
-y(1)(2)*y(3)(3)
Lead Term of Product:
y(1)(2)*y(3)(3)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(1)(3)*y(3)(1)+y(1)(1)*y(3)(3)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-2*y(1)(3)*y(2)(1)
Lead Term of Product:
2*y(1)(3)*y(2)(1)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(4)(3)*x(3)(3)-y(3)(3)*x(4)(3)
Lead Term of Product:
y(2)(2)*y(4)(3)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(4)(2)*x(3)(3)+y(3)(2)*x(4)(3)
Lead Term of Product:
-y(2)(3)*y(4)(2)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(2)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
y(4)(1)*x(2)(3)-y(2)(1)*x(4)(3)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(3)+y(2)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(3)*x(4)(3)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(3)*x(3)(3)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(2)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(2)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(2)*x(2)(3)+y(3)(2)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(2)*x(3)(3)-y(2)(2)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(2)*x(4)(3)+y(2)(2)*y(3)(3)*x(4)(3)) - (-y(3)(3)*x(2)(3))*(y(4)(2)*x(1)(1)-y(4)(1)*x(1)(2)-y(1)(2)*x(4)(1)+y(1)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(3)+y(3)(3)*y(4)(1)*x(1)(2)*x(2)(3)-y(2)(3)*y(4)(2)*x(1)(1)*x(3)(3)+y(2)(2)*y(4)(3)*x(1)(1)*x(3)(3)+y(1)(2)*y(3)(3)*x(2)(3)*x(4)(1)-y(1)(1)*y(3)(3)*x(2)(3)*x(4)(2)+y(2)(3)*y(3)(2)*x(1)(1)*x(4)(3)-y(2)(2)*y(3)(3)*x(1)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{4}{1}{2}, \lam{2}{3}{4}{2}{3}{3}) =
(y_{1, 2} y_{4, 3})  \del{2}{3}{1}{3} +(-y_{1, 3} y_{4, 1}-y_{1, 1} y_{4, 3})  \del{2}{3}{2}{3} +(-y_{1, 2} y_{3, 3})  \del{2}{4}{1}{3} +(y_{1, 3} y_{3, 1}+y_{1, 1} y_{3, 3})  \del{2}{4}{2}{3} +(y_{1, 3} y_{2, 2})  \del{3}{4}{1}{3} +(-2 y_{1, 3} y_{2, 1})  \del{3}{4}{2}{3} +(y_{4, 3} x_{3, 3}-y_{3, 3} x_{4, 3})  \eps{1}{2}{1}{2} +(-y_{4, 2} x_{3, 3}+y_{3, 2} x_{4, 3})  \eps{1}{2}{1}{3} +(-y_{4, 3} x_{2, 3})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{2, 3}-y_{2, 1} x_{4, 3})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{2, 3}+y_{2, 1} x_{3, 3})  \eps{1}{4}{2}{3} +(y_{1, 3} x_{4, 3})  \eps{2}{3}{1}{2} +(-y_{1, 3} x_{3, 3})  \eps{2}{4}{1}{2} +(-x_{2, 3})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,4
1,2
Lam:
2,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(2)*y(4)(3)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(3)*y(4)(1)-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(1)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(1)(2)*y(3)(3)
Lead Term of Product:
y(1)(2)*y(3)(3)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(3)*y(3)(1)+y(1)(1)*y(3)(3)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(1)*y(3)(2)
Lead Term of Product:
y(1)(1)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-2*y(1)(3)*y(2)(1)
Lead Term of Product:
2*y(1)(3)*y(2)(1)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(2)*y(2)(1)
Lead Term of Product:
-y(1)(2)*y(2)(1)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(4)(3)*x(3)(4)-y(3)(3)*x(4)(4)
Lead Term of Product:
y(2)(2)*y(4)(3)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(4)(2)*x(3)(4)+y(3)(2)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(2)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
y(4)(1)*x(2)(4)-y(2)(1)*x(4)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(3)*x(4)(4)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(3)*x(3)(4)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(3)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(3)*x(2)(4)+y(2)(3)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(3)*x(3)(4)-y(2)(3)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(3)*x(4)(4)) - (-y(3)(3)*x(2)(4))*(y(4)(2)*x(1)(1)-y(4)(1)*x(1)(2)-y(1)(2)*x(4)(1)+y(1)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(4)+y(3)(3)*y(4)(1)*x(1)(2)*x(2)(4)-y(2)(3)*y(4)(2)*x(1)(1)*x(3)(4)+y(2)(2)*y(4)(3)*x(1)(1)*x(3)(4)+y(1)(2)*y(3)(3)*x(2)(4)*x(4)(1)-y(1)(1)*y(3)(3)*x(2)(4)*x(4)(2)+y(2)(3)*y(3)(2)*x(1)(1)*x(4)(4)-y(2)(2)*y(3)(3)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{1}{2}, \lam{2}{3}{4}{2}{3}{4}) =
(y_{1, 2} y_{4, 3})  \del{2}{3}{1}{4} +(-y_{1, 3} y_{4, 1}-y_{1, 1} y_{4, 3})  \del{2}{3}{2}{4} +(y_{1, 1} y_{4, 2})  \del{2}{3}{3}{4} +(-y_{1, 2} y_{3, 3})  \del{2}{4}{1}{4} +(y_{1, 3} y_{3, 1}+y_{1, 1} y_{3, 3})  \del{2}{4}{2}{4} +(-y_{1, 1} y_{3, 2})  \del{2}{4}{3}{4} +(y_{1, 3} y_{2, 2})  \del{3}{4}{1}{4} +(-2 y_{1, 3} y_{2, 1})  \del{3}{4}{2}{4} +(y_{1, 2} y_{2, 1})  \del{3}{4}{3}{4} +(y_{4, 3} x_{3, 4}-y_{3, 3} x_{4, 4})  \eps{1}{2}{1}{2} +(-y_{4, 2} x_{3, 4}+y_{3, 2} x_{4, 4})  \eps{1}{2}{1}{3} +(-y_{4, 3} x_{2, 4})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{2, 4}-y_{2, 1} x_{4, 4})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{2}{3} +(y_{1, 3} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{1, 3} x_{3, 4})  \eps{2}{4}{1}{2} +(-x_{2, 4})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,4
1,2
Lam:
2,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(2)*y(4)(4)
Lead Term of Product:
-y(1)(2)*y(4)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(4)*y(4)(1)-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(1)(2)*y(3)(4)
Lead Term of Product:
y(1)(2)*y(3)(4)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(4)*y(3)(1)+y(1)(1)*y(3)(4)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(4)*y(2)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-2*y(1)(4)*y(2)(1)
Lead Term of Product:
2*y(1)(4)*y(2)(1)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(4)(4)*x(3)(4)-y(3)(4)*x(4)(4)
Lead Term of Product:
y(2)(2)*y(4)(4)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
-y(4)(2)*x(3)(4)+y(3)(2)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(2)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
y(4)(1)*x(2)(4)-y(2)(1)*x(4)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(2)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(4)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(2)(4))*(y(4)(2)*x(1)(1)-y(4)(1)*x(1)(2)-y(1)(2)*x(4)(1)+y(1)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(1)*x(2)(4)+y(3)(4)*y(4)(1)*x(1)(2)*x(2)(4)-y(2)(4)*y(4)(2)*x(1)(1)*x(3)(4)+y(2)(2)*y(4)(4)*x(1)(1)*x(3)(4)+y(1)(2)*y(3)(4)*x(2)(4)*x(4)(1)-y(1)(1)*y(3)(4)*x(2)(4)*x(4)(2)+y(2)(4)*y(3)(2)*x(1)(1)*x(4)(4)-y(2)(2)*y(3)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{1}{2}, \lam{2}{3}{4}{2}{4}{4}) =
(y_{1, 2} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{1, 4} y_{4, 1}-y_{1, 1} y_{4, 4})  \del{2}{3}{2}{4} +(-y_{1, 2} y_{3, 4})  \del{2}{4}{1}{4} +(y_{1, 4} y_{3, 1}+y_{1, 1} y_{3, 4})  \del{2}{4}{2}{4} +(y_{1, 4} y_{2, 2})  \del{3}{4}{1}{4} +(-2 y_{1, 4} y_{2, 1})  \del{3}{4}{2}{4} +(y_{4, 4} x_{3, 4}-y_{3, 4} x_{4, 4})  \eps{1}{2}{1}{2} +(-y_{4, 2} x_{3, 4}+y_{3, 2} x_{4, 4})  \eps{1}{2}{1}{4} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{2, 4}-y_{2, 1} x_{4, 4})  \eps{1}{3}{2}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{2}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{1, 4} x_{3, 4})  \eps{2}{4}{1}{2} +(-x_{2, 4})  \lam{1}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,4
1,2
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,2,4
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(4)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,2
1,4
Quotient:
y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(3)*y(4)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(4)*y(4)(1)-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(1)(3)*y(2)(4)
Lead Term of Product:
y(1)(3)*y(2)(4)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(2)(1)+y(1)(1)*y(2)(4)
Lead Term of Product:
-y(1)(4)*y(2)(1)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(3)*y(1)(4)
Lead Term of Product:
-y(1)(3)*y(1)(4)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-2*y(1)(1)*y(1)(4)
Lead Term of Product:
2*y(1)(1)*y(1)(4)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(4)(1)*x(1)(4)-y(1)(1)*x(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,3
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(1)*x(1)(4)+y(1)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(2)(4)*y(4)(3)*x(1)(4)+y(2)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(2)(4)-y(1)(3)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(4)(4)+y(1)(3)*y(2)(4)*x(4)(4)) - (-y(2)(4)*x(1)(4))*(y(4)(3)*x(1)(1)-y(4)(1)*x(1)(3)-y(1)(3)*x(4)(1)+y(1)(1)*x(4)(3))
-------
Rewrite:
-y(2)(3)*y(4)(4)*x(1)(1)*x(1)(4)+y(2)(4)*y(4)(1)*x(1)(3)*x(1)(4)-y(1)(4)*y(4)(3)*x(1)(1)*x(2)(4)+y(1)(3)*y(4)(4)*x(1)(1)*x(2)(4)+y(1)(3)*y(2)(4)*x(1)(4)*x(4)(1)-y(1)(1)*y(2)(4)*x(1)(4)*x(4)(3)+y(1)(4)*y(2)(3)*x(1)(1)*x(4)(4)-y(1)(3)*y(2)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{1}{3}, \lam{1}{2}{4}{3}{4}{4}) =
(y_{1, 3} y_{4, 4})  \del{1}{2}{1}{4} +(-y_{1, 4} y_{4, 1}-y_{1, 1} y_{4, 4})  \del{1}{2}{3}{4} +(-y_{1, 3} y_{2, 4})  \del{1}{4}{1}{4} +(y_{1, 4} y_{2, 1}+y_{1, 1} y_{2, 4})  \del{1}{4}{3}{4} +(y_{1, 3} y_{1, 4})  \del{2}{4}{1}{4} +(-2 y_{1, 1} y_{1, 4})  \del{2}{4}{3}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{2}{1}{3} +(y_{4, 1} x_{1, 4}-y_{1, 1} x_{4, 4})  \eps{1}{2}{3}{4} +(-y_{1, 4} x_{2, 4})  \eps{1}{4}{1}{3} +(-y_{2, 1} x_{1, 4}+y_{1, 1} x_{2, 4})  \eps{1}{4}{3}{4} +(-x_{1, 4})  \lam{1}{2}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(1)*x(1)(4)
Divisor:
Delta
1,3
1,4
Quotient:
y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(3)*y(4)(4)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(4)*y(4)(1)-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(1)(3)*y(3)(4)
Lead Term of Product:
y(1)(3)*y(3)(4)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(3)(1)+y(1)(1)*y(3)(4)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(3)*y(1)(4)
Lead Term of Product:
-y(1)(3)*y(1)(4)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-2*y(1)(1)*y(1)(4)
Lead Term of Product:
2*y(1)(1)*y(1)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(1)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
y(4)(1)*x(1)(4)-y(1)(1)*x(4)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,3
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*x(1)(4)+y(1)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(1)(4))*(y(4)(3)*x(1)(1)-y(4)(1)*x(1)(3)-y(1)(3)*x(4)(1)+y(1)(1)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(1)*x(1)(4)+y(3)(4)*y(4)(1)*x(1)(3)*x(1)(4)-y(1)(4)*y(4)(3)*x(1)(1)*x(3)(4)+y(1)(3)*y(4)(4)*x(1)(1)*x(3)(4)+y(1)(3)*y(3)(4)*x(1)(4)*x(4)(1)-y(1)(1)*y(3)(4)*x(1)(4)*x(4)(3)+y(1)(4)*y(3)(3)*x(1)(1)*x(4)(4)-y(1)(3)*y(3)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{1}{3}, \lam{1}{3}{4}{3}{4}{4}) =
(y_{1, 3} y_{4, 4})  \del{1}{3}{1}{4} +(-y_{1, 4} y_{4, 1}-y_{1, 1} y_{4, 4})  \del{1}{3}{3}{4} +(-y_{1, 3} y_{3, 4})  \del{1}{4}{1}{4} +(y_{1, 4} y_{3, 1}+y_{1, 1} y_{3, 4})  \del{1}{4}{3}{4} +(y_{1, 3} y_{1, 4})  \del{3}{4}{1}{4} +(-2 y_{1, 1} y_{1, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{3}{1}{3} +(y_{4, 1} x_{1, 4}-y_{1, 1} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{1, 4} x_{3, 4})  \eps{1}{4}{1}{3} +(-y_{3, 1} x_{1, 4}+y_{1, 1} x_{3, 4})  \eps{1}{4}{3}{4} +(-x_{1, 4})  \lam{1}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,4
1,3
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,3
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(3)*y(4)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(4)*y(4)(1)-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(1)(3)*y(3)(4)
Lead Term of Product:
y(1)(3)*y(3)(4)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(1)+y(1)(1)*y(3)(4)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-2*y(1)(4)*y(2)(1)
Lead Term of Product:
2*y(1)(4)*y(2)(1)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
y(4)(4)*x(3)(4)-y(3)(4)*x(4)(4)
Lead Term of Product:
y(2)(3)*y(4)(4)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
-y(4)(3)*x(3)(4)+y(3)(3)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(3)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
y(4)(1)*x(2)(4)-y(2)(1)*x(4)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,3
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(2)(4))*(y(4)(3)*x(1)(1)-y(4)(1)*x(1)(3)-y(1)(3)*x(4)(1)+y(1)(1)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(1)*x(2)(4)+y(3)(4)*y(4)(1)*x(1)(3)*x(2)(4)-y(2)(4)*y(4)(3)*x(1)(1)*x(3)(4)+y(2)(3)*y(4)(4)*x(1)(1)*x(3)(4)+y(1)(3)*y(3)(4)*x(2)(4)*x(4)(1)-y(1)(1)*y(3)(4)*x(2)(4)*x(4)(3)+y(2)(4)*y(3)(3)*x(1)(1)*x(4)(4)-y(2)(3)*y(3)(4)*x(1)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{1}{3}, \lam{2}{3}{4}{3}{4}{4}) =
(y_{1, 3} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{1, 4} y_{4, 1}-y_{1, 1} y_{4, 4})  \del{2}{3}{3}{4} +(-y_{1, 3} y_{3, 4})  \del{2}{4}{1}{4} +(y_{1, 4} y_{3, 1}+y_{1, 1} y_{3, 4})  \del{2}{4}{3}{4} +(y_{1, 4} y_{2, 3})  \del{3}{4}{1}{4} +(-2 y_{1, 4} y_{2, 1})  \del{3}{4}{3}{4} +(y_{4, 4} x_{3, 4}-y_{3, 4} x_{4, 4})  \eps{1}{2}{1}{3} +(-y_{4, 3} x_{3, 4}+y_{3, 3} x_{4, 4})  \eps{1}{2}{1}{4} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{1}{3} +(y_{4, 1} x_{2, 4}-y_{2, 1} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{1}{4}{3}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{1}{3} +(-y_{1, 4} x_{3, 4})  \eps{2}{4}{1}{3} +(-x_{2, 4})  \lam{1}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
1,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,3
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(3)(2)*y(4)(3)*x(1)(2)
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(1)*y(3)(2)*y(4)(3)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(1)(2)*y(3)(1)+y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(2)*y(3)(1)*y(4)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
y(1)(2)*y(2)(1)-y(1)(1)*y(2)(2)
Lead Term of Product:
y(1)(2)*y(2)(1)*y(4)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-y(4)(2)
Lead Term of Product:
y(2)(2)*y(3)(1)*y(4)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,3
Quotient:
-x(4)(2)
Lead Term of Product:
y(1)(3)*y(2)(2)*y(3)(1)*x(4)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(3))*(-y(2)(2)*y(3)(1)*x(1)(2)+y(2)(1)*y(3)(2)*x(1)(2)+y(1)(2)*y(3)(1)*x(2)(2)-y(1)(1)*y(3)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(3)(2)+y(1)(1)*y(2)(2)*x(3)(2)) - (-y(2)(2)*y(3)(1))*(y(4)(3)*x(1)(2)-y(4)(2)*x(1)(3)-y(1)(3)*x(4)(2)+y(1)(2)*x(4)(3))
-------
Rewrite:
-y(2)(1)*y(3)(2)*y(4)(3)*x(1)(2)+y(2)(2)*y(3)(1)*y(4)(2)*x(1)(3)-y(1)(2)*y(3)(1)*y(4)(3)*x(2)(2)+y(1)(1)*y(3)(2)*y(4)(3)*x(2)(2)+y(1)(2)*y(2)(1)*y(4)(3)*x(3)(2)-y(1)(1)*y(2)(2)*y(4)(3)*x(3)(2)+y(1)(3)*y(2)(2)*y(3)(1)*x(4)(2)-y(1)(2)*y(2)(2)*y(3)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{4}{2}{3}, \lam{1}{2}{3}{1}{2}{2}) =
(-y_{2, 1} y_{3, 2})  \eps{1}{4}{2}{3} +(-y_{1, 2} y_{3, 1}+y_{1, 1} y_{3, 2})  \eps{2}{4}{2}{3} +(y_{1, 2} y_{2, 1}-y_{1, 1} y_{2, 2})  \eps{3}{4}{2}{3} +(-y_{4, 2})  \lam{1}{2}{3}{1}{2}{3} +(-x_{4, 2})  \psi{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,4
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(4)(2)*y(4)(3)*x(1)(2)
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(4)(2)*y(4)(3)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(1)(2)*y(4)(1)+y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(4)(1)*y(4)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-y(4)(2)
Lead Term of Product:
y(2)(2)*y(4)(1)*y(4)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,3
Quotient:
-x(4)(2)
Lead Term of Product:
y(1)(3)*y(2)(2)*y(4)(1)*x(4)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(3))*(-y(2)(2)*y(4)(1)*x(1)(2)+y(2)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(2)(2)-y(1)(1)*y(4)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(4)(2)+y(1)(1)*y(2)(2)*x(4)(2)) - (-y(2)(2)*y(4)(1))*(y(4)(3)*x(1)(2)-y(4)(2)*x(1)(3)-y(1)(3)*x(4)(2)+y(1)(2)*x(4)(3))
-------
Rewrite:
-y(2)(1)*y(4)(2)*y(4)(3)*x(1)(2)+y(2)(2)*y(4)(1)*y(4)(2)*x(1)(3)-y(1)(2)*y(4)(1)*y(4)(3)*x(2)(2)+y(1)(1)*y(4)(2)*y(4)(3)*x(2)(2)+y(1)(3)*y(2)(2)*y(4)(1)*x(4)(2)+y(1)(2)*y(2)(1)*y(4)(3)*x(4)(2)-y(1)(1)*y(2)(2)*y(4)(3)*x(4)(2)-y(1)(2)*y(2)(2)*y(4)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{4}{2}{3}, \lam{1}{2}{4}{1}{2}{2}) =
(-y_{2, 1} y_{4, 2})  \eps{1}{4}{2}{3} +(-y_{1, 2} y_{4, 1}+y_{1, 1} y_{4, 2})  \eps{2}{4}{2}{3} +(-y_{4, 2})  \lam{1}{2}{4}{1}{2}{3} +(-x_{4, 2})  \psi{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,2,4
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(4)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,2
2,4
Quotient:
y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(3)*y(4)(4)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(1)(4)*y(4)(2)-y(1)(2)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
-y(1)(3)*y(2)(4)
Lead Term of Product:
y(1)(3)*y(2)(4)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(2)(2)+y(1)(2)*y(2)(4)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(3)*y(1)(4)
Lead Term of Product:
-y(1)(3)*y(1)(4)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-2*y(1)(2)*y(1)(4)
Lead Term of Product:
2*y(1)(2)*y(1)(4)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(4)(2)*x(1)(4)-y(1)(2)*x(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(2)*x(1)(4)+y(1)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
2,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(2)(4)*y(4)(3)*x(1)(4)+y(2)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(2)(4)-y(1)(3)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(4)(4)+y(1)(3)*y(2)(4)*x(4)(4)) - (-y(2)(4)*x(1)(4))*(y(4)(3)*x(1)(2)-y(4)(2)*x(1)(3)-y(1)(3)*x(4)(2)+y(1)(2)*x(4)(3))
-------
Rewrite:
-y(2)(3)*y(4)(4)*x(1)(2)*x(1)(4)+y(2)(4)*y(4)(2)*x(1)(3)*x(1)(4)-y(1)(4)*y(4)(3)*x(1)(2)*x(2)(4)+y(1)(3)*y(4)(4)*x(1)(2)*x(2)(4)+y(1)(3)*y(2)(4)*x(1)(4)*x(4)(2)-y(1)(2)*y(2)(4)*x(1)(4)*x(4)(3)+y(1)(4)*y(2)(3)*x(1)(2)*x(4)(4)-y(1)(3)*y(2)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{2}{3}, \lam{1}{2}{4}{3}{4}{4}) =
(y_{1, 3} y_{4, 4})  \del{1}{2}{2}{4} +(-y_{1, 4} y_{4, 2}-y_{1, 2} y_{4, 4})  \del{1}{2}{3}{4} +(-y_{1, 3} y_{2, 4})  \del{1}{4}{2}{4} +(y_{1, 4} y_{2, 2}+y_{1, 2} y_{2, 4})  \del{1}{4}{3}{4} +(y_{1, 3} y_{1, 4})  \del{2}{4}{2}{4} +(-2 y_{1, 2} y_{1, 4})  \del{2}{4}{3}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{2}{2}{3} +(y_{4, 2} x_{1, 4}-y_{1, 2} x_{4, 4})  \eps{1}{2}{3}{4} +(-y_{1, 4} x_{2, 4})  \eps{1}{4}{2}{3} +(-y_{2, 2} x_{1, 4}+y_{1, 2} x_{2, 4})  \eps{1}{4}{3}{4} +(-x_{1, 4})  \lam{1}{2}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*y(4)(3)*x(1)(2)
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*y(4)(3)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
-y(1)(2)*y(4)(1)+y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(4)(1)*y(4)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-y(4)(2)
Lead Term of Product:
y(3)(2)*y(4)(1)*y(4)(2)*x(1)(3)
Lead term is well behaved
Divisor:
Psi
1,3,4
1,2,3
Quotient:
-x(4)(2)
Lead Term of Product:
y(1)(3)*y(3)(2)*y(4)(1)*x(4)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(3))*(-y(3)(2)*y(4)(1)*x(1)(2)+y(3)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(3)(2)-y(1)(1)*y(4)(2)*x(3)(2)-y(1)(2)*y(3)(1)*x(4)(2)+y(1)(1)*y(3)(2)*x(4)(2)) - (-y(3)(2)*y(4)(1))*(y(4)(3)*x(1)(2)-y(4)(2)*x(1)(3)-y(1)(3)*x(4)(2)+y(1)(2)*x(4)(3))
-------
Rewrite:
-y(3)(1)*y(4)(2)*y(4)(3)*x(1)(2)+y(3)(2)*y(4)(1)*y(4)(2)*x(1)(3)-y(1)(2)*y(4)(1)*y(4)(3)*x(3)(2)+y(1)(1)*y(4)(2)*y(4)(3)*x(3)(2)+y(1)(3)*y(3)(2)*y(4)(1)*x(4)(2)+y(1)(2)*y(3)(1)*y(4)(3)*x(4)(2)-y(1)(1)*y(3)(2)*y(4)(3)*x(4)(2)-y(1)(2)*y(3)(2)*y(4)(1)*x(4)(3)
-----------
TeX output:
S(\eps{1}{4}{2}{3}, \lam{1}{3}{4}{1}{2}{2}) =
(-y_{3, 1} y_{4, 2})  \eps{1}{4}{2}{3} +(-y_{1, 2} y_{4, 1}+y_{1, 1} y_{4, 2})  \eps{3}{4}{2}{3} +(-y_{4, 2})  \lam{1}{3}{4}{1}{2}{3} +(-x_{4, 2})  \psi{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(2)*x(1)(4)
Divisor:
Delta
1,3
2,4
Quotient:
y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(3)*y(4)(4)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(1)(4)*y(4)(2)-y(1)(2)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
-y(1)(3)*y(3)(4)
Lead Term of Product:
y(1)(3)*y(3)(4)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(1)(4)*y(3)(2)+y(1)(2)*y(3)(4)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
y(1)(3)*y(1)(4)
Lead Term of Product:
-y(1)(3)*y(1)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-2*y(1)(2)*y(1)(4)
Lead Term of Product:
2*y(1)(2)*y(1)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(4)(4)*x(1)(4)+y(1)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
y(4)(2)*x(1)(4)-y(1)(2)*x(4)(4)
Lead Term of Product:
y(3)(4)*y(4)(2)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(2)*x(1)(4)+y(1)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
2,3,4
Quotient:
-x(1)(4)
Lead Term of Product:
y(3)(3)*y(4)(2)*x(1)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(1)(4))*(y(4)(3)*x(1)(2)-y(4)(2)*x(1)(3)-y(1)(3)*x(4)(2)+y(1)(2)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(2)*x(1)(4)+y(3)(4)*y(4)(2)*x(1)(3)*x(1)(4)-y(1)(4)*y(4)(3)*x(1)(2)*x(3)(4)+y(1)(3)*y(4)(4)*x(1)(2)*x(3)(4)+y(1)(3)*y(3)(4)*x(1)(4)*x(4)(2)-y(1)(2)*y(3)(4)*x(1)(4)*x(4)(3)+y(1)(4)*y(3)(3)*x(1)(2)*x(4)(4)-y(1)(3)*y(3)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{2}{3}, \lam{1}{3}{4}{3}{4}{4}) =
(y_{1, 3} y_{4, 4})  \del{1}{3}{2}{4} +(-y_{1, 4} y_{4, 2}-y_{1, 2} y_{4, 4})  \del{1}{3}{3}{4} +(-y_{1, 3} y_{3, 4})  \del{1}{4}{2}{4} +(y_{1, 4} y_{3, 2}+y_{1, 2} y_{3, 4})  \del{1}{4}{3}{4} +(y_{1, 3} y_{1, 4})  \del{3}{4}{2}{4} +(-2 y_{1, 2} y_{1, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{1, 4}+y_{1, 4} x_{4, 4})  \eps{1}{3}{2}{3} +(y_{4, 2} x_{1, 4}-y_{1, 2} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{1, 4} x_{3, 4})  \eps{1}{4}{2}{3} +(-y_{3, 2} x_{1, 4}+y_{1, 2} x_{3, 4})  \eps{1}{4}{3}{4} +(-x_{1, 4})  \lam{1}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,4
2,3
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,3
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(3)*y(4)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(4)*y(4)(2)-y(1)(2)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(1)(3)*y(3)(4)
Lead Term of Product:
y(1)(3)*y(3)(4)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(2)+y(1)(2)*y(3)(4)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-2*y(1)(4)*y(2)(2)
Lead Term of Product:
2*y(1)(4)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(4)*x(3)(4)-y(3)(4)*x(4)(4)
Lead Term of Product:
y(2)(3)*y(4)(4)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
-y(4)(3)*x(3)(4)+y(3)(3)*x(4)(4)
Lead Term of Product:
-y(2)(4)*y(4)(3)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
y(4)(2)*x(2)(4)-y(2)(2)*x(4)(4)
Lead Term of Product:
y(3)(4)*y(4)(2)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(2)*x(2)(4)+y(2)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
2,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(2)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(2))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(2)(4))*(y(4)(3)*x(1)(2)-y(4)(2)*x(1)(3)-y(1)(3)*x(4)(2)+y(1)(2)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(2)*x(2)(4)+y(3)(4)*y(4)(2)*x(1)(3)*x(2)(4)-y(2)(4)*y(4)(3)*x(1)(2)*x(3)(4)+y(2)(3)*y(4)(4)*x(1)(2)*x(3)(4)+y(1)(3)*y(3)(4)*x(2)(4)*x(4)(2)-y(1)(2)*y(3)(4)*x(2)(4)*x(4)(3)+y(2)(4)*y(3)(3)*x(1)(2)*x(4)(4)-y(2)(3)*y(3)(4)*x(1)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{2}{3}, \lam{2}{3}{4}{3}{4}{4}) =
(y_{1, 3} y_{4, 4})  \del{2}{3}{2}{4} +(-y_{1, 4} y_{4, 2}-y_{1, 2} y_{4, 4})  \del{2}{3}{3}{4} +(-y_{1, 3} y_{3, 4})  \del{2}{4}{2}{4} +(y_{1, 4} y_{3, 2}+y_{1, 2} y_{3, 4})  \del{2}{4}{3}{4} +(y_{1, 4} y_{2, 3})  \del{3}{4}{2}{4} +(-2 y_{1, 4} y_{2, 2})  \del{3}{4}{3}{4} +(y_{4, 4} x_{3, 4}-y_{3, 4} x_{4, 4})  \eps{1}{2}{2}{3} +(-y_{4, 3} x_{3, 4}+y_{3, 3} x_{4, 4})  \eps{1}{2}{2}{4} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{2}{3} +(y_{4, 2} x_{2, 4}-y_{2, 2} x_{4, 4})  \eps{1}{3}{3}{4} +(-y_{3, 2} x_{2, 4}+y_{2, 2} x_{3, 4})  \eps{1}{4}{3}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{2}{3} +(-y_{1, 4} x_{3, 4})  \eps{2}{4}{2}{3} +(-x_{2, 4})  \lam{1}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,3
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(3)(2)*y(4)(4)*x(1)(2)
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(1)*y(3)(2)*y(4)(4)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
-y(1)(2)*y(3)(1)+y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(2)*y(3)(1)*y(4)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,4
Quotient:
y(1)(2)*y(2)(1)-y(1)(1)*y(2)(2)
Lead Term of Product:
y(1)(2)*y(2)(1)*y(4)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
-y(4)(2)
Lead Term of Product:
y(2)(2)*y(3)(1)*y(4)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,4
Quotient:
-x(4)(2)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(3)(1)*x(4)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(2)(2)*y(3)(1)*x(1)(2)+y(2)(1)*y(3)(2)*x(1)(2)+y(1)(2)*y(3)(1)*x(2)(2)-y(1)(1)*y(3)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(3)(2)+y(1)(1)*y(2)(2)*x(3)(2)) - (-y(2)(2)*y(3)(1))*(y(4)(4)*x(1)(2)-y(4)(2)*x(1)(4)-y(1)(4)*x(4)(2)+y(1)(2)*x(4)(4))
-------
Rewrite:
-y(2)(1)*y(3)(2)*y(4)(4)*x(1)(2)+y(2)(2)*y(3)(1)*y(4)(2)*x(1)(4)-y(1)(2)*y(3)(1)*y(4)(4)*x(2)(2)+y(1)(1)*y(3)(2)*y(4)(4)*x(2)(2)+y(1)(2)*y(2)(1)*y(4)(4)*x(3)(2)-y(1)(1)*y(2)(2)*y(4)(4)*x(3)(2)+y(1)(4)*y(2)(2)*y(3)(1)*x(4)(2)-y(1)(2)*y(2)(2)*y(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{2}{4}, \lam{1}{2}{3}{1}{2}{2}) =
(-y_{2, 1} y_{3, 2})  \eps{1}{4}{2}{4} +(-y_{1, 2} y_{3, 1}+y_{1, 1} y_{3, 2})  \eps{2}{4}{2}{4} +(y_{1, 2} y_{2, 1}-y_{1, 1} y_{2, 2})  \eps{3}{4}{2}{4} +(-y_{4, 2})  \lam{1}{2}{3}{1}{2}{4} +(-x_{4, 2})  \psi{1}{2}{3}{1}{2}{4}
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,4
1,2,2
Lead Term of Spoly:
-y(2)(1)*y(4)(2)*y(4)(4)*x(1)(2)
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(4)(2)*y(4)(4)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
-y(1)(2)*y(4)(1)+y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(4)(1)*y(4)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-y(4)(2)
Lead Term of Product:
y(2)(2)*y(4)(1)*y(4)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,4
Quotient:
-x(4)(2)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(4)(1)*x(4)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(2)(2)*y(4)(1)*x(1)(2)+y(2)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(2)(2)-y(1)(1)*y(4)(2)*x(2)(2)-y(1)(2)*y(2)(1)*x(4)(2)+y(1)(1)*y(2)(2)*x(4)(2)) - (-y(2)(2)*y(4)(1))*(y(4)(4)*x(1)(2)-y(4)(2)*x(1)(4)-y(1)(4)*x(4)(2)+y(1)(2)*x(4)(4))
-------
Rewrite:
-y(2)(1)*y(4)(2)*y(4)(4)*x(1)(2)+y(2)(2)*y(4)(1)*y(4)(2)*x(1)(4)-y(1)(2)*y(4)(1)*y(4)(4)*x(2)(2)+y(1)(1)*y(4)(2)*y(4)(4)*x(2)(2)+y(1)(4)*y(2)(2)*y(4)(1)*x(4)(2)+y(1)(2)*y(2)(1)*y(4)(4)*x(4)(2)-y(1)(1)*y(2)(2)*y(4)(4)*x(4)(2)-y(1)(2)*y(2)(2)*y(4)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{2}{4}, \lam{1}{2}{4}{1}{2}{2}) =
(-y_{2, 1} y_{4, 2})  \eps{1}{4}{2}{4} +(-y_{1, 2} y_{4, 1}+y_{1, 1} y_{4, 2})  \eps{2}{4}{2}{4} +(-y_{4, 2})  \lam{1}{2}{4}{1}{2}{4} +(-x_{4, 2})  \psi{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*y(4)(4)*x(1)(2)
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*y(4)(4)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,4
Quotient:
-y(1)(2)*y(4)(1)+y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(4)(1)*y(4)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,4
Quotient:
-y(4)(2)
Lead Term of Product:
y(3)(2)*y(4)(1)*y(4)(2)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,3,4
1,2,4
Quotient:
-x(4)(2)
Lead Term of Product:
y(1)(4)*y(3)(2)*y(4)(1)*x(4)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(3)(2)*y(4)(1)*x(1)(2)+y(3)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(3)(2)-y(1)(1)*y(4)(2)*x(3)(2)-y(1)(2)*y(3)(1)*x(4)(2)+y(1)(1)*y(3)(2)*x(4)(2)) - (-y(3)(2)*y(4)(1))*(y(4)(4)*x(1)(2)-y(4)(2)*x(1)(4)-y(1)(4)*x(4)(2)+y(1)(2)*x(4)(4))
-------
Rewrite:
-y(3)(1)*y(4)(2)*y(4)(4)*x(1)(2)+y(3)(2)*y(4)(1)*y(4)(2)*x(1)(4)-y(1)(2)*y(4)(1)*y(4)(4)*x(3)(2)+y(1)(1)*y(4)(2)*y(4)(4)*x(3)(2)+y(1)(4)*y(3)(2)*y(4)(1)*x(4)(2)+y(1)(2)*y(3)(1)*y(4)(4)*x(4)(2)-y(1)(1)*y(3)(2)*y(4)(4)*x(4)(2)-y(1)(2)*y(3)(2)*y(4)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{2}{4}, \lam{1}{3}{4}{1}{2}{2}) =
(-y_{3, 1} y_{4, 2})  \eps{1}{4}{2}{4} +(-y_{1, 2} y_{4, 1}+y_{1, 1} y_{4, 2})  \eps{3}{4}{2}{4} +(-y_{4, 2})  \lam{1}{3}{4}{1}{2}{4} +(-x_{4, 2})  \psi{1}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
2,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,3
1,2,3
Lead Term of Spoly:
-y(2)(1)*y(3)(2)*y(4)(4)*x(1)(3)
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(1)*y(3)(2)*y(4)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(1)(2)*y(3)(1)+y(1)(1)*y(3)(2)
Lead Term of Product:
-y(1)(2)*y(3)(1)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
y(1)(2)*y(2)(1)-y(1)(1)*y(2)(2)
Lead Term of Product:
y(1)(2)*y(2)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(2)(2)*y(3)(1)*y(4)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,3
Quotient:
x(4)(4)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(3)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,2,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(3)(1)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(2)(2)*y(3)(1)*x(1)(3)+y(2)(1)*y(3)(2)*x(1)(3)+y(1)(2)*y(3)(1)*x(2)(3)-y(1)(1)*y(3)(2)*x(2)(3)-y(1)(2)*y(2)(1)*x(3)(3)+y(1)(1)*y(2)(2)*x(3)(3)) - (-y(2)(2)*y(3)(1))*(y(4)(4)*x(1)(3)-y(4)(3)*x(1)(4)-y(1)(4)*x(4)(3)+y(1)(3)*x(4)(4))
-------
Rewrite:
-y(2)(1)*y(3)(2)*y(4)(4)*x(1)(3)+y(2)(2)*y(3)(1)*y(4)(3)*x(1)(4)-y(1)(2)*y(3)(1)*y(4)(4)*x(2)(3)+y(1)(1)*y(3)(2)*y(4)(4)*x(2)(3)+y(1)(2)*y(2)(1)*y(4)(4)*x(3)(3)-y(1)(1)*y(2)(2)*y(4)(4)*x(3)(3)+y(1)(4)*y(2)(2)*y(3)(1)*x(4)(3)-y(1)(3)*y(2)(2)*y(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{3}{4}, \lam{1}{2}{3}{1}{2}{3}) =
(-y_{2, 1} y_{3, 2})  \eps{1}{4}{3}{4} +(-y_{1, 2} y_{3, 1}+y_{1, 1} y_{3, 2})  \eps{2}{4}{3}{4} +(y_{1, 2} y_{2, 1}-y_{1, 1} y_{2, 2})  \eps{3}{4}{3}{4} +(-y_{4, 3})  \lam{1}{2}{3}{1}{2}{4} +(x_{4, 4})  \psi{1}{2}{3}{1}{2}{3} +(-x_{4, 3})  \psi{1}{2}{3}{1}{2}{4}
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,3
1,3,3
Lead Term of Spoly:
-y(2)(1)*y(3)(3)*y(4)(4)*x(1)(3)
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(1)*y(3)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*y(4)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(1)(3)*y(3)(1)+y(1)(1)*y(3)(3)
Lead Term of Product:
-y(1)(3)*y(3)(1)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
y(1)(3)*y(2)(1)-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(3)*y(2)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,3,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(2)(3)*y(3)(1)*y(4)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
1,3,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(3)(1)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(2)(3)*y(3)(1)*x(1)(3)+y(2)(1)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(1)*x(2)(3)-y(1)(1)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(1)*x(3)(3)+y(1)(1)*y(2)(3)*x(3)(3)) - (-y(2)(3)*y(3)(1))*(y(4)(4)*x(1)(3)-y(4)(3)*x(1)(4)-y(1)(4)*x(4)(3)+y(1)(3)*x(4)(4))
-------
Rewrite:
-y(2)(1)*y(3)(3)*y(4)(4)*x(1)(3)+y(2)(3)*y(3)(1)*y(4)(3)*x(1)(4)-y(1)(3)*y(3)(1)*y(4)(4)*x(2)(3)+y(1)(1)*y(3)(3)*y(4)(4)*x(2)(3)+y(1)(3)*y(2)(1)*y(4)(4)*x(3)(3)-y(1)(1)*y(2)(3)*y(4)(4)*x(3)(3)+y(1)(4)*y(2)(3)*y(3)(1)*x(4)(3)-y(1)(3)*y(2)(3)*y(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{3}{4}, \lam{1}{2}{3}{1}{3}{3}) =
(-y_{2, 1} y_{3, 3})  \eps{1}{4}{3}{4} +(-y_{1, 3} y_{3, 1}+y_{1, 1} y_{3, 3})  \eps{2}{4}{3}{4} +(y_{1, 3} y_{2, 1}-y_{1, 1} y_{2, 3})  \eps{3}{4}{3}{4} +(-y_{4, 3})  \lam{1}{2}{3}{1}{3}{4} +(-x_{4, 3})  \psi{1}{2}{3}{1}{3}{4}
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,3
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(3)(3)*y(4)(4)*x(1)(3)
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(2)*y(3)(3)
Lead Term of Product:
-y(2)(2)*y(3)(3)*y(4)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(1)(3)*y(3)(2)+y(1)(2)*y(3)(3)
Lead Term of Product:
-y(1)(3)*y(3)(2)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
y(1)(3)*y(2)(2)-y(1)(2)*y(2)(3)
Lead Term of Product:
y(1)(3)*y(2)(2)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
2,3,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(2)(3)*y(3)(2)*y(4)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,3
2,3,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(3)(2)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(2)(3)*y(3)(2)*x(1)(3)+y(2)(2)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(2)*x(2)(3)-y(1)(2)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(3)(3)+y(1)(2)*y(2)(3)*x(3)(3)) - (-y(2)(3)*y(3)(2))*(y(4)(4)*x(1)(3)-y(4)(3)*x(1)(4)-y(1)(4)*x(4)(3)+y(1)(3)*x(4)(4))
-------
Rewrite:
-y(2)(2)*y(3)(3)*y(4)(4)*x(1)(3)+y(2)(3)*y(3)(2)*y(4)(3)*x(1)(4)-y(1)(3)*y(3)(2)*y(4)(4)*x(2)(3)+y(1)(2)*y(3)(3)*y(4)(4)*x(2)(3)+y(1)(3)*y(2)(2)*y(4)(4)*x(3)(3)-y(1)(2)*y(2)(3)*y(4)(4)*x(3)(3)+y(1)(4)*y(2)(3)*y(3)(2)*x(4)(3)-y(1)(3)*y(2)(3)*y(3)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{3}{4}, \lam{1}{2}{3}{2}{3}{3}) =
(-y_{2, 2} y_{3, 3})  \eps{1}{4}{3}{4} +(-y_{1, 3} y_{3, 2}+y_{1, 2} y_{3, 3})  \eps{2}{4}{3}{4} +(y_{1, 3} y_{2, 2}-y_{1, 2} y_{2, 3})  \eps{3}{4}{3}{4} +(-y_{4, 3})  \lam{1}{2}{3}{2}{3}{4} +(-x_{4, 3})  \psi{1}{2}{3}{2}{3}{4}
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,4
1,2,3
Lead Term of Spoly:
-y(2)(1)*y(4)(2)*y(4)(4)*x(1)(3)
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(4)(2)*y(4)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(1)(2)*y(4)(1)+y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(4)(1)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(2)(2)*y(4)(1)*y(4)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,3
Quotient:
x(4)(4)
Lead Term of Product:
-y(1)(3)*y(2)(2)*y(4)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,2,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(4)*y(2)(2)*y(4)(1)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(2)(2)*y(4)(1)*x(1)(3)+y(2)(1)*y(4)(2)*x(1)(3)+y(1)(2)*y(4)(1)*x(2)(3)-y(1)(1)*y(4)(2)*x(2)(3)-y(1)(2)*y(2)(1)*x(4)(3)+y(1)(1)*y(2)(2)*x(4)(3)) - (-y(2)(2)*y(4)(1))*(y(4)(4)*x(1)(3)-y(4)(3)*x(1)(4)-y(1)(4)*x(4)(3)+y(1)(3)*x(4)(4))
-------
Rewrite:
-y(2)(1)*y(4)(2)*y(4)(4)*x(1)(3)+y(2)(2)*y(4)(1)*y(4)(3)*x(1)(4)-y(1)(2)*y(4)(1)*y(4)(4)*x(2)(3)+y(1)(1)*y(4)(2)*y(4)(4)*x(2)(3)+y(1)(4)*y(2)(2)*y(4)(1)*x(4)(3)+y(1)(2)*y(2)(1)*y(4)(4)*x(4)(3)-y(1)(1)*y(2)(2)*y(4)(4)*x(4)(3)-y(1)(3)*y(2)(2)*y(4)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{3}{4}, \lam{1}{2}{4}{1}{2}{3}) =
(-y_{2, 1} y_{4, 2})  \eps{1}{4}{3}{4} +(-y_{1, 2} y_{4, 1}+y_{1, 1} y_{4, 2})  \eps{2}{4}{3}{4} +(-y_{4, 3})  \lam{1}{2}{4}{1}{2}{4} +(x_{4, 4})  \psi{1}{2}{4}{1}{2}{3} +(-x_{4, 3})  \psi{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,4
1,3,3
Lead Term of Spoly:
-y(2)(1)*y(4)(3)*y(4)(4)*x(1)(3)
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(1)*y(4)(3)
Lead Term of Product:
-y(2)(1)*y(4)(3)*y(4)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(1)(3)*y(4)(1)+y(1)(1)*y(4)(3)
Lead Term of Product:
-y(1)(3)*y(4)(1)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,3,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(2)(3)*y(4)(1)*y(4)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
1,3,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(4)(1)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(2)(3)*y(4)(1)*x(1)(3)+y(2)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(2)(3)-y(1)(1)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(1)*x(4)(3)+y(1)(1)*y(2)(3)*x(4)(3)) - (-y(2)(3)*y(4)(1))*(y(4)(4)*x(1)(3)-y(4)(3)*x(1)(4)-y(1)(4)*x(4)(3)+y(1)(3)*x(4)(4))
-------
Rewrite:
-y(2)(1)*y(4)(3)*y(4)(4)*x(1)(3)+y(2)(3)*y(4)(1)*y(4)(3)*x(1)(4)-y(1)(3)*y(4)(1)*y(4)(4)*x(2)(3)+y(1)(1)*y(4)(3)*y(4)(4)*x(2)(3)+y(1)(4)*y(2)(3)*y(4)(1)*x(4)(3)+y(1)(3)*y(2)(1)*y(4)(4)*x(4)(3)-y(1)(1)*y(2)(3)*y(4)(4)*x(4)(3)-y(1)(3)*y(2)(3)*y(4)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{3}{4}, \lam{1}{2}{4}{1}{3}{3}) =
(-y_{2, 1} y_{4, 3})  \eps{1}{4}{3}{4} +(-y_{1, 3} y_{4, 1}+y_{1, 1} y_{4, 3})  \eps{2}{4}{3}{4} +(-y_{4, 3})  \lam{1}{2}{4}{1}{3}{4} +(-x_{4, 3})  \psi{1}{2}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,4
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(4)(3)*y(4)(4)*x(1)(3)
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(2)*y(4)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*y(4)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(1)(3)*y(4)(2)+y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(3)*y(4)(2)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
2,3,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(2)(3)*y(4)(2)*y(4)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,2,4
2,3,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(4)*y(2)(3)*y(4)(2)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(2)(3)*y(4)(2)*x(1)(3)+y(2)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(2)(3)-y(1)(2)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(4)(3)+y(1)(2)*y(2)(3)*x(4)(3)) - (-y(2)(3)*y(4)(2))*(y(4)(4)*x(1)(3)-y(4)(3)*x(1)(4)-y(1)(4)*x(4)(3)+y(1)(3)*x(4)(4))
-------
Rewrite:
-y(2)(2)*y(4)(3)*y(4)(4)*x(1)(3)+y(2)(3)*y(4)(2)*y(4)(3)*x(1)(4)-y(1)(3)*y(4)(2)*y(4)(4)*x(2)(3)+y(1)(2)*y(4)(3)*y(4)(4)*x(2)(3)+y(1)(4)*y(2)(3)*y(4)(2)*x(4)(3)+y(1)(3)*y(2)(2)*y(4)(4)*x(4)(3)-y(1)(2)*y(2)(3)*y(4)(4)*x(4)(3)-y(1)(3)*y(2)(3)*y(4)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{3}{4}, \lam{1}{2}{4}{2}{3}{3}) =
(-y_{2, 2} y_{4, 3})  \eps{1}{4}{3}{4} +(-y_{1, 3} y_{4, 2}+y_{1, 2} y_{4, 3})  \eps{2}{4}{3}{4} +(-y_{4, 3})  \lam{1}{2}{4}{2}{3}{4} +(-x_{4, 3})  \psi{1}{2}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,3,4
1,2,3
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*y(4)(4)*x(1)(3)
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*y(4)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(2)*y(4)(1)+y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(2)*y(4)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*y(4)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,3,4
1,2,3
Quotient:
x(4)(4)
Lead Term of Product:
-y(1)(3)*y(3)(2)*y(4)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Psi
1,3,4
1,2,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(4)*y(3)(2)*y(4)(1)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(3)(2)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(2)*x(1)(3)+y(1)(2)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(2)*x(3)(3)-y(1)(2)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(2)*x(4)(3)) - (-y(3)(2)*y(4)(1))*(y(4)(4)*x(1)(3)-y(4)(3)*x(1)(4)-y(1)(4)*x(4)(3)+y(1)(3)*x(4)(4))
-------
Rewrite:
-y(3)(1)*y(4)(2)*y(4)(4)*x(1)(3)+y(3)(2)*y(4)(1)*y(4)(3)*x(1)(4)-y(1)(2)*y(4)(1)*y(4)(4)*x(3)(3)+y(1)(1)*y(4)(2)*y(4)(4)*x(3)(3)+y(1)(4)*y(3)(2)*y(4)(1)*x(4)(3)+y(1)(2)*y(3)(1)*y(4)(4)*x(4)(3)-y(1)(1)*y(3)(2)*y(4)(4)*x(4)(3)-y(1)(3)*y(3)(2)*y(4)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{3}{4}, \lam{1}{3}{4}{1}{2}{3}) =
(-y_{3, 1} y_{4, 2})  \eps{1}{4}{3}{4} +(-y_{1, 2} y_{4, 1}+y_{1, 1} y_{4, 2})  \eps{3}{4}{3}{4} +(-y_{4, 3})  \lam{1}{3}{4}{1}{2}{4} +(x_{4, 4})  \psi{1}{3}{4}{1}{2}{3} +(-x_{4, 3})  \psi{1}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*y(4)(4)*x(1)(3)
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*y(4)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*y(4)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(3)*y(4)(1)+y(1)(1)*y(4)(3)
Lead Term of Product:
-y(1)(3)*y(4)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,3,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(3)(3)*y(4)(1)*y(4)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,3,4
1,3,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(4)*y(3)(3)*y(4)(1)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(3)(3)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(3)*x(4)(3)) - (-y(3)(3)*y(4)(1))*(y(4)(4)*x(1)(3)-y(4)(3)*x(1)(4)-y(1)(4)*x(4)(3)+y(1)(3)*x(4)(4))
-------
Rewrite:
-y(3)(1)*y(4)(3)*y(4)(4)*x(1)(3)+y(3)(3)*y(4)(1)*y(4)(3)*x(1)(4)-y(1)(3)*y(4)(1)*y(4)(4)*x(3)(3)+y(1)(1)*y(4)(3)*y(4)(4)*x(3)(3)+y(1)(4)*y(3)(3)*y(4)(1)*x(4)(3)+y(1)(3)*y(3)(1)*y(4)(4)*x(4)(3)-y(1)(1)*y(3)(3)*y(4)(4)*x(4)(3)-y(1)(3)*y(3)(3)*y(4)(1)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{3}{4}, \lam{1}{3}{4}{1}{3}{3}) =
(-y_{3, 1} y_{4, 3})  \eps{1}{4}{3}{4} +(-y_{1, 3} y_{4, 1}+y_{1, 1} y_{4, 3})  \eps{3}{4}{3}{4} +(-y_{4, 3})  \lam{1}{3}{4}{1}{3}{4} +(-x_{4, 3})  \psi{1}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*y(4)(4)*x(1)(3)
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*y(4)(4)*x(1)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(1)(3)*y(4)(2)+y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(3)*y(4)(2)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
2,3,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(3)(3)*y(4)(2)*y(4)(3)*x(1)(4)
Lead term is well behaved
Divisor:
Psi
1,3,4
2,3,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(4)*y(3)(3)*y(4)(2)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(3)(3)*y(4)(2)*x(1)(3)+y(3)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(3)(3)-y(1)(2)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(2)*x(4)(3)+y(1)(2)*y(3)(3)*x(4)(3)) - (-y(3)(3)*y(4)(2))*(y(4)(4)*x(1)(3)-y(4)(3)*x(1)(4)-y(1)(4)*x(4)(3)+y(1)(3)*x(4)(4))
-------
Rewrite:
-y(3)(2)*y(4)(3)*y(4)(4)*x(1)(3)+y(3)(3)*y(4)(2)*y(4)(3)*x(1)(4)-y(1)(3)*y(4)(2)*y(4)(4)*x(3)(3)+y(1)(2)*y(4)(3)*y(4)(4)*x(3)(3)+y(1)(4)*y(3)(3)*y(4)(2)*x(4)(3)+y(1)(3)*y(3)(2)*y(4)(4)*x(4)(3)-y(1)(2)*y(3)(3)*y(4)(4)*x(4)(3)-y(1)(3)*y(3)(3)*y(4)(2)*x(4)(4)
-----------
TeX output:
S(\eps{1}{4}{3}{4}, \lam{1}{3}{4}{2}{3}{3}) =
(-y_{3, 2} y_{4, 3})  \eps{1}{4}{3}{4} +(-y_{1, 3} y_{4, 2}+y_{1, 2} y_{4, 3})  \eps{3}{4}{3}{4} +(-y_{4, 3})  \lam{1}{3}{4}{2}{3}{4} +(-x_{4, 3})  \psi{1}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
1,4
3,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,3
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(3)(3)*x(1)(3)*x(2)(1)
Divisor:
Delta
1,2
1,3
Quotient:
y(2)(2)*y(3)(3)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,3
Quotient:
-y(2)(3)*y(3)(1)
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
1,3
Quotient:
-y(2)(2)*y(2)(3)
Lead Term of Product:
y(2)(2)*y(2)(3)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
y(2)(1)*y(2)(3)
Lead Term of Product:
-y(2)(1)*y(2)(3)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,3
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(3)(3)*x(2)(3)+y(2)(3)*x(3)(3)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(3)(1)*x(2)(3)
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(1)(3)*x(2)(3)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(2)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(1)(1)*x(2)(3)
Lead Term of Product:
y(1)(1)*y(3)(3)*x(2)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-x(2)(3)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(3)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(2)(3)*y(3)(2)*x(1)(3)+y(2)(2)*y(3)(3)*x(1)(3)+y(1)(3)*y(3)(2)*x(2)(3)-y(1)(2)*y(3)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(3)(3)+y(1)(2)*y(2)(3)*x(3)(3)) - (-y(2)(3)*x(1)(3))*(y(3)(2)*x(2)(1)-y(3)(1)*x(2)(2)-y(2)(2)*x(3)(1)+y(2)(1)*x(3)(2))
-------
Rewrite:
-y(2)(2)*y(3)(3)*x(1)(3)*x(2)(1)+y(2)(3)*y(3)(1)*x(1)(3)*x(2)(2)-y(1)(3)*y(3)(2)*x(2)(1)*x(2)(3)+y(1)(2)*y(3)(3)*x(2)(1)*x(2)(3)+y(2)(2)*y(2)(3)*x(1)(3)*x(3)(1)-y(2)(1)*y(2)(3)*x(1)(3)*x(3)(2)+y(1)(3)*y(2)(2)*x(2)(1)*x(3)(3)-y(1)(2)*y(2)(3)*x(2)(1)*x(3)(3)
-----------
TeX output:
S(\eps{2}{3}{1}{2}, \lam{1}{2}{3}{2}{3}{3}) =
(y_{2, 2} y_{3, 3})  \del{1}{2}{1}{3} +(-y_{2, 3} y_{3, 1})  \del{1}{2}{2}{3} +(-y_{2, 2} y_{2, 3})  \del{1}{3}{1}{3} +(y_{2, 1} y_{2, 3})  \del{1}{3}{2}{3} +(y_{1, 3} y_{2, 2})  \del{2}{3}{1}{3} +(-y_{1, 1} y_{2, 3})  \del{2}{3}{2}{3} +(-y_{3, 3} x_{2, 3}+y_{2, 3} x_{3, 3})  \eps{1}{2}{1}{2} +(y_{3, 1} x_{2, 3})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{2, 3})  \eps{1}{3}{2}{3} +(-y_{1, 3} x_{2, 3})  \eps{2}{3}{1}{2} +(y_{1, 1} x_{2, 3})  \eps{2}{3}{2}{3} +(-x_{2, 3})  \lam{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,3
2,3,4
Lead Term of Spoly:
-y(2)(2)*y(3)(3)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(2)(2)*y(3)(3)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(2)(3)*y(3)(1)
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(2)(2)*y(2)(3)
Lead Term of Product:
y(2)(2)*y(2)(3)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(2)(1)*y(2)(3)
Lead Term of Product:
-y(2)(1)*y(2)(3)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(3)(3)*x(2)(4)+y(2)(3)*x(3)(4)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(3)(1)*x(2)(4)
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(1)(3)*x(2)(4)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(1)(1)*x(2)(4)
Lead Term of Product:
y(1)(1)*y(3)(3)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-x(2)(4)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(2)(3)*y(3)(2)*x(1)(4)+y(2)(2)*y(3)(3)*x(1)(4)+y(1)(3)*y(3)(2)*x(2)(4)-y(1)(2)*y(3)(3)*x(2)(4)-y(1)(3)*y(2)(2)*x(3)(4)+y(1)(2)*y(2)(3)*x(3)(4)) - (-y(2)(3)*x(1)(4))*(y(3)(2)*x(2)(1)-y(3)(1)*x(2)(2)-y(2)(2)*x(3)(1)+y(2)(1)*x(3)(2))
-------
Rewrite:
-y(2)(2)*y(3)(3)*x(1)(4)*x(2)(1)+y(2)(3)*y(3)(1)*x(1)(4)*x(2)(2)-y(1)(3)*y(3)(2)*x(2)(1)*x(2)(4)+y(1)(2)*y(3)(3)*x(2)(1)*x(2)(4)+y(2)(2)*y(2)(3)*x(1)(4)*x(3)(1)-y(2)(1)*y(2)(3)*x(1)(4)*x(3)(2)+y(1)(3)*y(2)(2)*x(2)(1)*x(3)(4)-y(1)(2)*y(2)(3)*x(2)(1)*x(3)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{2}, \lam{1}{2}{3}{2}{3}{4}) =
(y_{2, 2} y_{3, 3})  \del{1}{2}{1}{4} +(-y_{2, 3} y_{3, 1})  \del{1}{2}{2}{4} +(-y_{2, 2} y_{2, 3})  \del{1}{3}{1}{4} +(y_{2, 1} y_{2, 3})  \del{1}{3}{2}{4} +(y_{1, 3} y_{2, 2})  \del{2}{3}{1}{4} +(-y_{1, 1} y_{2, 3})  \del{2}{3}{2}{4} +(-y_{3, 3} x_{2, 4}+y_{2, 3} x_{3, 4})  \eps{1}{2}{1}{2} +(y_{3, 1} x_{2, 4})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{2, 4})  \eps{1}{3}{2}{3} +(-y_{1, 3} x_{2, 4})  \eps{2}{3}{1}{2} +(y_{1, 1} x_{2, 4})  \eps{2}{3}{2}{3} +(-x_{2, 4})  \lam{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,3
2,4,4
Lead Term of Spoly:
-y(2)(2)*y(3)(4)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(2)(2)*y(3)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(2)(4)*y(3)(1)
Lead Term of Product:
y(2)(4)*y(3)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(2)(2)*y(2)(4)
Lead Term of Product:
y(2)(2)*y(2)(4)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(2)(1)*y(2)(4)
Lead Term of Product:
-y(2)(1)*y(2)(4)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(4)*y(2)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(1)*y(2)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(3)(4)*x(2)(4)+y(2)(4)*x(3)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
y(3)(1)*x(2)(4)
Lead Term of Product:
y(2)(4)*y(3)(1)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
-y(2)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
y(1)(1)*x(2)(4)
Lead Term of Product:
y(1)(1)*y(3)(4)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(2)(4)*y(3)(2)*x(1)(4)+y(2)(2)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(2)*x(2)(4)-y(1)(2)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(2)*x(3)(4)+y(1)(2)*y(2)(4)*x(3)(4)) - (-y(2)(4)*x(1)(4))*(y(3)(2)*x(2)(1)-y(3)(1)*x(2)(2)-y(2)(2)*x(3)(1)+y(2)(1)*x(3)(2))
-------
Rewrite:
-y(2)(2)*y(3)(4)*x(1)(4)*x(2)(1)+y(2)(4)*y(3)(1)*x(1)(4)*x(2)(2)-y(1)(4)*y(3)(2)*x(2)(1)*x(2)(4)+y(1)(2)*y(3)(4)*x(2)(1)*x(2)(4)+y(2)(2)*y(2)(4)*x(1)(4)*x(3)(1)-y(2)(1)*y(2)(4)*x(1)(4)*x(3)(2)+y(1)(4)*y(2)(2)*x(2)(1)*x(3)(4)-y(1)(2)*y(2)(4)*x(2)(1)*x(3)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{2}, \lam{1}{2}{3}{2}{4}{4}) =
(y_{2, 2} y_{3, 4})  \del{1}{2}{1}{4} +(-y_{2, 4} y_{3, 1})  \del{1}{2}{2}{4} +(-y_{2, 2} y_{2, 4})  \del{1}{3}{1}{4} +(y_{2, 1} y_{2, 4})  \del{1}{3}{2}{4} +(y_{1, 4} y_{2, 2})  \del{2}{3}{1}{4} +(-y_{1, 1} y_{2, 4})  \del{2}{3}{2}{4} +(-y_{3, 4} x_{2, 4}+y_{2, 4} x_{3, 4})  \eps{1}{2}{1}{2} +(y_{3, 1} x_{2, 4})  \eps{1}{2}{2}{4} +(-y_{2, 1} x_{2, 4})  \eps{1}{3}{2}{4} +(-y_{1, 4} x_{2, 4})  \eps{2}{3}{1}{2} +(y_{1, 1} x_{2, 4})  \eps{2}{3}{2}{4} +(-x_{2, 4})  \lam{1}{2}{3}{1}{2}{4}
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(1)(2)*x(2)(1)
Divisor:
Delta
1,2
1,2
Quotient:
y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(2)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,2
Quotient:
-y(2)(2)*y(4)(1)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,2
Quotient:
y(1)(2)*y(3)(1)
Lead Term of Product:
-y(1)(2)*y(3)(1)*x(2)(2)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,2
Quotient:
-y(1)(1)*y(2)(2)
Lead Term of Product:
y(1)(1)*y(2)(2)*x(3)(2)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(4)(1)*x(3)(2)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(1)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(3)(1)*x(2)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(1)(1)*x(4)(2)
Lead Term of Product:
-y(1)(1)*y(3)(2)*x(2)(1)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
y(1)(1)*x(3)(2)
Lead Term of Product:
y(1)(1)*y(4)(2)*x(2)(1)*x(3)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(2)*y(4)(1)*x(1)(2)+y(3)(1)*y(4)(2)*x(1)(2)+y(1)(2)*y(4)(1)*x(3)(2)-y(1)(1)*y(4)(2)*x(3)(2)-y(1)(2)*y(3)(1)*x(4)(2)+y(1)(1)*y(3)(2)*x(4)(2)) - (-y(4)(1)*x(1)(2))*(y(3)(2)*x(2)(1)-y(3)(1)*x(2)(2)-y(2)(2)*x(3)(1)+y(2)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(1)(2)*x(2)(1)+y(3)(1)*y(4)(1)*x(1)(2)*x(2)(2)+y(2)(2)*y(4)(1)*x(1)(2)*x(3)(1)-y(2)(1)*y(4)(1)*x(1)(2)*x(3)(2)-y(1)(2)*y(4)(1)*x(2)(1)*x(3)(2)+y(1)(1)*y(4)(2)*x(2)(1)*x(3)(2)+y(1)(2)*y(3)(1)*x(2)(1)*x(4)(2)-y(1)(1)*y(3)(2)*x(2)(1)*x(4)(2)
-----------
TeX output:
S(\eps{2}{3}{1}{2}, \lam{1}{3}{4}{1}{2}{2}) =
(y_{3, 1} y_{4, 2})  \del{1}{2}{1}{2} +(-y_{2, 2} y_{4, 1})  \del{1}{3}{1}{2} +(y_{1, 2} y_{3, 1})  \del{2}{4}{1}{2} +(-y_{1, 1} y_{2, 2})  \del{3}{4}{1}{2} +(y_{4, 1} x_{3, 2})  \eps{1}{2}{1}{2} +(-y_{3, 1} x_{2, 2})  \eps{1}{4}{1}{2} +(-y_{1, 1} x_{4, 2})  \eps{2}{3}{1}{2} +(y_{1, 1} x_{3, 2})  \eps{2}{4}{1}{2}
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,3,4
1,2,3
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(1)(3)*x(2)(1)
Divisor:
Delta
1,2
1,3
Quotient:
y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,3
Quotient:
-y(3)(1)*y(4)(1)
Lead Term of Product:
y(3)(1)*y(4)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
1,3
Quotient:
-y(2)(2)*y(4)(1)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
y(2)(1)*y(4)(1)
Lead Term of Product:
-y(2)(1)*y(4)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
y(1)(2)*y(3)(1)
Lead Term of Product:
-y(1)(2)*y(3)(1)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
-y(1)(1)*y(3)(1)
Lead Term of Product:
y(1)(1)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
-y(1)(1)*y(2)(2)
Lead Term of Product:
y(1)(1)*y(2)(2)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
y(1)(1)*y(2)(1)
Lead Term of Product:
-y(1)(1)*y(2)(1)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(4)(1)*x(3)(3)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(3)(1)*x(2)(3)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(1)(1)*x(4)(3)
Lead Term of Product:
-y(1)(1)*y(3)(2)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
y(1)(1)*x(3)(3)
Lead Term of Product:
y(1)(1)*y(4)(2)*x(2)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(2)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(2)*x(1)(3)+y(1)(2)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(2)*x(3)(3)-y(1)(2)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(2)*x(4)(3)) - (-y(4)(1)*x(1)(3))*(y(3)(2)*x(2)(1)-y(3)(1)*x(2)(2)-y(2)(2)*x(3)(1)+y(2)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(1)(3)*x(2)(1)+y(3)(1)*y(4)(1)*x(1)(3)*x(2)(2)+y(2)(2)*y(4)(1)*x(1)(3)*x(3)(1)-y(2)(1)*y(4)(1)*x(1)(3)*x(3)(2)-y(1)(2)*y(4)(1)*x(2)(1)*x(3)(3)+y(1)(1)*y(4)(2)*x(2)(1)*x(3)(3)+y(1)(2)*y(3)(1)*x(2)(1)*x(4)(3)-y(1)(1)*y(3)(2)*x(2)(1)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{1}{2}, \lam{1}{3}{4}{1}{2}{3}) =
(y_{3, 1} y_{4, 2})  \del{1}{2}{1}{3} +(-y_{3, 1} y_{4, 1})  \del{1}{2}{2}{3} +(-y_{2, 2} y_{4, 1})  \del{1}{3}{1}{3} +(y_{2, 1} y_{4, 1})  \del{1}{3}{2}{3} +(y_{1, 2} y_{3, 1})  \del{2}{4}{1}{3} +(-y_{1, 1} y_{3, 1})  \del{2}{4}{2}{3} +(-y_{1, 1} y_{2, 2})  \del{3}{4}{1}{3} +(y_{1, 1} y_{2, 1})  \del{3}{4}{2}{3} +(y_{4, 1} x_{3, 3})  \eps{1}{2}{1}{2} +(-y_{3, 1} x_{2, 3})  \eps{1}{4}{1}{2} +(-y_{1, 1} x_{4, 3})  \eps{2}{3}{1}{2} +(y_{1, 1} x_{3, 3})  \eps{2}{4}{1}{2}
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,3,4
1,2,4
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(3)(1)*y(4)(1)
Lead Term of Product:
y(3)(1)*y(4)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(2)(2)*y(4)(1)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
y(2)(1)*y(4)(1)
Lead Term of Product:
-y(2)(1)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(2)*y(3)(1)
Lead Term of Product:
-y(1)(2)*y(3)(1)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(1)(1)*y(3)(1)
Lead Term of Product:
y(1)(1)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(1)(1)*y(2)(2)
Lead Term of Product:
y(1)(1)*y(2)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
y(1)(1)*y(2)(1)
Lead Term of Product:
-y(1)(1)*y(2)(1)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,2
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(2)*x(2)(1)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(2)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(2)*x(1)(4)+y(1)(2)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(2)*x(3)(4)-y(1)(2)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(2)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(2)*x(2)(1)-y(3)(1)*x(2)(2)-y(2)(2)*x(3)(1)+y(2)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(1)(4)*x(2)(1)+y(3)(1)*y(4)(1)*x(1)(4)*x(2)(2)+y(2)(2)*y(4)(1)*x(1)(4)*x(3)(1)-y(2)(1)*y(4)(1)*x(1)(4)*x(3)(2)-y(1)(2)*y(4)(1)*x(2)(1)*x(3)(4)+y(1)(1)*y(4)(2)*x(2)(1)*x(3)(4)+y(1)(2)*y(3)(1)*x(2)(1)*x(4)(4)-y(1)(1)*y(3)(2)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{2}, \lam{1}{3}{4}{1}{2}{4}) =
(y_{3, 1} y_{4, 2})  \del{1}{2}{1}{4} +(-y_{3, 1} y_{4, 1})  \del{1}{2}{2}{4} +(-y_{2, 2} y_{4, 1})  \del{1}{3}{1}{4} +(y_{2, 1} y_{4, 1})  \del{1}{3}{2}{4} +(y_{1, 2} y_{3, 1})  \del{2}{4}{1}{4} +(-y_{1, 1} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{1, 1} y_{2, 2})  \del{3}{4}{1}{4} +(y_{1, 1} y_{2, 1})  \del{3}{4}{2}{4} +(y_{4, 1} x_{3, 4})  \eps{1}{2}{1}{2} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{1}{2} +(-y_{1, 1} x_{4, 4})  \eps{2}{3}{1}{2} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{1}{2}
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
2,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(2)(1)*x(2)(2)
Divisor:
Delta
2,3
1,2
Quotient:
-y(2)(2)*y(4)(1)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(2)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,2
Quotient:
y(2)(2)*y(3)(1)
Lead Term of Product:
-y(2)(2)*y(3)(1)*x(2)(2)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,2
Quotient:
-y(2)(1)*y(2)(2)
Lead Term of Product:
y(2)(1)*y(2)(2)*x(3)(2)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(2)(1)*x(4)(2)
Lead Term of Product:
-y(2)(1)*y(3)(2)*x(2)(1)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(3)(1)*x(2)(2)+y(2)(1)*x(3)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(2)(1)*x(2)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(2)*y(4)(1)*x(2)(2)+y(3)(1)*y(4)(2)*x(2)(2)+y(2)(2)*y(4)(1)*x(3)(2)-y(2)(1)*y(4)(2)*x(3)(2)-y(2)(2)*y(3)(1)*x(4)(2)+y(2)(1)*y(3)(2)*x(4)(2)) - (-y(4)(1)*x(2)(2))*(y(3)(2)*x(2)(1)-y(3)(1)*x(2)(2)-y(2)(2)*x(3)(1)+y(2)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(2)(1)*x(2)(2)+y(3)(1)*y(4)(1)*x(2)(2)^2+y(2)(2)*y(4)(1)*x(2)(2)*x(3)(1)-y(2)(2)*y(4)(1)*x(2)(1)*x(3)(2)+y(2)(1)*y(4)(2)*x(2)(1)*x(3)(2)-y(2)(1)*y(4)(1)*x(2)(2)*x(3)(2)+y(2)(2)*y(3)(1)*x(2)(1)*x(4)(2)-y(2)(1)*y(3)(2)*x(2)(1)*x(4)(2)
-----------
TeX output:
S(\eps{2}{3}{1}{2}, \lam{2}{3}{4}{1}{2}{2}) =
(-y_{2, 2} y_{4, 1})  \del{2}{3}{1}{2} +(y_{2, 2} y_{3, 1})  \del{2}{4}{1}{2} +(-y_{2, 1} y_{2, 2})  \del{3}{4}{1}{2} +(-y_{2, 1} x_{4, 2})  \eps{2}{3}{1}{2} +(-y_{3, 1} x_{2, 2}+y_{2, 1} x_{3, 2})  \eps{2}{4}{1}{2}
----------------------------------
Epsilon:
2,3
1,2
Lam:
2,3,4
1,2,3
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(2)(1)*x(2)(3)
Divisor:
Delta
2,3
1,3
Quotient:
-y(2)(2)*y(4)(1)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
y(2)(1)*y(4)(1)
Lead Term of Product:
-y(2)(1)*y(4)(1)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
y(2)(2)*y(3)(1)
Lead Term of Product:
-y(2)(2)*y(3)(1)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
-y(2)(1)*y(3)(1)
Lead Term of Product:
y(2)(1)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
-y(2)(1)*y(2)(2)
Lead Term of Product:
y(2)(1)*y(2)(2)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
y(2)(1)^2
Lead Term of Product:
-y(2)(1)^2*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(2)(1)*x(4)(3)
Lead Term of Product:
-y(2)(1)*y(3)(2)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(3)(1)*x(2)(3)+y(2)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(2)(1)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(2)*y(4)(1)*x(2)(3)+y(3)(1)*y(4)(2)*x(2)(3)+y(2)(2)*y(4)(1)*x(3)(3)-y(2)(1)*y(4)(2)*x(3)(3)-y(2)(2)*y(3)(1)*x(4)(3)+y(2)(1)*y(3)(2)*x(4)(3)) - (-y(4)(1)*x(2)(3))*(y(3)(2)*x(2)(1)-y(3)(1)*x(2)(2)-y(2)(2)*x(3)(1)+y(2)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(2)(1)*x(2)(3)+y(3)(1)*y(4)(1)*x(2)(2)*x(2)(3)+y(2)(2)*y(4)(1)*x(2)(3)*x(3)(1)-y(2)(1)*y(4)(1)*x(2)(3)*x(3)(2)-y(2)(2)*y(4)(1)*x(2)(1)*x(3)(3)+y(2)(1)*y(4)(2)*x(2)(1)*x(3)(3)+y(2)(2)*y(3)(1)*x(2)(1)*x(4)(3)-y(2)(1)*y(3)(2)*x(2)(1)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{1}{2}, \lam{2}{3}{4}{1}{2}{3}) =
(-y_{2, 2} y_{4, 1})  \del{2}{3}{1}{3} +(y_{2, 1} y_{4, 1})  \del{2}{3}{2}{3} +(y_{2, 2} y_{3, 1})  \del{2}{4}{1}{3} +(-y_{2, 1} y_{3, 1})  \del{2}{4}{2}{3} +(-y_{2, 1} y_{2, 2})  \del{3}{4}{1}{3} +(y_{2, 1}^2)  \del{3}{4}{2}{3} +(-y_{2, 1} x_{4, 3})  \eps{2}{3}{1}{2} +(-y_{3, 1} x_{2, 3}+y_{2, 1} x_{3, 3})  \eps{2}{4}{1}{2}
----------------------------------
Epsilon:
2,3
1,2
Lam:
2,3,4
1,2,4
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*x(2)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(2)(2)*y(4)(1)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
y(2)(1)*y(4)(1)
Lead Term of Product:
-y(2)(1)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(2)(2)*y(3)(1)
Lead Term of Product:
-y(2)(2)*y(3)(1)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(2)(1)*y(3)(1)
Lead Term of Product:
y(2)(1)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(2)(1)*y(2)(2)
Lead Term of Product:
y(2)(1)*y(2)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
y(2)(1)^2
Lead Term of Product:
-y(2)(1)^2*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(2)*x(2)(1)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(2)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(2)*x(2)(4)+y(2)(2)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(2)*x(3)(4)-y(2)(2)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(2)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(2)*x(2)(1)-y(3)(1)*x(2)(2)-y(2)(2)*x(3)(1)+y(2)(1)*x(3)(2))
-------
Rewrite:
-y(3)(1)*y(4)(2)*x(2)(1)*x(2)(4)+y(3)(1)*y(4)(1)*x(2)(2)*x(2)(4)+y(2)(2)*y(4)(1)*x(2)(4)*x(3)(1)-y(2)(1)*y(4)(1)*x(2)(4)*x(3)(2)-y(2)(2)*y(4)(1)*x(2)(1)*x(3)(4)+y(2)(1)*y(4)(2)*x(2)(1)*x(3)(4)+y(2)(2)*y(3)(1)*x(2)(1)*x(4)(4)-y(2)(1)*y(3)(2)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{2}, \lam{2}{3}{4}{1}{2}{4}) =
(-y_{2, 2} y_{4, 1})  \del{2}{3}{1}{4} +(y_{2, 1} y_{4, 1})  \del{2}{3}{2}{4} +(y_{2, 2} y_{3, 1})  \del{2}{4}{1}{4} +(-y_{2, 1} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{2, 1} y_{2, 2})  \del{3}{4}{1}{4} +(y_{2, 1}^2)  \del{3}{4}{2}{4} +(-y_{2, 1} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{1}{2}
----------------------------------
Epsilon:
2,3
1,2
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,2
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,3
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(3)(4)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(2)(3)*y(3)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(2)(4)*y(3)(1)
Lead Term of Product:
y(2)(4)*y(3)(1)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(2)(3)*y(2)(4)
Lead Term of Product:
y(2)(3)*y(2)(4)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(2)(1)*y(2)(4)
Lead Term of Product:
-y(2)(1)*y(2)(4)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(1)*y(2)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(3)(4)*x(2)(4)+y(2)(4)*x(3)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(3)(1)*x(2)(4)
Lead Term of Product:
y(2)(4)*y(3)(1)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(3)(3)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
y(1)(1)*x(2)(4)
Lead Term of Product:
y(1)(1)*y(3)(4)*x(2)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(2)(4)*y(3)(3)*x(1)(4)+y(2)(3)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(3)*x(2)(4)-y(1)(3)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(3)(4)+y(1)(3)*y(2)(4)*x(3)(4)) - (-y(2)(4)*x(1)(4))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3))
-------
Rewrite:
-y(2)(3)*y(3)(4)*x(1)(4)*x(2)(1)+y(2)(4)*y(3)(1)*x(1)(4)*x(2)(3)-y(1)(4)*y(3)(3)*x(2)(1)*x(2)(4)+y(1)(3)*y(3)(4)*x(2)(1)*x(2)(4)+y(2)(3)*y(2)(4)*x(1)(4)*x(3)(1)-y(2)(1)*y(2)(4)*x(1)(4)*x(3)(3)+y(1)(4)*y(2)(3)*x(2)(1)*x(3)(4)-y(1)(3)*y(2)(4)*x(2)(1)*x(3)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{3}, \lam{1}{2}{3}{3}{4}{4}) =
(y_{2, 3} y_{3, 4})  \del{1}{2}{1}{4} +(-y_{2, 4} y_{3, 1})  \del{1}{2}{3}{4} +(-y_{2, 3} y_{2, 4})  \del{1}{3}{1}{4} +(y_{2, 1} y_{2, 4})  \del{1}{3}{3}{4} +(y_{1, 4} y_{2, 3})  \del{2}{3}{1}{4} +(-y_{1, 1} y_{2, 4})  \del{2}{3}{3}{4} +(-y_{3, 4} x_{2, 4}+y_{2, 4} x_{3, 4})  \eps{1}{2}{1}{3} +(y_{3, 1} x_{2, 4})  \eps{1}{2}{3}{4} +(-y_{2, 1} x_{2, 4})  \eps{1}{3}{3}{4} +(-y_{1, 4} x_{2, 4})  \eps{2}{3}{1}{3} +(y_{1, 1} x_{2, 4})  \eps{2}{3}{3}{4} +(-x_{2, 4})  \lam{1}{2}{3}{1}{3}{4}
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(3)*x(2)(1)
Divisor:
Delta
1,2
1,3
Quotient:
y(3)(1)*y(4)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,3
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
y(4)(1)*x(3)(3)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,3
Quotient:
-y(3)(1)*x(2)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(1)(1)*x(4)(3)
Lead Term of Product:
-y(1)(1)*y(3)(3)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,3
Quotient:
y(1)(1)*x(3)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(3)*x(4)(3)) - (-y(4)(1)*x(1)(3))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(3)*x(2)(1)+y(3)(1)*y(4)(1)*x(1)(3)*x(2)(3)+y(2)(3)*y(4)(1)*x(1)(3)*x(3)(1)-y(2)(1)*y(4)(1)*x(1)(3)*x(3)(3)-y(1)(3)*y(4)(1)*x(2)(1)*x(3)(3)+y(1)(1)*y(4)(3)*x(2)(1)*x(3)(3)+y(1)(3)*y(3)(1)*x(2)(1)*x(4)(3)-y(1)(1)*y(3)(3)*x(2)(1)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{1}{3}, \lam{1}{3}{4}{1}{3}{3}) =
(y_{3, 1} y_{4, 3})  \del{1}{2}{1}{3} +(-y_{2, 3} y_{4, 1})  \del{1}{3}{1}{3} +(y_{1, 3} y_{3, 1})  \del{2}{4}{1}{3} +(-y_{1, 1} y_{2, 3})  \del{3}{4}{1}{3} +(y_{4, 1} x_{3, 3})  \eps{1}{2}{1}{3} +(-y_{3, 1} x_{2, 3})  \eps{1}{4}{1}{3} +(-y_{1, 1} x_{4, 3})  \eps{2}{3}{1}{3} +(y_{1, 1} x_{3, 3})  \eps{2}{4}{1}{3}
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,3,4
1,3,4
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(3)(1)*y(4)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(3)(1)*y(4)(1)
Lead Term of Product:
y(3)(1)*y(4)(1)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(2)(1)*y(4)(1)
Lead Term of Product:
-y(2)(1)*y(4)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(1)*y(3)(1)
Lead Term of Product:
y(1)(1)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(1)*y(2)(1)
Lead Term of Product:
-y(1)(1)*y(2)(1)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,3
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(3)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,3
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(1)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(3)*x(3)(4)-y(1)(3)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(3)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(4)*x(2)(1)+y(3)(1)*y(4)(1)*x(1)(4)*x(2)(3)+y(2)(3)*y(4)(1)*x(1)(4)*x(3)(1)-y(2)(1)*y(4)(1)*x(1)(4)*x(3)(3)-y(1)(3)*y(4)(1)*x(2)(1)*x(3)(4)+y(1)(1)*y(4)(3)*x(2)(1)*x(3)(4)+y(1)(3)*y(3)(1)*x(2)(1)*x(4)(4)-y(1)(1)*y(3)(3)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{3}, \lam{1}{3}{4}{1}{3}{4}) =
(y_{3, 1} y_{4, 3})  \del{1}{2}{1}{4} +(-y_{3, 1} y_{4, 1})  \del{1}{2}{3}{4} +(-y_{2, 3} y_{4, 1})  \del{1}{3}{1}{4} +(y_{2, 1} y_{4, 1})  \del{1}{3}{3}{4} +(y_{1, 3} y_{3, 1})  \del{2}{4}{1}{4} +(-y_{1, 1} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{1, 1} y_{2, 3})  \del{3}{4}{1}{4} +(y_{1, 1} y_{2, 1})  \del{3}{4}{3}{4} +(y_{4, 1} x_{3, 4})  \eps{1}{2}{1}{3} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{1}{3} +(-y_{1, 1} x_{4, 4})  \eps{2}{3}{1}{3} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{1}{3}
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(3)*x(2)(1)
Divisor:
Delta
1,2
1,3
Quotient:
y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,3
Quotient:
-y(2)(3)*y(4)(2)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
1,3
Quotient:
y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(2)*y(4)(3)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
y(4)(2)*x(3)(3)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(2)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(3)*x(4)(3)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(1)(2)*x(4)(3)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(1)*x(3)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,2,3
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(3)*y(2)(2)*x(3)(1)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(2)*x(1)(3)+y(3)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(3)(3)-y(1)(2)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(2)*x(4)(3)+y(1)(2)*y(3)(3)*x(4)(3)) - (-y(4)(2)*x(1)(3))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(3)*x(2)(1)+y(3)(1)*y(4)(2)*x(1)(3)*x(2)(3)+y(2)(3)*y(4)(2)*x(1)(3)*x(3)(1)-y(2)(1)*y(4)(2)*x(1)(3)*x(3)(3)-y(1)(3)*y(4)(2)*x(2)(1)*x(3)(3)+y(1)(2)*y(4)(3)*x(2)(1)*x(3)(3)+y(1)(3)*y(3)(2)*x(2)(1)*x(4)(3)-y(1)(2)*y(3)(3)*x(2)(1)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{1}{3}, \lam{1}{3}{4}{2}{3}{3}) =
(y_{3, 2} y_{4, 3})  \del{1}{2}{1}{3} +(-y_{2, 3} y_{4, 2})  \del{1}{3}{1}{3} +(y_{1, 2} y_{4, 3})  \del{2}{3}{1}{3} +(-y_{1, 1} y_{4, 3})  \del{2}{3}{2}{3} +(y_{1, 3} y_{3, 1})  \del{2}{4}{2}{3} +(-y_{1, 1} y_{2, 3})  \del{3}{4}{2}{3} +(y_{4, 2} x_{3, 3})  \eps{1}{2}{1}{3} +(-y_{4, 3} x_{2, 3})  \eps{1}{3}{1}{2} +(-y_{3, 1} x_{2, 3})  \eps{1}{4}{2}{3} +(y_{1, 3} x_{4, 3})  \eps{2}{3}{1}{2} +(-y_{1, 2} x_{4, 3})  \eps{2}{3}{1}{3} +(y_{1, 1} x_{3, 3})  \eps{2}{4}{2}{3} +(-x_{4, 3})  \pho{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
y(3)(1)*y(4)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(2)(3)*y(4)(2)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(4)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(2)*y(4)(3)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(2)*y(3)(1)
Lead Term of Product:
y(1)(2)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(1)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
y(4)(2)*x(3)(4)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(3)*x(4)(4)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,2,3
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(3)*y(2)(2)*x(3)(1)*x(4)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(3)*x(3)(4)-y(1)(3)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(3)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(4)*x(2)(1)+y(3)(1)*y(4)(2)*x(1)(4)*x(2)(3)+y(2)(3)*y(4)(2)*x(1)(4)*x(3)(1)-y(2)(1)*y(4)(2)*x(1)(4)*x(3)(3)-y(1)(3)*y(4)(2)*x(2)(1)*x(3)(4)+y(1)(2)*y(4)(3)*x(2)(1)*x(3)(4)+y(1)(3)*y(3)(2)*x(2)(1)*x(4)(4)-y(1)(2)*y(3)(3)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{3}, \lam{1}{3}{4}{2}{3}{4}) =
(y_{3, 2} y_{4, 3})  \del{1}{2}{1}{4} +(-y_{3, 1} y_{4, 2})  \del{1}{2}{3}{4} +(-y_{2, 3} y_{4, 2})  \del{1}{3}{1}{4} +(y_{2, 1} y_{4, 2})  \del{1}{3}{3}{4} +(y_{1, 2} y_{4, 3})  \del{2}{3}{1}{4} +(-y_{1, 1} y_{4, 3})  \del{2}{3}{2}{4} +(y_{1, 3} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{1, 2} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{1, 1} y_{2, 3})  \del{3}{4}{2}{4} +(y_{1, 1} y_{2, 2})  \del{3}{4}{3}{4} +(y_{4, 2} x_{3, 4})  \eps{1}{2}{1}{3} +(-y_{4, 3} x_{2, 4})  \eps{1}{3}{1}{2} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{2}{3} +(y_{1, 3} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{1, 2} x_{4, 4})  \eps{2}{3}{1}{3} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{2}{3} +(-x_{4, 4})  \pho{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
2,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(2)(1)*x(2)(3)
Divisor:
Delta
2,3
1,3
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
y(2)(3)*y(3)(1)
Lead Term of Product:
-y(2)(3)*y(3)(1)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
-y(2)(1)*y(2)(3)
Lead Term of Product:
y(2)(1)*y(2)(3)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(2)(1)*x(4)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,3
Quotient:
-y(3)(1)*x(2)(3)+y(2)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(2)(1)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(1)*x(2)(3)+y(3)(1)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(1)*x(3)(3)-y(2)(1)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(1)*x(4)(3)+y(2)(1)*y(3)(3)*x(4)(3)) - (-y(4)(1)*x(2)(3))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(2)(1)*x(2)(3)+y(3)(1)*y(4)(1)*x(2)(3)^2+y(2)(3)*y(4)(1)*x(2)(3)*x(3)(1)-y(2)(3)*y(4)(1)*x(2)(1)*x(3)(3)+y(2)(1)*y(4)(3)*x(2)(1)*x(3)(3)-y(2)(1)*y(4)(1)*x(2)(3)*x(3)(3)+y(2)(3)*y(3)(1)*x(2)(1)*x(4)(3)-y(2)(1)*y(3)(3)*x(2)(1)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{1}{3}, \lam{2}{3}{4}{1}{3}{3}) =
(-y_{2, 3} y_{4, 1})  \del{2}{3}{1}{3} +(y_{2, 3} y_{3, 1})  \del{2}{4}{1}{3} +(-y_{2, 1} y_{2, 3})  \del{3}{4}{1}{3} +(-y_{2, 1} x_{4, 3})  \eps{2}{3}{1}{3} +(-y_{3, 1} x_{2, 3}+y_{2, 1} x_{3, 3})  \eps{2}{4}{1}{3}
----------------------------------
Epsilon:
2,3
1,3
Lam:
2,3,4
1,3,4
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(2)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(2)(1)*y(4)(1)
Lead Term of Product:
-y(2)(1)*y(4)(1)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(2)(3)*y(3)(1)
Lead Term of Product:
-y(2)(3)*y(3)(1)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(2)(1)*y(3)(1)
Lead Term of Product:
y(2)(1)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(2)(1)*y(2)(3)
Lead Term of Product:
y(2)(1)*y(2)(3)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(2)(1)^2
Lead Term of Product:
-y(2)(1)^2*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,3
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(2)(1)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(3)*x(2)(4)+y(2)(3)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(3)*x(3)(4)-y(2)(3)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(3)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(2)(1)*x(2)(4)+y(3)(1)*y(4)(1)*x(2)(3)*x(2)(4)+y(2)(3)*y(4)(1)*x(2)(4)*x(3)(1)-y(2)(1)*y(4)(1)*x(2)(4)*x(3)(3)-y(2)(3)*y(4)(1)*x(2)(1)*x(3)(4)+y(2)(1)*y(4)(3)*x(2)(1)*x(3)(4)+y(2)(3)*y(3)(1)*x(2)(1)*x(4)(4)-y(2)(1)*y(3)(3)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{3}, \lam{2}{3}{4}{1}{3}{4}) =
(-y_{2, 3} y_{4, 1})  \del{2}{3}{1}{4} +(y_{2, 1} y_{4, 1})  \del{2}{3}{3}{4} +(y_{2, 3} y_{3, 1})  \del{2}{4}{1}{4} +(-y_{2, 1} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{2, 1} y_{2, 3})  \del{3}{4}{1}{4} +(y_{2, 1}^2)  \del{3}{4}{3}{4} +(-y_{2, 1} x_{4, 4})  \eps{2}{3}{1}{3} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{1}{3}
----------------------------------
Epsilon:
2,3
1,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
2,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(3)
Divisor:
Delta
2,3
1,3
Quotient:
-y(2)(3)*y(4)(2)+y(2)(2)*y(4)(3)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-y(2)(1)*y(4)(3)
Lead Term of Product:
y(2)(1)*y(4)(3)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(2)(3)*y(3)(1)
Lead Term of Product:
-y(2)(3)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(2)(1)*y(2)(3)
Lead Term of Product:
y(2)(1)*y(2)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(4)(3)*x(2)(3)+y(2)(3)*x(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(2)(2)*x(4)(3)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(3)(1)*x(2)(3)+y(2)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(2)(2)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(2)*x(2)(3)+y(3)(2)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(2)*x(3)(3)-y(2)(2)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(2)*x(4)(3)+y(2)(2)*y(3)(3)*x(4)(3)) - (-y(4)(2)*x(2)(3))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(3)+y(3)(1)*y(4)(2)*x(2)(3)^2+y(2)(3)*y(4)(2)*x(2)(3)*x(3)(1)-y(2)(3)*y(4)(2)*x(2)(1)*x(3)(3)+y(2)(2)*y(4)(3)*x(2)(1)*x(3)(3)-y(2)(1)*y(4)(2)*x(2)(3)*x(3)(3)+y(2)(3)*y(3)(2)*x(2)(1)*x(4)(3)-y(2)(2)*y(3)(3)*x(2)(1)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{1}{3}, \lam{2}{3}{4}{2}{3}{3}) =
(-y_{2, 3} y_{4, 2}+y_{2, 2} y_{4, 3})  \del{2}{3}{1}{3} +(-y_{2, 1} y_{4, 3})  \del{2}{3}{2}{3} +(y_{2, 3} y_{3, 1})  \del{2}{4}{2}{3} +(-y_{2, 1} y_{2, 3})  \del{3}{4}{2}{3} +(-y_{4, 3} x_{2, 3}+y_{2, 3} x_{4, 3})  \eps{2}{3}{1}{2} +(-y_{2, 2} x_{4, 3})  \eps{2}{3}{1}{3} +(-y_{3, 1} x_{2, 3}+y_{2, 1} x_{3, 3})  \eps{2}{4}{2}{3}
----------------------------------
Epsilon:
2,3
1,3
Lam:
2,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(2)(3)*y(4)(2)+y(2)(2)*y(4)(3)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(2)(1)*y(4)(3)
Lead Term of Product:
y(2)(1)*y(4)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(2)(3)*y(3)(1)
Lead Term of Product:
-y(2)(3)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(2)(2)*y(3)(1)
Lead Term of Product:
y(2)(2)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(2)(1)*y(2)(3)
Lead Term of Product:
y(2)(1)*y(2)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(2)(1)*y(2)(2)
Lead Term of Product:
-y(2)(1)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(4)(3)*x(2)(4)+y(2)(3)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(2)(2)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(2)(2)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(3)*x(2)(4)+y(2)(3)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(3)*x(3)(4)-y(2)(3)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(3)*x(4)(4)) - (-y(4)(2)*x(2)(4))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(4)+y(3)(1)*y(4)(2)*x(2)(3)*x(2)(4)+y(2)(3)*y(4)(2)*x(2)(4)*x(3)(1)-y(2)(1)*y(4)(2)*x(2)(4)*x(3)(3)-y(2)(3)*y(4)(2)*x(2)(1)*x(3)(4)+y(2)(2)*y(4)(3)*x(2)(1)*x(3)(4)+y(2)(3)*y(3)(2)*x(2)(1)*x(4)(4)-y(2)(2)*y(3)(3)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{3}, \lam{2}{3}{4}{2}{3}{4}) =
(-y_{2, 3} y_{4, 2}+y_{2, 2} y_{4, 3})  \del{2}{3}{1}{4} +(-y_{2, 1} y_{4, 3})  \del{2}{3}{2}{4} +(y_{2, 1} y_{4, 2})  \del{2}{3}{3}{4} +(y_{2, 3} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{2, 2} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{2, 1} y_{2, 3})  \del{3}{4}{2}{4} +(y_{2, 1} y_{2, 2})  \del{3}{4}{3}{4} +(-y_{4, 3} x_{2, 4}+y_{2, 3} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{2, 2} x_{4, 4})  \eps{2}{3}{1}{3} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{2}{3}
----------------------------------
Epsilon:
2,3
1,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(3)(1)*y(4)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(2)(4)*y(4)(1)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(1)*y(2)(4)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
1,4
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,4
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(4)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,4
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(1)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(4)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(4)*x(2)(1)-y(3)(1)*x(2)(4)-y(2)(4)*x(3)(1)+y(2)(1)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(1)(4)*x(2)(1)+y(3)(1)*y(4)(1)*x(1)(4)*x(2)(4)+y(2)(4)*y(4)(1)*x(1)(4)*x(3)(1)-y(2)(1)*y(4)(1)*x(1)(4)*x(3)(4)-y(1)(4)*y(4)(1)*x(2)(1)*x(3)(4)+y(1)(1)*y(4)(4)*x(2)(1)*x(3)(4)+y(1)(4)*y(3)(1)*x(2)(1)*x(4)(4)-y(1)(1)*y(3)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{4}, \lam{1}{3}{4}{1}{4}{4}) =
(y_{3, 1} y_{4, 4})  \del{1}{2}{1}{4} +(-y_{2, 4} y_{4, 1})  \del{1}{3}{1}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{1}{4} +(-y_{1, 1} y_{2, 4})  \del{3}{4}{1}{4} +(y_{4, 1} x_{3, 4})  \eps{1}{2}{1}{4} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{1}{4} +(-y_{1, 1} x_{4, 4})  \eps{2}{3}{1}{4} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{1}{4}
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(3)(2)*y(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(2)(4)*y(4)(2)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(2)*y(4)(4)
Lead Term of Product:
-y(1)(2)*y(4)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(1)*y(2)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
y(4)(2)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,4
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(4)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,2,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(4)*y(2)(2)*x(3)(1)*x(4)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(4)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(3)(4)*x(2)(1)-y(3)(1)*x(2)(4)-y(2)(4)*x(3)(1)+y(2)(1)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(1)+y(3)(1)*y(4)(2)*x(1)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(1)(4)*x(3)(1)-y(2)(1)*y(4)(2)*x(1)(4)*x(3)(4)-y(1)(4)*y(4)(2)*x(2)(1)*x(3)(4)+y(1)(2)*y(4)(4)*x(2)(1)*x(3)(4)+y(1)(4)*y(3)(2)*x(2)(1)*x(4)(4)-y(1)(2)*y(3)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{4}, \lam{1}{3}{4}{2}{4}{4}) =
(y_{3, 2} y_{4, 4})  \del{1}{2}{1}{4} +(-y_{2, 4} y_{4, 2})  \del{1}{3}{1}{4} +(y_{1, 2} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{1, 1} y_{4, 4})  \del{2}{3}{2}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{1, 1} y_{2, 4})  \del{3}{4}{2}{4} +(y_{4, 2} x_{3, 4})  \eps{1}{2}{1}{4} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{1}{2} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{2}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{1, 2} x_{4, 4})  \eps{2}{3}{1}{4} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{2}{4} +(-x_{4, 4})  \pho{1}{2}{3}{1}{2}{4}
----------------------------------
Epsilon:
2,3
1,4
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(3)(3)*y(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,4
Quotient:
-y(2)(4)*y(4)(3)
Lead Term of Product:
y(2)(4)*y(4)(3)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(3)*y(4)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(1)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
y(4)(3)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(4)(3)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,4
Quotient:
-y(1)(3)*x(4)(4)
Lead Term of Product:
-y(1)(3)*y(3)(4)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,3,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(4)*y(2)(3)*x(3)(1)*x(4)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(1)(4))*(y(3)(4)*x(2)(1)-y(3)(1)*x(2)(4)-y(2)(4)*x(3)(1)+y(2)(1)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(1)+y(3)(1)*y(4)(3)*x(1)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(1)(4)*x(3)(1)-y(2)(1)*y(4)(3)*x(1)(4)*x(3)(4)-y(1)(4)*y(4)(3)*x(2)(1)*x(3)(4)+y(1)(3)*y(4)(4)*x(2)(1)*x(3)(4)+y(1)(4)*y(3)(3)*x(2)(1)*x(4)(4)-y(1)(3)*y(3)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{4}, \lam{1}{3}{4}{3}{4}{4}) =
(y_{3, 3} y_{4, 4})  \del{1}{2}{1}{4} +(-y_{2, 4} y_{4, 3})  \del{1}{3}{1}{4} +(y_{1, 3} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{1, 1} y_{4, 4})  \del{2}{3}{3}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{1, 1} y_{2, 4})  \del{3}{4}{3}{4} +(y_{4, 3} x_{3, 4})  \eps{1}{2}{1}{4} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{1}{3} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{3}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{1}{3} +(-y_{1, 3} x_{4, 4})  \eps{2}{3}{1}{4} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{4, 4})  \pho{1}{2}{3}{1}{3}{4}
----------------------------------
Epsilon:
2,3
1,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
2,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(2)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(2)(4)*y(4)(1)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(2)(4)*y(3)(1)
Lead Term of Product:
-y(2)(4)*y(3)(1)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
-y(2)(1)*y(2)(4)
Lead Term of Product:
y(2)(1)*y(2)(4)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,4
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(2)(1)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(4)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(4)*x(2)(1)-y(3)(1)*x(2)(4)-y(2)(4)*x(3)(1)+y(2)(1)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(2)(1)*x(2)(4)+y(3)(1)*y(4)(1)*x(2)(4)^2+y(2)(4)*y(4)(1)*x(2)(4)*x(3)(1)-y(2)(4)*y(4)(1)*x(2)(1)*x(3)(4)+y(2)(1)*y(4)(4)*x(2)(1)*x(3)(4)-y(2)(1)*y(4)(1)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(1)*x(2)(1)*x(4)(4)-y(2)(1)*y(3)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{4}, \lam{2}{3}{4}{1}{4}{4}) =
(-y_{2, 4} y_{4, 1})  \del{2}{3}{1}{4} +(y_{2, 4} y_{3, 1})  \del{2}{4}{1}{4} +(-y_{2, 1} y_{2, 4})  \del{3}{4}{1}{4} +(-y_{2, 1} x_{4, 4})  \eps{2}{3}{1}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{1}{4}
----------------------------------
Epsilon:
2,3
1,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
1,4
Lam:
2,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(2)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(2)(4)*y(4)(2)+y(2)(2)*y(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(2)(1)*y(4)(4)
Lead Term of Product:
y(2)(1)*y(4)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(2)(4)*y(3)(1)
Lead Term of Product:
-y(2)(4)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(2)(1)*y(2)(4)
Lead Term of Product:
y(2)(1)*y(2)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(4)(4)*x(2)(4)+y(2)(4)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,4
Quotient:
-y(2)(2)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(2)(2)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(4)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(2)(4))*(y(3)(4)*x(2)(1)-y(3)(1)*x(2)(4)-y(2)(4)*x(3)(1)+y(2)(1)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(2)(1)*x(2)(4)+y(3)(1)*y(4)(2)*x(2)(4)^2+y(2)(4)*y(4)(2)*x(2)(4)*x(3)(1)-y(2)(4)*y(4)(2)*x(2)(1)*x(3)(4)+y(2)(2)*y(4)(4)*x(2)(1)*x(3)(4)-y(2)(1)*y(4)(2)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(2)*x(2)(1)*x(4)(4)-y(2)(2)*y(3)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{4}, \lam{2}{3}{4}{2}{4}{4}) =
(-y_{2, 4} y_{4, 2}+y_{2, 2} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{2, 1} y_{4, 4})  \del{2}{3}{2}{4} +(y_{2, 4} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{2, 1} y_{2, 4})  \del{3}{4}{2}{4} +(-y_{4, 4} x_{2, 4}+y_{2, 4} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{2, 2} x_{4, 4})  \eps{2}{3}{1}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{2}{4}
----------------------------------
Epsilon:
2,3
1,4
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(2)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
-y(2)(4)*y(4)(3)+y(2)(3)*y(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(3)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(2)(1)*y(4)(4)
Lead Term of Product:
y(2)(1)*y(4)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(2)(4)*y(3)(1)
Lead Term of Product:
-y(2)(4)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(2)(1)*y(2)(4)
Lead Term of Product:
y(2)(1)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(4)(4)*x(2)(4)+y(2)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,4
Quotient:
-y(2)(3)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(2)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(2)(4))*(y(3)(4)*x(2)(1)-y(3)(1)*x(2)(4)-y(2)(4)*x(3)(1)+y(2)(1)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(2)(1)*x(2)(4)+y(3)(1)*y(4)(3)*x(2)(4)^2+y(2)(4)*y(4)(3)*x(2)(4)*x(3)(1)-y(2)(4)*y(4)(3)*x(2)(1)*x(3)(4)+y(2)(3)*y(4)(4)*x(2)(1)*x(3)(4)-y(2)(1)*y(4)(3)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(3)*x(2)(1)*x(4)(4)-y(2)(3)*y(3)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{1}{4}, \lam{2}{3}{4}{3}{4}{4}) =
(-y_{2, 4} y_{4, 3}+y_{2, 3} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{2, 1} y_{4, 4})  \del{2}{3}{3}{4} +(y_{2, 4} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{2, 1} y_{2, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{2, 4}+y_{2, 4} x_{4, 4})  \eps{2}{3}{1}{3} +(-y_{2, 3} x_{4, 4})  \eps{2}{3}{1}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{3}{4}
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,3
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(3)(4)*x(1)(4)*x(2)(2)
Divisor:
Delta
1,2
2,4
Quotient:
y(2)(3)*y(3)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(2)(4)*y(3)(2)
Lead Term of Product:
y(2)(4)*y(3)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(2)(3)*y(2)(4)
Lead Term of Product:
y(2)(3)*y(2)(4)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(2)(2)*y(2)(4)
Lead Term of Product:
-y(2)(2)*y(2)(4)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(2)*y(2)(4)
Lead Term of Product:
y(1)(2)*y(2)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(3)(4)*x(2)(4)+y(2)(4)*x(3)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(3)(2)*x(2)(4)
Lead Term of Product:
y(2)(4)*y(3)(2)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
-y(2)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(3)(3)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
y(1)(2)*x(2)(4)
Lead Term of Product:
y(1)(2)*y(3)(4)*x(2)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
2,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(2)(3)*y(3)(2)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(2)(4)*y(3)(3)*x(1)(4)+y(2)(3)*y(3)(4)*x(1)(4)+y(1)(4)*y(3)(3)*x(2)(4)-y(1)(3)*y(3)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(3)(4)+y(1)(3)*y(2)(4)*x(3)(4)) - (-y(2)(4)*x(1)(4))*(y(3)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3))
-------
Rewrite:
-y(2)(3)*y(3)(4)*x(1)(4)*x(2)(2)+y(2)(4)*y(3)(2)*x(1)(4)*x(2)(3)-y(1)(4)*y(3)(3)*x(2)(2)*x(2)(4)+y(1)(3)*y(3)(4)*x(2)(2)*x(2)(4)+y(2)(3)*y(2)(4)*x(1)(4)*x(3)(2)-y(2)(2)*y(2)(4)*x(1)(4)*x(3)(3)+y(1)(4)*y(2)(3)*x(2)(2)*x(3)(4)-y(1)(3)*y(2)(4)*x(2)(2)*x(3)(4)
-----------
TeX output:
S(\eps{2}{3}{2}{3}, \lam{1}{2}{3}{3}{4}{4}) =
(y_{2, 3} y_{3, 4})  \del{1}{2}{2}{4} +(-y_{2, 4} y_{3, 2})  \del{1}{2}{3}{4} +(-y_{2, 3} y_{2, 4})  \del{1}{3}{2}{4} +(y_{2, 2} y_{2, 4})  \del{1}{3}{3}{4} +(y_{1, 4} y_{2, 3})  \del{2}{3}{2}{4} +(-y_{1, 2} y_{2, 4})  \del{2}{3}{3}{4} +(-y_{3, 4} x_{2, 4}+y_{2, 4} x_{3, 4})  \eps{1}{2}{2}{3} +(y_{3, 2} x_{2, 4})  \eps{1}{2}{3}{4} +(-y_{2, 2} x_{2, 4})  \eps{1}{3}{3}{4} +(-y_{1, 4} x_{2, 4})  \eps{2}{3}{2}{3} +(y_{1, 2} x_{2, 4})  \eps{2}{3}{3}{4} +(-x_{2, 4})  \lam{1}{2}{3}{2}{3}{4}
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(3)*x(2)(2)
Divisor:
Delta
1,2
2,3
Quotient:
y(3)(1)*y(4)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(1)*x(3)(3)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(1)(1)*x(4)(3)
Lead Term of Product:
-y(1)(1)*y(3)(3)*x(2)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(1)*x(3)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(2)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(3)*y(4)(1)*x(1)(3)+y(3)(1)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(1)*x(3)(3)-y(1)(1)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(1)*x(4)(3)+y(1)(1)*y(3)(3)*x(4)(3)) - (-y(4)(1)*x(1)(3))*(y(3)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(3)*x(2)(2)+y(3)(2)*y(4)(1)*x(1)(3)*x(2)(3)+y(2)(3)*y(4)(1)*x(1)(3)*x(3)(2)-y(2)(2)*y(4)(1)*x(1)(3)*x(3)(3)-y(1)(3)*y(4)(1)*x(2)(2)*x(3)(3)+y(1)(1)*y(4)(3)*x(2)(2)*x(3)(3)+y(1)(3)*y(3)(1)*x(2)(2)*x(4)(3)-y(1)(1)*y(3)(3)*x(2)(2)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{2}{3}, \lam{1}{3}{4}{1}{3}{3}) =
(y_{3, 1} y_{4, 3})  \del{1}{2}{2}{3} +(-y_{2, 3} y_{4, 1})  \del{1}{3}{2}{3} +(y_{1, 3} y_{3, 1})  \del{2}{4}{2}{3} +(-y_{1, 1} y_{2, 3})  \del{3}{4}{2}{3} +(y_{4, 1} x_{3, 3})  \eps{1}{2}{2}{3} +(-y_{3, 1} x_{2, 3})  \eps{1}{4}{2}{3} +(-y_{1, 1} x_{4, 3})  \eps{2}{3}{2}{3} +(y_{1, 1} x_{3, 3})  \eps{2}{4}{2}{3} +(-x_{2, 3})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,3,4
1,3,4
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(1)(4)*x(2)(2)
Divisor:
Delta
1,2
2,4
Quotient:
y(3)(1)*y(4)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(3)(2)*y(4)(1)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(2)(2)*y(4)(1)
Lead Term of Product:
-y(2)(2)*y(4)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(2)*y(4)(1)+y(1)(1)*y(4)(2)
Lead Term of Product:
y(1)(2)*y(4)(1)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(1)*y(3)(2)
Lead Term of Product:
y(1)(1)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(1)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(3)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(3)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(3)*x(3)(4)-y(1)(3)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(3)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(1)(4)*x(2)(2)+y(3)(2)*y(4)(1)*x(1)(4)*x(2)(3)+y(2)(3)*y(4)(1)*x(1)(4)*x(3)(2)-y(2)(2)*y(4)(1)*x(1)(4)*x(3)(3)-y(1)(3)*y(4)(1)*x(2)(2)*x(3)(4)+y(1)(1)*y(4)(3)*x(2)(2)*x(3)(4)+y(1)(3)*y(3)(1)*x(2)(2)*x(4)(4)-y(1)(1)*y(3)(3)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{2}{3}, \lam{1}{3}{4}{1}{3}{4}) =
(y_{3, 1} y_{4, 3})  \del{1}{2}{2}{4} +(-y_{3, 2} y_{4, 1})  \del{1}{2}{3}{4} +(-y_{2, 3} y_{4, 1})  \del{1}{3}{2}{4} +(y_{2, 2} y_{4, 1})  \del{1}{3}{3}{4} +(-y_{1, 2} y_{4, 1}+y_{1, 1} y_{4, 2})  \del{2}{3}{3}{4} +(y_{1, 3} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{1, 1} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{1, 1} y_{2, 3})  \del{3}{4}{2}{4} +(y_{1, 1} y_{2, 2})  \del{3}{4}{3}{4} +(y_{4, 1} x_{3, 4})  \eps{1}{2}{2}{3} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{2}{3} +(-y_{1, 1} x_{4, 4})  \eps{2}{3}{2}{3} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{2}{3} +(-x_{2, 4})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(3)*x(2)(2)
Divisor:
Delta
1,2
2,3
Quotient:
y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
-y(2)(3)*y(4)(2)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(1)(3)*y(3)(2)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(2)*y(2)(3)
Lead Term of Product:
y(1)(2)*y(2)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(2)*x(3)(3)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(2)*x(2)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(1)(2)*x(4)(3)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(2)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(2)*x(3)(3)
Lead Term of Product:
y(1)(2)*y(4)(3)*x(2)(2)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(3)*y(4)(2)*x(1)(3)+y(3)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(3)(3)-y(1)(2)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(2)*x(4)(3)+y(1)(2)*y(3)(3)*x(4)(3)) - (-y(4)(2)*x(1)(3))*(y(3)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(3)*x(2)(2)+y(3)(2)*y(4)(2)*x(1)(3)*x(2)(3)+y(2)(3)*y(4)(2)*x(1)(3)*x(3)(2)-y(2)(2)*y(4)(2)*x(1)(3)*x(3)(3)-y(1)(3)*y(4)(2)*x(2)(2)*x(3)(3)+y(1)(2)*y(4)(3)*x(2)(2)*x(3)(3)+y(1)(3)*y(3)(2)*x(2)(2)*x(4)(3)-y(1)(2)*y(3)(3)*x(2)(2)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{2}{3}, \lam{1}{3}{4}{2}{3}{3}) =
(y_{3, 2} y_{4, 3})  \del{1}{2}{2}{3} +(-y_{2, 3} y_{4, 2})  \del{1}{3}{2}{3} +(y_{1, 3} y_{3, 2})  \del{2}{4}{2}{3} +(-y_{1, 2} y_{2, 3})  \del{3}{4}{2}{3} +(y_{4, 2} x_{3, 3})  \eps{1}{2}{2}{3} +(-y_{3, 2} x_{2, 3})  \eps{1}{4}{2}{3} +(-y_{1, 2} x_{4, 3})  \eps{2}{3}{2}{3} +(y_{1, 2} x_{3, 3})  \eps{2}{4}{2}{3}
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(4)*x(2)(2)
Divisor:
Delta
1,2
2,4
Quotient:
y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(3)(2)*y(4)(2)
Lead Term of Product:
y(3)(2)*y(4)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(2)(3)*y(4)(2)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
y(2)(2)*y(4)(2)
Lead Term of Product:
-y(2)(2)*y(4)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(3)*y(3)(2)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(2)*y(3)(2)
Lead Term of Product:
y(1)(2)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(2)*y(2)(3)
Lead Term of Product:
y(1)(2)*y(2)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(2)*y(2)(2)
Lead Term of Product:
-y(1)(2)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(2)*x(3)(4)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(2)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(2)*x(3)(4)
Lead Term of Product:
y(1)(2)*y(4)(3)*x(2)(2)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(3)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(3)*x(3)(4)-y(1)(3)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(3)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(3)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(4)*x(2)(2)+y(3)(2)*y(4)(2)*x(1)(4)*x(2)(3)+y(2)(3)*y(4)(2)*x(1)(4)*x(3)(2)-y(2)(2)*y(4)(2)*x(1)(4)*x(3)(3)-y(1)(3)*y(4)(2)*x(2)(2)*x(3)(4)+y(1)(2)*y(4)(3)*x(2)(2)*x(3)(4)+y(1)(3)*y(3)(2)*x(2)(2)*x(4)(4)-y(1)(2)*y(3)(3)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{2}{3}, \lam{1}{3}{4}{2}{3}{4}) =
(y_{3, 2} y_{4, 3})  \del{1}{2}{2}{4} +(-y_{3, 2} y_{4, 2})  \del{1}{2}{3}{4} +(-y_{2, 3} y_{4, 2})  \del{1}{3}{2}{4} +(y_{2, 2} y_{4, 2})  \del{1}{3}{3}{4} +(y_{1, 3} y_{3, 2})  \del{2}{4}{2}{4} +(-y_{1, 2} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{1, 2} y_{2, 3})  \del{3}{4}{2}{4} +(y_{1, 2} y_{2, 2})  \del{3}{4}{3}{4} +(y_{4, 2} x_{3, 4})  \eps{1}{2}{2}{3} +(-y_{3, 2} x_{2, 4})  \eps{1}{4}{2}{3} +(-y_{1, 2} x_{4, 4})  \eps{2}{3}{2}{3} +(y_{1, 2} x_{3, 4})  \eps{2}{4}{2}{3}
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
2,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(3)(3)*y(4)(2)*x(2)(2)
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(3)(3)*y(4)(2)*x(2)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
-y(2)(2)*y(3)(1)+y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(2)*y(3)(1)*y(4)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,3
Quotient:
-y(3)(2)
Lead Term of Product:
y(3)(2)^2*y(4)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Psi
2,3,4
1,2,3
Quotient:
-x(3)(2)
Lead Term of Product:
y(2)(3)*y(3)(2)*y(4)(1)*x(3)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(3))*(-y(3)(2)*y(4)(1)*x(2)(2)+y(3)(1)*y(4)(2)*x(2)(2)+y(2)(2)*y(4)(1)*x(3)(2)-y(2)(1)*y(4)(2)*x(3)(2)-y(2)(2)*y(3)(1)*x(4)(2)+y(2)(1)*y(3)(2)*x(4)(2)) - (-y(3)(2)*y(4)(1))*(y(3)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(3)(3)*y(4)(2)*x(2)(2)+y(3)(2)^2*y(4)(1)*x(2)(3)+y(2)(3)*y(3)(2)*y(4)(1)*x(3)(2)-y(2)(2)*y(3)(3)*y(4)(1)*x(3)(2)+y(2)(1)*y(3)(3)*y(4)(2)*x(3)(2)-y(2)(2)*y(3)(2)*y(4)(1)*x(3)(3)+y(2)(2)*y(3)(1)*y(3)(3)*x(4)(2)-y(2)(1)*y(3)(2)*y(3)(3)*x(4)(2)
-----------
TeX output:
S(\eps{2}{3}{2}{3}, \lam{2}{3}{4}{1}{2}{2}) =
(-y_{3, 1} y_{4, 2})  \eps{2}{3}{2}{3} +(-y_{2, 2} y_{3, 1}+y_{2, 1} y_{3, 2})  \eps{3}{4}{2}{3} +(-y_{3, 2})  \lam{2}{3}{4}{1}{2}{3} +(-x_{3, 2})  \psi{2}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,3
2,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
2,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(2)(2)*x(2)(3)
Divisor:
Delta
2,3
2,3
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(2)(3)*y(3)(1)
Lead Term of Product:
-y(2)(3)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(2)(1)*y(2)(3)
Lead Term of Product:
y(2)(1)*y(2)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(2)(1)*x(4)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(2)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(3)(1)*x(2)(3)+y(2)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(2)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,3
Quotient:
-x(2)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(2)(3)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(3)*y(4)(1)*x(2)(3)+y(3)(1)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(1)*x(3)(3)-y(2)(1)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(1)*x(4)(3)+y(2)(1)*y(3)(3)*x(4)(3)) - (-y(4)(1)*x(2)(3))*(y(3)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(2)(2)*x(2)(3)+y(3)(2)*y(4)(1)*x(2)(3)^2+y(2)(3)*y(4)(1)*x(2)(3)*x(3)(2)-y(2)(3)*y(4)(1)*x(2)(2)*x(3)(3)+y(2)(1)*y(4)(3)*x(2)(2)*x(3)(3)-y(2)(2)*y(4)(1)*x(2)(3)*x(3)(3)+y(2)(3)*y(3)(1)*x(2)(2)*x(4)(3)-y(2)(1)*y(3)(3)*x(2)(2)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{2}{3}, \lam{2}{3}{4}{1}{3}{3}) =
(-y_{2, 3} y_{4, 1})  \del{2}{3}{2}{3} +(y_{2, 3} y_{3, 1})  \del{2}{4}{2}{3} +(-y_{2, 1} y_{2, 3})  \del{3}{4}{2}{3} +(-y_{2, 1} x_{4, 3})  \eps{2}{3}{2}{3} +(-y_{3, 1} x_{2, 3}+y_{2, 1} x_{3, 3})  \eps{2}{4}{2}{3} +(-x_{2, 3})  \lam{2}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,3
2,3
Lam:
2,3,4
1,3,4
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*x(2)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(2)(3)*y(3)(1)
Lead Term of Product:
-y(2)(3)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(2)(1)*y(3)(2)
Lead Term of Product:
y(2)(1)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(2)(1)*y(2)(3)
Lead Term of Product:
y(2)(1)*y(2)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(2)(1)*y(2)(2)
Lead Term of Product:
-y(2)(1)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,3
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(2)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(3)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(3)*x(2)(4)+y(2)(3)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(3)*x(3)(4)-y(2)(3)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(3)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3))
-------
Rewrite:
-y(3)(1)*y(4)(3)*x(2)(2)*x(2)(4)+y(3)(2)*y(4)(1)*x(2)(3)*x(2)(4)+y(2)(3)*y(4)(1)*x(2)(4)*x(3)(2)-y(2)(2)*y(4)(1)*x(2)(4)*x(3)(3)-y(2)(3)*y(4)(1)*x(2)(2)*x(3)(4)+y(2)(1)*y(4)(3)*x(2)(2)*x(3)(4)+y(2)(3)*y(3)(1)*x(2)(2)*x(4)(4)-y(2)(1)*y(3)(3)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{2}{3}, \lam{2}{3}{4}{1}{3}{4}) =
(-y_{2, 3} y_{4, 1})  \del{2}{3}{2}{4} +(y_{2, 1} y_{4, 2})  \del{2}{3}{3}{4} +(y_{2, 3} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{2, 1} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{2, 1} y_{2, 3})  \del{3}{4}{2}{4} +(y_{2, 1} y_{2, 2})  \del{3}{4}{3}{4} +(-y_{2, 1} x_{4, 4})  \eps{2}{3}{2}{3} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{2}{3} +(-x_{2, 4})  \lam{2}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,3
2,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
2,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(2)(2)*x(2)(3)
Divisor:
Delta
2,3
2,3
Quotient:
-y(2)(3)*y(4)(2)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(2)(3)*y(3)(2)
Lead Term of Product:
-y(2)(3)*y(3)(2)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(2)(2)*y(2)(3)
Lead Term of Product:
y(2)(2)*y(2)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(2)(2)*x(4)(3)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(2)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(3)(2)*x(2)(3)+y(2)(2)*x(3)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(2)(2)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(3)*y(4)(2)*x(2)(3)+y(3)(2)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(2)*x(3)(3)-y(2)(2)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(2)*x(4)(3)+y(2)(2)*y(3)(3)*x(4)(3)) - (-y(4)(2)*x(2)(3))*(y(3)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(2)(2)*x(2)(3)+y(3)(2)*y(4)(2)*x(2)(3)^2+y(2)(3)*y(4)(2)*x(2)(3)*x(3)(2)-y(2)(3)*y(4)(2)*x(2)(2)*x(3)(3)+y(2)(2)*y(4)(3)*x(2)(2)*x(3)(3)-y(2)(2)*y(4)(2)*x(2)(3)*x(3)(3)+y(2)(3)*y(3)(2)*x(2)(2)*x(4)(3)-y(2)(2)*y(3)(3)*x(2)(2)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{2}{3}, \lam{2}{3}{4}{2}{3}{3}) =
(-y_{2, 3} y_{4, 2})  \del{2}{3}{2}{3} +(y_{2, 3} y_{3, 2})  \del{2}{4}{2}{3} +(-y_{2, 2} y_{2, 3})  \del{3}{4}{2}{3} +(-y_{2, 2} x_{4, 3})  \eps{2}{3}{2}{3} +(-y_{3, 2} x_{2, 3}+y_{2, 2} x_{3, 3})  \eps{2}{4}{2}{3}
----------------------------------
Epsilon:
2,3
2,3
Lam:
2,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(2)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
-y(2)(3)*y(4)(2)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(2)(2)*y(4)(2)
Lead Term of Product:
-y(2)(2)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(2)(3)*y(3)(2)
Lead Term of Product:
-y(2)(3)*y(3)(2)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(2)(2)*y(3)(2)
Lead Term of Product:
y(2)(2)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(2)(2)*y(2)(3)
Lead Term of Product:
y(2)(2)*y(2)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(2)(2)^2
Lead Term of Product:
-y(2)(2)^2*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(2)(2)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(3)(3)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(3)(2)*x(2)(4)+y(2)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(2)(2)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(3)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(3)*x(2)(4)+y(2)(3)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(3)*x(3)(4)-y(2)(3)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(3)*x(4)(4)) - (-y(4)(2)*x(2)(4))*(y(3)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(2)(2)*x(2)(4)+y(3)(2)*y(4)(2)*x(2)(3)*x(2)(4)+y(2)(3)*y(4)(2)*x(2)(4)*x(3)(2)-y(2)(2)*y(4)(2)*x(2)(4)*x(3)(3)-y(2)(3)*y(4)(2)*x(2)(2)*x(3)(4)+y(2)(2)*y(4)(3)*x(2)(2)*x(3)(4)+y(2)(3)*y(3)(2)*x(2)(2)*x(4)(4)-y(2)(2)*y(3)(3)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{2}{3}, \lam{2}{3}{4}{2}{3}{4}) =
(-y_{2, 3} y_{4, 2})  \del{2}{3}{2}{4} +(y_{2, 2} y_{4, 2})  \del{2}{3}{3}{4} +(y_{2, 3} y_{3, 2})  \del{2}{4}{2}{4} +(-y_{2, 2} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{2, 2} y_{2, 3})  \del{3}{4}{2}{4} +(y_{2, 2}^2)  \del{3}{4}{3}{4} +(-y_{2, 2} x_{4, 4})  \eps{2}{3}{2}{3} +(-y_{3, 2} x_{2, 4}+y_{2, 2} x_{3, 4})  \eps{2}{4}{2}{3}
----------------------------------
Epsilon:
2,3
2,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,3
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(1)(4)*x(2)(2)
Divisor:
Delta
1,2
2,4
Quotient:
y(3)(1)*y(4)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(2)(4)*y(4)(1)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(1)*y(2)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(4)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(4)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(4)*x(2)(2)-y(3)(2)*x(2)(4)-y(2)(4)*x(3)(2)+y(2)(2)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(1)(4)*x(2)(2)+y(3)(2)*y(4)(1)*x(1)(4)*x(2)(4)+y(2)(4)*y(4)(1)*x(1)(4)*x(3)(2)-y(2)(2)*y(4)(1)*x(1)(4)*x(3)(4)-y(1)(4)*y(4)(1)*x(2)(2)*x(3)(4)+y(1)(1)*y(4)(4)*x(2)(2)*x(3)(4)+y(1)(4)*y(3)(1)*x(2)(2)*x(4)(4)-y(1)(1)*y(3)(4)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{2}{4}, \lam{1}{3}{4}{1}{4}{4}) =
(y_{3, 1} y_{4, 4})  \del{1}{2}{2}{4} +(-y_{2, 4} y_{4, 1})  \del{1}{3}{2}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{1, 1} y_{2, 4})  \del{3}{4}{2}{4} +(y_{4, 1} x_{3, 4})  \eps{1}{2}{2}{4} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{2}{4} +(-y_{1, 1} x_{4, 4})  \eps{2}{3}{2}{4} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{2}{4} +(-x_{2, 4})  \lam{1}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(2)
Divisor:
Delta
1,2
2,4
Quotient:
y(3)(2)*y(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(2)(4)*y(4)(2)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(4)*y(3)(2)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(2)*y(2)(4)
Lead Term of Product:
y(1)(2)*y(2)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
y(4)(2)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(2)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(4)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
y(1)(2)*x(3)(4)
Lead Term of Product:
y(1)(2)*y(4)(4)*x(2)(2)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(4)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(3)(4)*x(2)(2)-y(3)(2)*x(2)(4)-y(2)(4)*x(3)(2)+y(2)(2)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(2)+y(3)(2)*y(4)(2)*x(1)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(1)(4)*x(3)(2)-y(2)(2)*y(4)(2)*x(1)(4)*x(3)(4)-y(1)(4)*y(4)(2)*x(2)(2)*x(3)(4)+y(1)(2)*y(4)(4)*x(2)(2)*x(3)(4)+y(1)(4)*y(3)(2)*x(2)(2)*x(4)(4)-y(1)(2)*y(3)(4)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{2}{4}, \lam{1}{3}{4}{2}{4}{4}) =
(y_{3, 2} y_{4, 4})  \del{1}{2}{2}{4} +(-y_{2, 4} y_{4, 2})  \del{1}{3}{2}{4} +(y_{1, 4} y_{3, 2})  \del{2}{4}{2}{4} +(-y_{1, 2} y_{2, 4})  \del{3}{4}{2}{4} +(y_{4, 2} x_{3, 4})  \eps{1}{2}{2}{4} +(-y_{3, 2} x_{2, 4})  \eps{1}{4}{2}{4} +(-y_{1, 2} x_{4, 4})  \eps{2}{3}{2}{4} +(y_{1, 2} x_{3, 4})  \eps{2}{4}{2}{4}
----------------------------------
Epsilon:
2,3
2,4
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(2)
Divisor:
Delta
1,2
2,4
Quotient:
y(3)(3)*y(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(2)(4)*y(4)(3)
Lead Term of Product:
y(2)(4)*y(4)(3)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(3)*y(4)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(2)*y(4)(4)
Lead Term of Product:
y(1)(2)*y(4)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(2)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(2)*y(2)(4)
Lead Term of Product:
y(1)(2)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
y(4)(3)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(4)(3)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(2)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(1)(3)*x(4)(4)
Lead Term of Product:
-y(1)(3)*y(3)(4)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
y(1)(2)*x(3)(4)
Lead Term of Product:
y(1)(2)*y(4)(4)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
2,3,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(4)*y(2)(3)*x(3)(2)*x(4)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(1)(4))*(y(3)(4)*x(2)(2)-y(3)(2)*x(2)(4)-y(2)(4)*x(3)(2)+y(2)(2)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(2)+y(3)(2)*y(4)(3)*x(1)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(1)(4)*x(3)(2)-y(2)(2)*y(4)(3)*x(1)(4)*x(3)(4)-y(1)(4)*y(4)(3)*x(2)(2)*x(3)(4)+y(1)(3)*y(4)(4)*x(2)(2)*x(3)(4)+y(1)(4)*y(3)(3)*x(2)(2)*x(4)(4)-y(1)(3)*y(3)(4)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{2}{4}, \lam{1}{3}{4}{3}{4}{4}) =
(y_{3, 3} y_{4, 4})  \del{1}{2}{2}{4} +(-y_{2, 4} y_{4, 3})  \del{1}{3}{2}{4} +(y_{1, 3} y_{4, 4})  \del{2}{3}{2}{4} +(-y_{1, 2} y_{4, 4})  \del{2}{3}{3}{4} +(y_{1, 4} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{1, 2} y_{2, 4})  \del{3}{4}{3}{4} +(y_{4, 3} x_{3, 4})  \eps{1}{2}{2}{4} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{2}{3} +(-y_{3, 2} x_{2, 4})  \eps{1}{4}{3}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{2}{3} +(-y_{1, 3} x_{4, 4})  \eps{2}{3}{2}{4} +(y_{1, 2} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{4, 4})  \pho{1}{2}{3}{2}{3}{4}
----------------------------------
Epsilon:
2,3
2,4
Lam:
2,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(3)(4)*y(4)(2)*x(2)(2)
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(3)(4)*y(4)(2)*x(2)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,4
Quotient:
-y(2)(2)*y(3)(1)+y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(2)*y(3)(1)*y(4)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,4
Quotient:
-y(3)(2)
Lead Term of Product:
y(3)(2)^2*y(4)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Psi
2,3,4
1,2,4
Quotient:
-x(3)(2)
Lead Term of Product:
y(2)(4)*y(3)(2)*y(4)(1)*x(3)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(3)(2)*y(4)(1)*x(2)(2)+y(3)(1)*y(4)(2)*x(2)(2)+y(2)(2)*y(4)(1)*x(3)(2)-y(2)(1)*y(4)(2)*x(3)(2)-y(2)(2)*y(3)(1)*x(4)(2)+y(2)(1)*y(3)(2)*x(4)(2)) - (-y(3)(2)*y(4)(1))*(y(3)(4)*x(2)(2)-y(3)(2)*x(2)(4)-y(2)(4)*x(3)(2)+y(2)(2)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(3)(4)*y(4)(2)*x(2)(2)+y(3)(2)^2*y(4)(1)*x(2)(4)+y(2)(4)*y(3)(2)*y(4)(1)*x(3)(2)-y(2)(2)*y(3)(4)*y(4)(1)*x(3)(2)+y(2)(1)*y(3)(4)*y(4)(2)*x(3)(2)-y(2)(2)*y(3)(2)*y(4)(1)*x(3)(4)+y(2)(2)*y(3)(1)*y(3)(4)*x(4)(2)-y(2)(1)*y(3)(2)*y(3)(4)*x(4)(2)
-----------
TeX output:
S(\eps{2}{3}{2}{4}, \lam{2}{3}{4}{1}{2}{2}) =
(-y_{3, 1} y_{4, 2})  \eps{2}{3}{2}{4} +(-y_{2, 2} y_{3, 1}+y_{2, 1} y_{3, 2})  \eps{3}{4}{2}{4} +(-y_{3, 2})  \lam{2}{3}{4}{1}{2}{4} +(-x_{3, 2})  \psi{2}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
2,3
2,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
2,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(2)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
-y(2)(4)*y(4)(1)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(2)(4)*y(3)(1)
Lead Term of Product:
-y(2)(4)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(2)(1)*y(2)(4)
Lead Term of Product:
y(2)(1)*y(2)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(2)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(4)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(4)*x(2)(2)-y(3)(2)*x(2)(4)-y(2)(4)*x(3)(2)+y(2)(2)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(2)(2)*x(2)(4)+y(3)(2)*y(4)(1)*x(2)(4)^2+y(2)(4)*y(4)(1)*x(2)(4)*x(3)(2)-y(2)(4)*y(4)(1)*x(2)(2)*x(3)(4)+y(2)(1)*y(4)(4)*x(2)(2)*x(3)(4)-y(2)(2)*y(4)(1)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(1)*x(2)(2)*x(4)(4)-y(2)(1)*y(3)(4)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{2}{4}, \lam{2}{3}{4}{1}{4}{4}) =
(-y_{2, 4} y_{4, 1})  \del{2}{3}{2}{4} +(y_{2, 4} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{2, 1} y_{2, 4})  \del{3}{4}{2}{4} +(-y_{2, 1} x_{4, 4})  \eps{2}{3}{2}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{2}{4} +(-x_{2, 4})  \lam{2}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
2,3
2,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
2,4
Lam:
2,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(2)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
-y(2)(4)*y(4)(2)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(2)(4)*y(3)(2)
Lead Term of Product:
-y(2)(4)*y(3)(2)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(2)(2)*y(2)(4)
Lead Term of Product:
y(2)(2)*y(2)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(2)(2)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
-y(3)(2)*x(2)(4)+y(2)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(2)(2)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(4)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(2)(4))*(y(3)(4)*x(2)(2)-y(3)(2)*x(2)(4)-y(2)(4)*x(3)(2)+y(2)(2)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(2)(2)*x(2)(4)+y(3)(2)*y(4)(2)*x(2)(4)^2+y(2)(4)*y(4)(2)*x(2)(4)*x(3)(2)-y(2)(4)*y(4)(2)*x(2)(2)*x(3)(4)+y(2)(2)*y(4)(4)*x(2)(2)*x(3)(4)-y(2)(2)*y(4)(2)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(2)*x(2)(2)*x(4)(4)-y(2)(2)*y(3)(4)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{2}{4}, \lam{2}{3}{4}{2}{4}{4}) =
(-y_{2, 4} y_{4, 2})  \del{2}{3}{2}{4} +(y_{2, 4} y_{3, 2})  \del{2}{4}{2}{4} +(-y_{2, 2} y_{2, 4})  \del{3}{4}{2}{4} +(-y_{2, 2} x_{4, 4})  \eps{2}{3}{2}{4} +(-y_{3, 2} x_{2, 4}+y_{2, 2} x_{3, 4})  \eps{2}{4}{2}{4}
----------------------------------
Epsilon:
2,3
2,4
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(2)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
-y(2)(4)*y(4)(3)+y(2)(3)*y(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(2)(2)*y(4)(4)
Lead Term of Product:
y(2)(2)*y(4)(4)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(2)(4)*y(3)(2)
Lead Term of Product:
-y(2)(4)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(2)(2)*y(2)(4)
Lead Term of Product:
y(2)(2)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(4)(4)*x(2)(4)+y(2)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(2)(3)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(2)*x(2)(4)+y(2)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(2)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(2)(4))*(y(3)(4)*x(2)(2)-y(3)(2)*x(2)(4)-y(2)(4)*x(3)(2)+y(2)(2)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(2)(2)*x(2)(4)+y(3)(2)*y(4)(3)*x(2)(4)^2+y(2)(4)*y(4)(3)*x(2)(4)*x(3)(2)-y(2)(4)*y(4)(3)*x(2)(2)*x(3)(4)+y(2)(3)*y(4)(4)*x(2)(2)*x(3)(4)-y(2)(2)*y(4)(3)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(3)*x(2)(2)*x(4)(4)-y(2)(3)*y(3)(4)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{2}{4}, \lam{2}{3}{4}{3}{4}{4}) =
(-y_{2, 4} y_{4, 3}+y_{2, 3} y_{4, 4})  \del{2}{3}{2}{4} +(-y_{2, 2} y_{4, 4})  \del{2}{3}{3}{4} +(y_{2, 4} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{2, 2} y_{2, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{2, 4}+y_{2, 4} x_{4, 4})  \eps{2}{3}{2}{3} +(-y_{2, 3} x_{4, 4})  \eps{2}{3}{2}{4} +(-y_{3, 2} x_{2, 4}+y_{2, 2} x_{3, 4})  \eps{2}{4}{3}{4}
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(1)(4)*x(2)(3)
Divisor:
Delta
1,2
3,4
Quotient:
y(3)(1)*y(4)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(2)(4)*y(4)(1)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(1)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(4)*x(2)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(3))*(-y(3)(4)*y(4)(1)*x(1)(4)+y(3)(1)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(1)*x(3)(4)-y(1)(1)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(1)*x(4)(4)+y(1)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(1)(4))*(y(3)(4)*x(2)(3)-y(3)(3)*x(2)(4)-y(2)(4)*x(3)(3)+y(2)(3)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(1)(4)*x(2)(3)+y(3)(3)*y(4)(1)*x(1)(4)*x(2)(4)+y(2)(4)*y(4)(1)*x(1)(4)*x(3)(3)-y(2)(3)*y(4)(1)*x(1)(4)*x(3)(4)-y(1)(4)*y(4)(1)*x(2)(3)*x(3)(4)+y(1)(1)*y(4)(4)*x(2)(3)*x(3)(4)+y(1)(4)*y(3)(1)*x(2)(3)*x(4)(4)-y(1)(1)*y(3)(4)*x(2)(3)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{3}{4}, \lam{1}{3}{4}{1}{4}{4}) =
(y_{3, 1} y_{4, 4})  \del{1}{2}{3}{4} +(-y_{2, 4} y_{4, 1})  \del{1}{3}{3}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{1, 1} y_{2, 4})  \del{3}{4}{3}{4} +(y_{4, 1} x_{3, 4})  \eps{1}{2}{3}{4} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{3}{4} +(-y_{1, 1} x_{4, 4})  \eps{2}{3}{3}{4} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{2, 4})  \lam{1}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(3)
Divisor:
Delta
1,2
3,4
Quotient:
y(3)(2)*y(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(2)(4)*y(4)(2)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(2)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(2)*y(2)(4)
Lead Term of Product:
y(1)(2)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(4)(2)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(2)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(4)*x(2)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
y(1)(2)*x(3)(4)
Lead Term of Product:
y(1)(2)*y(4)(4)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
2,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(2)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(3))*(-y(3)(4)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(1)(4))*(y(3)(4)*x(2)(3)-y(3)(3)*x(2)(4)-y(2)(4)*x(3)(3)+y(2)(3)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(3)+y(3)(3)*y(4)(2)*x(1)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(1)(4)*x(3)(3)-y(2)(3)*y(4)(2)*x(1)(4)*x(3)(4)-y(1)(4)*y(4)(2)*x(2)(3)*x(3)(4)+y(1)(2)*y(4)(4)*x(2)(3)*x(3)(4)+y(1)(4)*y(3)(2)*x(2)(3)*x(4)(4)-y(1)(2)*y(3)(4)*x(2)(3)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{3}{4}, \lam{1}{3}{4}{2}{4}{4}) =
(y_{3, 2} y_{4, 4})  \del{1}{2}{3}{4} +(-y_{2, 4} y_{4, 2})  \del{1}{3}{3}{4} +(y_{1, 4} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{1, 2} y_{2, 4})  \del{3}{4}{3}{4} +(y_{4, 2} x_{3, 4})  \eps{1}{2}{3}{4} +(-y_{3, 2} x_{2, 4})  \eps{1}{4}{3}{4} +(-y_{1, 2} x_{4, 4})  \eps{2}{3}{3}{4} +(y_{1, 2} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{2, 4})  \lam{1}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
2,3
3,4
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(3)
Divisor:
Delta
1,2
3,4
Quotient:
y(3)(3)*y(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(2)(4)*y(4)(3)
Lead Term of Product:
y(2)(4)*y(4)(3)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(3)
Lead Term of Product:
-y(1)(4)*y(3)(3)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(3)*y(2)(4)
Lead Term of Product:
y(1)(3)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(4)(3)*x(3)(4)
Lead Term of Product:
y(2)(4)*y(4)(3)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(3)*x(2)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(3)*x(4)(4)
Lead Term of Product:
-y(1)(3)*y(3)(4)*x(2)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
y(1)(3)*x(3)(4)
Lead Term of Product:
y(1)(3)*y(4)(4)*x(2)(3)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(3))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(1)(4))*(y(3)(4)*x(2)(3)-y(3)(3)*x(2)(4)-y(2)(4)*x(3)(3)+y(2)(3)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(3)+y(3)(3)*y(4)(3)*x(1)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(1)(4)*x(3)(3)-y(2)(3)*y(4)(3)*x(1)(4)*x(3)(4)-y(1)(4)*y(4)(3)*x(2)(3)*x(3)(4)+y(1)(3)*y(4)(4)*x(2)(3)*x(3)(4)+y(1)(4)*y(3)(3)*x(2)(3)*x(4)(4)-y(1)(3)*y(3)(4)*x(2)(3)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{3}{4}, \lam{1}{3}{4}{3}{4}{4}) =
(y_{3, 3} y_{4, 4})  \del{1}{2}{3}{4} +(-y_{2, 4} y_{4, 3})  \del{1}{3}{3}{4} +(y_{1, 4} y_{3, 3})  \del{2}{4}{3}{4} +(-y_{1, 3} y_{2, 4})  \del{3}{4}{3}{4} +(y_{4, 3} x_{3, 4})  \eps{1}{2}{3}{4} +(-y_{3, 3} x_{2, 4})  \eps{1}{4}{3}{4} +(-y_{1, 3} x_{4, 4})  \eps{2}{3}{3}{4} +(y_{1, 3} x_{3, 4})  \eps{2}{4}{3}{4}
----------------------------------
Epsilon:
2,3
3,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
2,3,4
1,2,3
Lead Term of Spoly:
-y(3)(1)*y(3)(4)*y(4)(2)*x(2)(3)
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(3)(4)*y(4)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(2)(2)*y(3)(1)+y(2)(1)*y(3)(2)
Lead Term of Product:
-y(2)(2)*y(3)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(3)(2)*y(3)(3)*y(4)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Psi
2,3,4
1,2,3
Quotient:
x(3)(4)
Lead Term of Product:
-y(2)(3)*y(3)(2)*y(4)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Psi
2,3,4
1,2,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(2)(4)*y(3)(2)*y(4)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(3)(2)*y(4)(1)*x(2)(3)+y(3)(1)*y(4)(2)*x(2)(3)+y(2)(2)*y(4)(1)*x(3)(3)-y(2)(1)*y(4)(2)*x(3)(3)-y(2)(2)*y(3)(1)*x(4)(3)+y(2)(1)*y(3)(2)*x(4)(3)) - (-y(3)(2)*y(4)(1))*(y(3)(4)*x(2)(3)-y(3)(3)*x(2)(4)-y(2)(4)*x(3)(3)+y(2)(3)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(3)(4)*y(4)(2)*x(2)(3)+y(3)(2)*y(3)(3)*y(4)(1)*x(2)(4)+y(2)(4)*y(3)(2)*y(4)(1)*x(3)(3)-y(2)(2)*y(3)(4)*y(4)(1)*x(3)(3)+y(2)(1)*y(3)(4)*y(4)(2)*x(3)(3)-y(2)(3)*y(3)(2)*y(4)(1)*x(3)(4)+y(2)(2)*y(3)(1)*y(3)(4)*x(4)(3)-y(2)(1)*y(3)(2)*y(3)(4)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{3}{4}, \lam{2}{3}{4}{1}{2}{3}) =
(-y_{3, 1} y_{4, 2})  \eps{2}{3}{3}{4} +(-y_{2, 2} y_{3, 1}+y_{2, 1} y_{3, 2})  \eps{3}{4}{3}{4} +(-y_{3, 3})  \lam{2}{3}{4}{1}{2}{4} +(x_{3, 4})  \psi{2}{3}{4}{1}{2}{3} +(-x_{3, 3})  \psi{2}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
2,3
3,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
2,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(3)(4)*y(4)(3)*x(2)(3)
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(3)(1)*y(4)(3)
Lead Term of Product:
-y(3)(1)*y(3)(4)*y(4)(3)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(2)(3)*y(3)(1)+y(2)(1)*y(3)(3)
Lead Term of Product:
-y(2)(3)*y(3)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,3,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(3)(3)^2*y(4)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Psi
2,3,4
1,3,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(2)(4)*y(3)(3)*y(4)(1)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(3)(3)*y(4)(1)*x(2)(3)+y(3)(1)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(1)*x(3)(3)-y(2)(1)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(1)*x(4)(3)+y(2)(1)*y(3)(3)*x(4)(3)) - (-y(3)(3)*y(4)(1))*(y(3)(4)*x(2)(3)-y(3)(3)*x(2)(4)-y(2)(4)*x(3)(3)+y(2)(3)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(3)(4)*y(4)(3)*x(2)(3)+y(3)(3)^2*y(4)(1)*x(2)(4)+y(2)(4)*y(3)(3)*y(4)(1)*x(3)(3)-y(2)(3)*y(3)(4)*y(4)(1)*x(3)(3)+y(2)(1)*y(3)(4)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(3)*y(4)(1)*x(3)(4)+y(2)(3)*y(3)(1)*y(3)(4)*x(4)(3)-y(2)(1)*y(3)(3)*y(3)(4)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{3}{4}, \lam{2}{3}{4}{1}{3}{3}) =
(-y_{3, 1} y_{4, 3})  \eps{2}{3}{3}{4} +(-y_{2, 3} y_{3, 1}+y_{2, 1} y_{3, 3})  \eps{3}{4}{3}{4} +(-y_{3, 3})  \lam{2}{3}{4}{1}{3}{4} +(-x_{3, 3})  \psi{2}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
2,3
3,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
2,3,4
1,4,4
Lead Term of Spoly:
-y(3)(1)*y(4)(4)*x(2)(3)*x(2)(4)
Divisor:
Delta
2,3
3,4
Quotient:
-y(2)(4)*y(4)(1)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(2)(4)*y(3)(1)
Lead Term of Product:
-y(2)(4)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(2)(1)*y(2)(4)
Lead Term of Product:
y(2)(1)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(2)(1)*x(4)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(2)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(2)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(2)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(3))*(-y(3)(4)*y(4)(1)*x(2)(4)+y(3)(1)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(1)*x(3)(4)-y(2)(1)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(1)*x(4)(4)+y(2)(1)*y(3)(4)*x(4)(4)) - (-y(4)(1)*x(2)(4))*(y(3)(4)*x(2)(3)-y(3)(3)*x(2)(4)-y(2)(4)*x(3)(3)+y(2)(3)*x(3)(4))
-------
Rewrite:
-y(3)(1)*y(4)(4)*x(2)(3)*x(2)(4)+y(3)(3)*y(4)(1)*x(2)(4)^2+y(2)(4)*y(4)(1)*x(2)(4)*x(3)(3)-y(2)(4)*y(4)(1)*x(2)(3)*x(3)(4)+y(2)(1)*y(4)(4)*x(2)(3)*x(3)(4)-y(2)(3)*y(4)(1)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(1)*x(2)(3)*x(4)(4)-y(2)(1)*y(3)(4)*x(2)(3)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{3}{4}, \lam{2}{3}{4}{1}{4}{4}) =
(-y_{2, 4} y_{4, 1})  \del{2}{3}{3}{4} +(y_{2, 4} y_{3, 1})  \del{2}{4}{3}{4} +(-y_{2, 1} y_{2, 4})  \del{3}{4}{3}{4} +(-y_{2, 1} x_{4, 4})  \eps{2}{3}{3}{4} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{2, 4})  \lam{2}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
2,3
3,4
Lam:
2,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(3)(4)*y(4)(3)*x(2)(3)
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(3)(4)*y(4)(3)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(2)(3)*y(3)(2)+y(2)(2)*y(3)(3)
Lead Term of Product:
-y(2)(3)*y(3)(2)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
2,3,4
2,3,4
Quotient:
-y(3)(3)
Lead Term of Product:
y(3)(3)^2*y(4)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Psi
2,3,4
2,3,4
Quotient:
-x(3)(3)
Lead Term of Product:
y(2)(4)*y(3)(3)*y(4)(2)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(4))*(-y(3)(3)*y(4)(2)*x(2)(3)+y(3)(2)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(2)*x(3)(3)-y(2)(2)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(2)*x(4)(3)+y(2)(2)*y(3)(3)*x(4)(3)) - (-y(3)(3)*y(4)(2))*(y(3)(4)*x(2)(3)-y(3)(3)*x(2)(4)-y(2)(4)*x(3)(3)+y(2)(3)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(3)(4)*y(4)(3)*x(2)(3)+y(3)(3)^2*y(4)(2)*x(2)(4)+y(2)(4)*y(3)(3)*y(4)(2)*x(3)(3)-y(2)(3)*y(3)(4)*y(4)(2)*x(3)(3)+y(2)(2)*y(3)(4)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(3)*y(4)(2)*x(3)(4)+y(2)(3)*y(3)(2)*y(3)(4)*x(4)(3)-y(2)(2)*y(3)(3)*y(3)(4)*x(4)(3)
-----------
TeX output:
S(\eps{2}{3}{3}{4}, \lam{2}{3}{4}{2}{3}{3}) =
(-y_{3, 2} y_{4, 3})  \eps{2}{3}{3}{4} +(-y_{2, 3} y_{3, 2}+y_{2, 2} y_{3, 3})  \eps{3}{4}{3}{4} +(-y_{3, 3})  \lam{2}{3}{4}{2}{3}{4} +(-x_{3, 3})  \psi{2}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
2,3
3,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,3
3,4
Lam:
2,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(2)(3)*x(2)(4)
Divisor:
Delta
2,3
3,4
Quotient:
-y(2)(4)*y(4)(2)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(2)(4)*y(3)(2)
Lead Term of Product:
-y(2)(4)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(2)(2)*y(2)(4)
Lead Term of Product:
y(2)(2)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(2)(2)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(2)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(2)*x(2)(4)+y(2)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(2)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
2,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(2)*x(2)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(3))*(-y(3)(4)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(4)*x(4)(4)) - (-y(4)(2)*x(2)(4))*(y(3)(4)*x(2)(3)-y(3)(3)*x(2)(4)-y(2)(4)*x(3)(3)+y(2)(3)*x(3)(4))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(2)(3)*x(2)(4)+y(3)(3)*y(4)(2)*x(2)(4)^2+y(2)(4)*y(4)(2)*x(2)(4)*x(3)(3)-y(2)(4)*y(4)(2)*x(2)(3)*x(3)(4)+y(2)(2)*y(4)(4)*x(2)(3)*x(3)(4)-y(2)(3)*y(4)(2)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(2)*x(2)(3)*x(4)(4)-y(2)(2)*y(3)(4)*x(2)(3)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{3}{4}, \lam{2}{3}{4}{2}{4}{4}) =
(-y_{2, 4} y_{4, 2})  \del{2}{3}{3}{4} +(y_{2, 4} y_{3, 2})  \del{2}{4}{3}{4} +(-y_{2, 2} y_{2, 4})  \del{3}{4}{3}{4} +(-y_{2, 2} x_{4, 4})  \eps{2}{3}{3}{4} +(-y_{3, 2} x_{2, 4}+y_{2, 2} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{2, 4})  \lam{2}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
2,3
3,4
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(2)(3)*x(2)(4)
Divisor:
Delta
2,3
3,4
Quotient:
-y(2)(4)*y(4)(3)
Lead Term of Product:
y(2)(4)*y(4)(3)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(2)(4)*y(3)(3)
Lead Term of Product:
-y(2)(4)*y(3)(3)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(2)(3)*y(2)(4)
Lead Term of Product:
y(2)(3)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(2)(3)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(3)(4)*x(2)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(3)*x(2)(4)+y(2)(3)*x(3)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(2)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(3))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(4)(3)*x(2)(4))*(y(3)(4)*x(2)(3)-y(3)(3)*x(2)(4)-y(2)(4)*x(3)(3)+y(2)(3)*x(3)(4))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(2)(3)*x(2)(4)+y(3)(3)*y(4)(3)*x(2)(4)^2+y(2)(4)*y(4)(3)*x(2)(4)*x(3)(3)-y(2)(4)*y(4)(3)*x(2)(3)*x(3)(4)+y(2)(3)*y(4)(4)*x(2)(3)*x(3)(4)-y(2)(3)*y(4)(3)*x(2)(4)*x(3)(4)+y(2)(4)*y(3)(3)*x(2)(3)*x(4)(4)-y(2)(3)*y(3)(4)*x(2)(3)*x(4)(4)
-----------
TeX output:
S(\eps{2}{3}{3}{4}, \lam{2}{3}{4}{3}{4}{4}) =
(-y_{2, 4} y_{4, 3})  \del{2}{3}{3}{4} +(y_{2, 4} y_{3, 3})  \del{2}{4}{3}{4} +(-y_{2, 3} y_{2, 4})  \del{3}{4}{3}{4} +(-y_{2, 3} x_{4, 4})  \eps{2}{3}{3}{4} +(-y_{3, 3} x_{2, 4}+y_{2, 3} x_{3, 4})  \eps{2}{4}{3}{4}
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,4
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(4)(3)*x(1)(3)*x(2)(1)
Divisor:
Delta
1,2
1,3
Quotient:
y(2)(2)*y(4)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,3
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,3
Quotient:
-y(2)(2)*y(2)(3)
Lead Term of Product:
y(2)(2)*y(2)(3)*x(1)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(2)(1)*y(2)(3)
Lead Term of Product:
-y(2)(1)*y(2)(3)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(3)*x(2)(3)+y(2)(3)*x(4)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(1)*x(2)(3)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*x(2)(3)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(3)*x(2)(3)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(2)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(1)*x(2)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-x(2)(3)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(3)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(2)(3)*y(4)(2)*x(1)(3)+y(2)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(2)(3)-y(1)(2)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(4)(3)+y(1)(2)*y(2)(3)*x(4)(3)) - (-y(2)(3)*x(1)(3))*(y(4)(2)*x(2)(1)-y(4)(1)*x(2)(2)-y(2)(2)*x(4)(1)+y(2)(1)*x(4)(2))
-------
Rewrite:
-y(2)(2)*y(4)(3)*x(1)(3)*x(2)(1)+y(2)(3)*y(4)(1)*x(1)(3)*x(2)(2)-y(1)(3)*y(4)(2)*x(2)(1)*x(2)(3)+y(1)(2)*y(4)(3)*x(2)(1)*x(2)(3)+y(2)(2)*y(2)(3)*x(1)(3)*x(4)(1)-y(2)(1)*y(2)(3)*x(1)(3)*x(4)(2)+y(1)(3)*y(2)(2)*x(2)(1)*x(4)(3)-y(1)(2)*y(2)(3)*x(2)(1)*x(4)(3)
-----------
TeX output:
S(\eps{2}{4}{1}{2}, \lam{1}{2}{4}{2}{3}{3}) =
(y_{2, 2} y_{4, 3})  \del{1}{2}{1}{3} +(-y_{2, 3} y_{4, 1})  \del{1}{2}{2}{3} +(-y_{2, 2} y_{2, 3})  \del{1}{4}{1}{3} +(y_{2, 1} y_{2, 3})  \del{1}{4}{2}{3} +(y_{1, 3} y_{2, 2})  \del{2}{4}{1}{3} +(-y_{1, 1} y_{2, 3})  \del{2}{4}{2}{3} +(-y_{4, 3} x_{2, 3}+y_{2, 3} x_{4, 3})  \eps{1}{2}{1}{2} +(y_{4, 1} x_{2, 3})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{2, 3})  \eps{1}{4}{2}{3} +(-y_{1, 3} x_{2, 3})  \eps{2}{4}{1}{2} +(y_{1, 1} x_{2, 3})  \eps{2}{4}{2}{3} +(-x_{2, 3})  \lam{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,4
2,3,4
Lead Term of Spoly:
-y(2)(2)*y(4)(3)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(2)(2)*y(4)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(2)(2)*y(2)(3)
Lead Term of Product:
y(2)(2)*y(2)(3)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(2)(1)*y(2)(3)
Lead Term of Product:
-y(2)(1)*y(2)(3)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(3)*x(2)(4)+y(2)(3)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(1)*x(2)(4)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(3)*x(2)(4)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(1)*x(2)(4)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-x(2)(4)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(2)(3)*y(4)(2)*x(1)(4)+y(2)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(2)(4)-y(1)(2)*y(4)(3)*x(2)(4)-y(1)(3)*y(2)(2)*x(4)(4)+y(1)(2)*y(2)(3)*x(4)(4)) - (-y(2)(3)*x(1)(4))*(y(4)(2)*x(2)(1)-y(4)(1)*x(2)(2)-y(2)(2)*x(4)(1)+y(2)(1)*x(4)(2))
-------
Rewrite:
-y(2)(2)*y(4)(3)*x(1)(4)*x(2)(1)+y(2)(3)*y(4)(1)*x(1)(4)*x(2)(2)-y(1)(3)*y(4)(2)*x(2)(1)*x(2)(4)+y(1)(2)*y(4)(3)*x(2)(1)*x(2)(4)+y(2)(2)*y(2)(3)*x(1)(4)*x(4)(1)-y(2)(1)*y(2)(3)*x(1)(4)*x(4)(2)+y(1)(3)*y(2)(2)*x(2)(1)*x(4)(4)-y(1)(2)*y(2)(3)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{1}{2}, \lam{1}{2}{4}{2}{3}{4}) =
(y_{2, 2} y_{4, 3})  \del{1}{2}{1}{4} +(-y_{2, 3} y_{4, 1})  \del{1}{2}{2}{4} +(-y_{2, 2} y_{2, 3})  \del{1}{4}{1}{4} +(y_{2, 1} y_{2, 3})  \del{1}{4}{2}{4} +(y_{1, 3} y_{2, 2})  \del{2}{4}{1}{4} +(-y_{1, 1} y_{2, 3})  \del{2}{4}{2}{4} +(-y_{4, 3} x_{2, 4}+y_{2, 3} x_{4, 4})  \eps{1}{2}{1}{2} +(y_{4, 1} x_{2, 4})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{2, 4})  \eps{1}{4}{2}{3} +(-y_{1, 3} x_{2, 4})  \eps{2}{4}{1}{2} +(y_{1, 1} x_{2, 4})  \eps{2}{4}{2}{3} +(-x_{2, 4})  \lam{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,4
2,4,4
Lead Term of Spoly:
-y(2)(2)*y(4)(4)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(2)(2)*y(4)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(2)(4)*y(4)(1)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(2)(2)*y(2)(4)
Lead Term of Product:
y(2)(2)*y(2)(4)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(2)(1)*y(2)(4)
Lead Term of Product:
-y(2)(1)*y(2)(4)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(4)*y(2)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(1)*y(2)(4)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(4)*x(2)(4)+y(2)(4)*x(4)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
y(4)(1)*x(2)(4)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(2)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(4)(2)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
y(1)(1)*x(2)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(2)(4)*y(4)(2)*x(1)(4)+y(2)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(2)(4)-y(1)(2)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(2)*x(4)(4)+y(1)(2)*y(2)(4)*x(4)(4)) - (-y(2)(4)*x(1)(4))*(y(4)(2)*x(2)(1)-y(4)(1)*x(2)(2)-y(2)(2)*x(4)(1)+y(2)(1)*x(4)(2))
-------
Rewrite:
-y(2)(2)*y(4)(4)*x(1)(4)*x(2)(1)+y(2)(4)*y(4)(1)*x(1)(4)*x(2)(2)-y(1)(4)*y(4)(2)*x(2)(1)*x(2)(4)+y(1)(2)*y(4)(4)*x(2)(1)*x(2)(4)+y(2)(2)*y(2)(4)*x(1)(4)*x(4)(1)-y(2)(1)*y(2)(4)*x(1)(4)*x(4)(2)+y(1)(4)*y(2)(2)*x(2)(1)*x(4)(4)-y(1)(2)*y(2)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{1}{2}, \lam{1}{2}{4}{2}{4}{4}) =
(y_{2, 2} y_{4, 4})  \del{1}{2}{1}{4} +(-y_{2, 4} y_{4, 1})  \del{1}{2}{2}{4} +(-y_{2, 2} y_{2, 4})  \del{1}{4}{1}{4} +(y_{2, 1} y_{2, 4})  \del{1}{4}{2}{4} +(y_{1, 4} y_{2, 2})  \del{2}{4}{1}{4} +(-y_{1, 1} y_{2, 4})  \del{2}{4}{2}{4} +(-y_{4, 4} x_{2, 4}+y_{2, 4} x_{4, 4})  \eps{1}{2}{1}{2} +(y_{4, 1} x_{2, 4})  \eps{1}{2}{2}{4} +(-y_{2, 1} x_{2, 4})  \eps{1}{4}{2}{4} +(-y_{1, 4} x_{2, 4})  \eps{2}{4}{1}{2} +(y_{1, 1} x_{2, 4})  \eps{2}{4}{2}{4} +(-x_{2, 4})  \lam{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(3)*x(2)(1)
Divisor:
Delta
1,2
1,3
Quotient:
y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,3
Quotient:
-y(3)(3)*y(4)(1)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,3
Quotient:
-y(2)(2)*y(3)(3)
Lead Term of Product:
y(2)(2)*y(3)(3)*x(1)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(2)(1)*y(3)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,3
Quotient:
y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(2)*y(4)(3)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-y(1)(3)*y(4)(1)-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(3)*y(2)(1)-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(3)*y(2)(1)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(3)(3)*x(4)(3)
Lead Term of Product:
y(2)(2)*y(3)(3)*x(1)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(2)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
y(4)(1)*x(2)(3)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(3)*x(4)(3)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(1)(1)*x(4)(3)
Lead Term of Product:
-y(1)(1)*y(3)(3)*x(2)(2)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(3)*x(3)(3)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(2)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(1)*x(3)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(2)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(2)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(2)*x(1)(3)+y(3)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(3)(3)-y(1)(2)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(2)*x(4)(3)+y(1)(2)*y(3)(3)*x(4)(3)) - (-y(3)(3)*x(1)(3))*(y(4)(2)*x(2)(1)-y(4)(1)*x(2)(2)-y(2)(2)*x(4)(1)+y(2)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(3)*x(2)(1)+y(3)(3)*y(4)(1)*x(1)(3)*x(2)(2)-y(1)(3)*y(4)(2)*x(2)(1)*x(3)(3)+y(1)(2)*y(4)(3)*x(2)(1)*x(3)(3)+y(2)(2)*y(3)(3)*x(1)(3)*x(4)(1)-y(2)(1)*y(3)(3)*x(1)(3)*x(4)(2)+y(1)(3)*y(3)(2)*x(2)(1)*x(4)(3)-y(1)(2)*y(3)(3)*x(2)(1)*x(4)(3)
-----------
TeX output:
S(\eps{2}{4}{1}{2}, \lam{1}{3}{4}{2}{3}{3}) =
(y_{3, 2} y_{4, 3})  \del{1}{2}{1}{3} +(-y_{3, 3} y_{4, 1})  \del{1}{2}{2}{3} +(-y_{2, 2} y_{3, 3})  \del{1}{4}{1}{3} +(y_{2, 1} y_{3, 3})  \del{1}{4}{2}{3} +(y_{1, 2} y_{4, 3})  \del{2}{3}{1}{3} +(-y_{1, 3} y_{4, 1}-y_{1, 1} y_{4, 3})  \del{2}{3}{2}{3} +(y_{1, 3} y_{3, 1})  \del{2}{4}{2}{3} +(y_{1, 3} y_{2, 2})  \del{3}{4}{1}{3} +(-y_{1, 3} y_{2, 1}-y_{1, 1} y_{2, 3})  \del{3}{4}{2}{3} +(y_{3, 3} x_{4, 3})  \eps{1}{2}{1}{2} +(-y_{4, 3} x_{2, 3})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{2, 3})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{2, 3})  \eps{1}{4}{2}{3} +(y_{1, 3} x_{4, 3})  \eps{2}{3}{1}{2} +(-y_{1, 1} x_{4, 3})  \eps{2}{3}{2}{3} +(-y_{1, 3} x_{3, 3})  \eps{2}{4}{1}{2} +(y_{1, 1} x_{3, 3})  \eps{2}{4}{2}{3} +(-x_{2, 3})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(3)(3)*y(4)(1)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(2)(2)*y(3)(3)
Lead Term of Product:
y(2)(2)*y(3)(3)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(2)(1)*y(3)(3)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(2)*y(4)(3)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(3)*y(4)(1)-y(1)(1)*y(4)(3)
Lead Term of Product:
y(1)(3)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(1)(1)*y(4)(2)
Lead Term of Product:
-y(1)(1)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(3)*y(3)(1)
Lead Term of Product:
-y(1)(3)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(1)*y(3)(2)
Lead Term of Product:
y(1)(1)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(3)*y(2)(1)-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(3)*y(2)(1)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(1)(1)*y(2)(2)
Lead Term of Product:
-y(1)(1)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(3)(3)*x(4)(4)
Lead Term of Product:
y(2)(2)*y(3)(3)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
y(4)(1)*x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(3)*x(4)(4)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(3)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(3)*x(3)(4)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(3)*x(3)(4)-y(1)(3)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(3)*x(4)(4)) - (-y(3)(3)*x(1)(4))*(y(4)(2)*x(2)(1)-y(4)(1)*x(2)(2)-y(2)(2)*x(4)(1)+y(2)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(4)*x(2)(1)+y(3)(3)*y(4)(1)*x(1)(4)*x(2)(2)-y(1)(3)*y(4)(2)*x(2)(1)*x(3)(4)+y(1)(2)*y(4)(3)*x(2)(1)*x(3)(4)+y(2)(2)*y(3)(3)*x(1)(4)*x(4)(1)-y(2)(1)*y(3)(3)*x(1)(4)*x(4)(2)+y(1)(3)*y(3)(2)*x(2)(1)*x(4)(4)-y(1)(2)*y(3)(3)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{1}{2}, \lam{1}{3}{4}{2}{3}{4}) =
(y_{3, 2} y_{4, 3})  \del{1}{2}{1}{4} +(-y_{3, 3} y_{4, 1})  \del{1}{2}{2}{4} +(-y_{2, 2} y_{3, 3})  \del{1}{4}{1}{4} +(y_{2, 1} y_{3, 3})  \del{1}{4}{2}{4} +(y_{1, 2} y_{4, 3})  \del{2}{3}{1}{4} +(-y_{1, 3} y_{4, 1}-y_{1, 1} y_{4, 3})  \del{2}{3}{2}{4} +(y_{1, 1} y_{4, 2})  \del{2}{3}{3}{4} +(y_{1, 3} y_{3, 1})  \del{2}{4}{2}{4} +(-y_{1, 1} y_{3, 2})  \del{2}{4}{3}{4} +(y_{1, 3} y_{2, 2})  \del{3}{4}{1}{4} +(-y_{1, 3} y_{2, 1}-y_{1, 1} y_{2, 3})  \del{3}{4}{2}{4} +(y_{1, 1} y_{2, 2})  \del{3}{4}{3}{4} +(y_{3, 3} x_{4, 4})  \eps{1}{2}{1}{2} +(-y_{4, 3} x_{2, 4})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{2, 4})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{2}{3} +(y_{1, 3} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{1, 1} x_{4, 4})  \eps{2}{3}{2}{3} +(-y_{1, 3} x_{3, 4})  \eps{2}{4}{1}{2} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{2}{3} +(-x_{2, 4})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(3)(2)*y(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,4
Quotient:
-y(3)(4)*y(4)(1)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(2)(2)*y(3)(4)
Lead Term of Product:
y(2)(2)*y(3)(4)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(2)(1)*y(3)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(2)*y(4)(4)
Lead Term of Product:
-y(1)(2)*y(4)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(1)(4)*y(4)(1)-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(4)*y(2)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(4)*y(2)(1)-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(4)*y(2)(1)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
y(3)(4)*x(4)(4)
Lead Term of Product:
y(2)(2)*y(3)(4)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
y(4)(1)*x(2)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(4)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(2)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(4)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(1)(4))*(y(4)(2)*x(2)(1)-y(4)(1)*x(2)(2)-y(2)(2)*x(4)(1)+y(2)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(4)*x(2)(1)+y(3)(4)*y(4)(1)*x(1)(4)*x(2)(2)-y(1)(4)*y(4)(2)*x(2)(1)*x(3)(4)+y(1)(2)*y(4)(4)*x(2)(1)*x(3)(4)+y(2)(2)*y(3)(4)*x(1)(4)*x(4)(1)-y(2)(1)*y(3)(4)*x(1)(4)*x(4)(2)+y(1)(4)*y(3)(2)*x(2)(1)*x(4)(4)-y(1)(2)*y(3)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{1}{2}, \lam{1}{3}{4}{2}{4}{4}) =
(y_{3, 2} y_{4, 4})  \del{1}{2}{1}{4} +(-y_{3, 4} y_{4, 1})  \del{1}{2}{2}{4} +(-y_{2, 2} y_{3, 4})  \del{1}{4}{1}{4} +(y_{2, 1} y_{3, 4})  \del{1}{4}{2}{4} +(y_{1, 2} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{1, 4} y_{4, 1}-y_{1, 1} y_{4, 4})  \del{2}{3}{2}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{2}{4} +(y_{1, 4} y_{2, 2})  \del{3}{4}{1}{4} +(-y_{1, 4} y_{2, 1}-y_{1, 1} y_{2, 4})  \del{3}{4}{2}{4} +(y_{3, 4} x_{4, 4})  \eps{1}{2}{1}{2} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{2, 4})  \eps{1}{3}{2}{4} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{2}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{1, 1} x_{4, 4})  \eps{2}{3}{2}{4} +(-y_{1, 4} x_{3, 4})  \eps{2}{4}{1}{2} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{2}{4} +(-x_{2, 4})  \lam{1}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
2,4
1,2
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,2
Lam:
2,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(3)
Divisor:
Delta
2,3
1,3
Quotient:
y(2)(2)*y(4)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-y(2)(3)*y(4)(1)-y(2)(1)*y(4)(3)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
-y(2)(2)*y(3)(3)
Lead Term of Product:
y(2)(2)*y(3)(3)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(2)(3)*y(3)(1)+y(2)(1)*y(3)(3)
Lead Term of Product:
-y(2)(3)*y(3)(1)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
y(2)(2)*y(2)(3)
Lead Term of Product:
-y(2)(2)*y(2)(3)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-2*y(2)(1)*y(2)(3)
Lead Term of Product:
2*y(2)(1)*y(2)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(4)(3)*x(2)(3)+y(2)(3)*x(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(4)(1)*x(2)(3)-y(2)(1)*x(4)(3)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(2)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(2)(3)*x(3)(3)
Lead Term of Product:
-y(2)(3)*y(4)(2)*x(2)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(3)(1)*x(2)(3)+y(2)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(2)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,3
Quotient:
-x(2)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(2)(3)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(2)*x(2)(3)+y(3)(2)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(2)*x(3)(3)-y(2)(2)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(2)*x(4)(3)+y(2)(2)*y(3)(3)*x(4)(3)) - (-y(3)(3)*x(2)(3))*(y(4)(2)*x(2)(1)-y(4)(1)*x(2)(2)-y(2)(2)*x(4)(1)+y(2)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(3)+y(3)(3)*y(4)(1)*x(2)(2)*x(2)(3)-y(2)(3)*y(4)(2)*x(2)(1)*x(3)(3)+y(2)(2)*y(4)(3)*x(2)(1)*x(3)(3)+y(2)(2)*y(3)(3)*x(2)(3)*x(4)(1)-y(2)(1)*y(3)(3)*x(2)(3)*x(4)(2)+y(2)(3)*y(3)(2)*x(2)(1)*x(4)(3)-y(2)(2)*y(3)(3)*x(2)(1)*x(4)(3)
-----------
TeX output:
S(\eps{2}{4}{1}{2}, \lam{2}{3}{4}{2}{3}{3}) =
(y_{2, 2} y_{4, 3})  \del{2}{3}{1}{3} +(-y_{2, 3} y_{4, 1}-y_{2, 1} y_{4, 3})  \del{2}{3}{2}{3} +(-y_{2, 2} y_{3, 3})  \del{2}{4}{1}{3} +(y_{2, 3} y_{3, 1}+y_{2, 1} y_{3, 3})  \del{2}{4}{2}{3} +(y_{2, 2} y_{2, 3})  \del{3}{4}{1}{3} +(-2 y_{2, 1} y_{2, 3})  \del{3}{4}{2}{3} +(-y_{4, 3} x_{2, 3}+y_{2, 3} x_{4, 3})  \eps{2}{3}{1}{2} +(y_{4, 1} x_{2, 3}-y_{2, 1} x_{4, 3})  \eps{2}{3}{2}{3} +(-y_{2, 3} x_{3, 3})  \eps{2}{4}{1}{2} +(-y_{3, 1} x_{2, 3}+y_{2, 1} x_{3, 3})  \eps{2}{4}{2}{3} +(-x_{2, 3})  \lam{2}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,4
1,2
Lam:
2,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
y(2)(2)*y(4)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(2)(3)*y(4)(1)-y(2)(1)*y(4)(3)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(1)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(2)(2)*y(3)(3)
Lead Term of Product:
y(2)(2)*y(3)(3)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(2)(3)*y(3)(1)+y(2)(1)*y(3)(3)
Lead Term of Product:
-y(2)(3)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(2)(1)*y(3)(2)
Lead Term of Product:
y(2)(1)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(2)(2)*y(2)(3)
Lead Term of Product:
-y(2)(2)*y(2)(3)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-2*y(2)(1)*y(2)(3)
Lead Term of Product:
2*y(2)(1)*y(2)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
y(2)(1)*y(2)(2)
Lead Term of Product:
-y(2)(1)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(4)(3)*x(2)(4)+y(2)(3)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(4)(1)*x(2)(4)-y(2)(1)*x(4)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(2)(3)*x(3)(4)
Lead Term of Product:
-y(2)(3)*y(4)(2)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,3
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(2)(3)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(3)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(3)*x(2)(4)+y(2)(3)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(3)*x(3)(4)-y(2)(3)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(3)*x(4)(4)) - (-y(3)(3)*x(2)(4))*(y(4)(2)*x(2)(1)-y(4)(1)*x(2)(2)-y(2)(2)*x(4)(1)+y(2)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(2)(1)*x(2)(4)+y(3)(3)*y(4)(1)*x(2)(2)*x(2)(4)-y(2)(3)*y(4)(2)*x(2)(1)*x(3)(4)+y(2)(2)*y(4)(3)*x(2)(1)*x(3)(4)+y(2)(2)*y(3)(3)*x(2)(4)*x(4)(1)-y(2)(1)*y(3)(3)*x(2)(4)*x(4)(2)+y(2)(3)*y(3)(2)*x(2)(1)*x(4)(4)-y(2)(2)*y(3)(3)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{1}{2}, \lam{2}{3}{4}{2}{3}{4}) =
(y_{2, 2} y_{4, 3})  \del{2}{3}{1}{4} +(-y_{2, 3} y_{4, 1}-y_{2, 1} y_{4, 3})  \del{2}{3}{2}{4} +(y_{2, 1} y_{4, 2})  \del{2}{3}{3}{4} +(-y_{2, 2} y_{3, 3})  \del{2}{4}{1}{4} +(y_{2, 3} y_{3, 1}+y_{2, 1} y_{3, 3})  \del{2}{4}{2}{4} +(-y_{2, 1} y_{3, 2})  \del{2}{4}{3}{4} +(y_{2, 2} y_{2, 3})  \del{3}{4}{1}{4} +(-2 y_{2, 1} y_{2, 3})  \del{3}{4}{2}{4} +(y_{2, 1} y_{2, 2})  \del{3}{4}{3}{4} +(-y_{4, 3} x_{2, 4}+y_{2, 3} x_{4, 4})  \eps{2}{3}{1}{2} +(y_{4, 1} x_{2, 4}-y_{2, 1} x_{4, 4})  \eps{2}{3}{2}{3} +(-y_{2, 3} x_{3, 4})  \eps{2}{4}{1}{2} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{2}{3} +(-x_{2, 4})  \lam{2}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,4
1,2
Lam:
2,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(2)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
y(2)(2)*y(4)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(2)(4)*y(4)(1)-y(2)(1)*y(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(2)(2)*y(3)(4)
Lead Term of Product:
y(2)(2)*y(3)(4)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(2)(4)*y(3)(1)+y(2)(1)*y(3)(4)
Lead Term of Product:
-y(2)(4)*y(3)(1)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(2)(2)*y(2)(4)
Lead Term of Product:
-y(2)(2)*y(2)(4)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-2*y(2)(1)*y(2)(4)
Lead Term of Product:
2*y(2)(1)*y(2)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(4)(4)*x(2)(4)+y(2)(4)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
y(4)(1)*x(2)(4)-y(2)(1)*x(4)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(2)(4)*x(3)(4)
Lead Term of Product:
-y(2)(4)*y(4)(2)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(2)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(4)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(2)(4))*(y(4)(2)*x(2)(1)-y(4)(1)*x(2)(2)-y(2)(2)*x(4)(1)+y(2)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(2)(1)*x(2)(4)+y(3)(4)*y(4)(1)*x(2)(2)*x(2)(4)-y(2)(4)*y(4)(2)*x(2)(1)*x(3)(4)+y(2)(2)*y(4)(4)*x(2)(1)*x(3)(4)+y(2)(2)*y(3)(4)*x(2)(4)*x(4)(1)-y(2)(1)*y(3)(4)*x(2)(4)*x(4)(2)+y(2)(4)*y(3)(2)*x(2)(1)*x(4)(4)-y(2)(2)*y(3)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{1}{2}, \lam{2}{3}{4}{2}{4}{4}) =
(y_{2, 2} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{2, 4} y_{4, 1}-y_{2, 1} y_{4, 4})  \del{2}{3}{2}{4} +(-y_{2, 2} y_{3, 4})  \del{2}{4}{1}{4} +(y_{2, 4} y_{3, 1}+y_{2, 1} y_{3, 4})  \del{2}{4}{2}{4} +(y_{2, 2} y_{2, 4})  \del{3}{4}{1}{4} +(-2 y_{2, 1} y_{2, 4})  \del{3}{4}{2}{4} +(-y_{4, 4} x_{2, 4}+y_{2, 4} x_{4, 4})  \eps{2}{3}{1}{2} +(y_{4, 1} x_{2, 4}-y_{2, 1} x_{4, 4})  \eps{2}{3}{2}{4} +(-y_{2, 4} x_{3, 4})  \eps{2}{4}{1}{2} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{2}{4} +(-x_{2, 4})  \lam{2}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
2,4
1,2
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,2,4
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(4)(4)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(2)(3)*y(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(2)(4)*y(4)(1)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(2)(3)*y(2)(4)
Lead Term of Product:
y(2)(3)*y(2)(4)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(2)(1)*y(2)(4)
Lead Term of Product:
-y(2)(1)*y(2)(4)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(1)*y(2)(4)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(4)(4)*x(2)(4)+y(2)(4)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(4)(1)*x(2)(4)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(1)*x(2)(4)
Lead Term of Product:
-y(2)(1)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,3
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
y(1)(1)*x(2)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(2)(4)*y(4)(3)*x(1)(4)+y(2)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(2)(4)-y(1)(3)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(4)(4)+y(1)(3)*y(2)(4)*x(4)(4)) - (-y(2)(4)*x(1)(4))*(y(4)(3)*x(2)(1)-y(4)(1)*x(2)(3)-y(2)(3)*x(4)(1)+y(2)(1)*x(4)(3))
-------
Rewrite:
-y(2)(3)*y(4)(4)*x(1)(4)*x(2)(1)+y(2)(4)*y(4)(1)*x(1)(4)*x(2)(3)-y(1)(4)*y(4)(3)*x(2)(1)*x(2)(4)+y(1)(3)*y(4)(4)*x(2)(1)*x(2)(4)+y(2)(3)*y(2)(4)*x(1)(4)*x(4)(1)-y(2)(1)*y(2)(4)*x(1)(4)*x(4)(3)+y(1)(4)*y(2)(3)*x(2)(1)*x(4)(4)-y(1)(3)*y(2)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{1}{3}, \lam{1}{2}{4}{3}{4}{4}) =
(y_{2, 3} y_{4, 4})  \del{1}{2}{1}{4} +(-y_{2, 4} y_{4, 1})  \del{1}{2}{3}{4} +(-y_{2, 3} y_{2, 4})  \del{1}{4}{1}{4} +(y_{2, 1} y_{2, 4})  \del{1}{4}{3}{4} +(y_{1, 4} y_{2, 3})  \del{2}{4}{1}{4} +(-y_{1, 1} y_{2, 4})  \del{2}{4}{3}{4} +(-y_{4, 4} x_{2, 4}+y_{2, 4} x_{4, 4})  \eps{1}{2}{1}{3} +(y_{4, 1} x_{2, 4})  \eps{1}{2}{3}{4} +(-y_{2, 1} x_{2, 4})  \eps{1}{4}{3}{4} +(-y_{1, 4} x_{2, 4})  \eps{2}{4}{1}{3} +(y_{1, 1} x_{2, 4})  \eps{2}{4}{3}{4} +(-x_{2, 4})  \lam{1}{2}{4}{1}{3}{4}
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(1)
Divisor:
Delta
1,2
1,4
Quotient:
y(3)(3)*y(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(3)(4)*y(4)(1)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(2)(3)*y(3)(4)
Lead Term of Product:
y(2)(3)*y(3)(4)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(2)(1)*y(3)(4)
Lead Term of Product:
-y(2)(1)*y(3)(4)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(3)*y(4)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(4)*y(4)(1)-y(1)(1)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(1)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(1)
Lead Term of Product:
-y(1)(4)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(4)*y(2)(1)-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(4)*y(2)(1)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
y(3)(4)*x(4)(4)
Lead Term of Product:
y(2)(3)*y(3)(4)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
y(4)(1)*x(2)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*x(2)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(1)*x(4)(4)
Lead Term of Product:
-y(1)(1)*y(3)(4)*x(2)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,3
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(1)(4))*(y(4)(3)*x(2)(1)-y(4)(1)*x(2)(3)-y(2)(3)*x(4)(1)+y(2)(1)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(1)+y(3)(4)*y(4)(1)*x(1)(4)*x(2)(3)-y(1)(4)*y(4)(3)*x(2)(1)*x(3)(4)+y(1)(3)*y(4)(4)*x(2)(1)*x(3)(4)+y(2)(3)*y(3)(4)*x(1)(4)*x(4)(1)-y(2)(1)*y(3)(4)*x(1)(4)*x(4)(3)+y(1)(4)*y(3)(3)*x(2)(1)*x(4)(4)-y(1)(3)*y(3)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{1}{3}, \lam{1}{3}{4}{3}{4}{4}) =
(y_{3, 3} y_{4, 4})  \del{1}{2}{1}{4} +(-y_{3, 4} y_{4, 1})  \del{1}{2}{3}{4} +(-y_{2, 3} y_{3, 4})  \del{1}{4}{1}{4} +(y_{2, 1} y_{3, 4})  \del{1}{4}{3}{4} +(y_{1, 3} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{1, 4} y_{4, 1}-y_{1, 1} y_{4, 4})  \del{2}{3}{3}{4} +(y_{1, 4} y_{3, 1})  \del{2}{4}{3}{4} +(y_{1, 4} y_{2, 3})  \del{3}{4}{1}{4} +(-y_{1, 4} y_{2, 1}-y_{1, 1} y_{2, 4})  \del{3}{4}{3}{4} +(y_{3, 4} x_{4, 4})  \eps{1}{2}{1}{3} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{1}{3} +(y_{4, 1} x_{2, 4})  \eps{1}{3}{3}{4} +(-y_{3, 1} x_{2, 4})  \eps{1}{4}{3}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{1}{3} +(-y_{1, 1} x_{4, 4})  \eps{2}{3}{3}{4} +(-y_{1, 4} x_{3, 4})  \eps{2}{4}{1}{3} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{2, 4})  \lam{1}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
2,4
1,3
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,3
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(2)(1)*x(2)(4)
Divisor:
Delta
2,3
1,4
Quotient:
y(2)(3)*y(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(2)(4)*y(4)(1)-y(2)(1)*y(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(2)(3)*y(3)(4)
Lead Term of Product:
y(2)(3)*y(3)(4)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(2)(4)*y(3)(1)+y(2)(1)*y(3)(4)
Lead Term of Product:
-y(2)(4)*y(3)(1)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(2)(3)*y(2)(4)
Lead Term of Product:
-y(2)(3)*y(2)(4)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-2*y(2)(1)*y(2)(4)
Lead Term of Product:
2*y(2)(1)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(4)(4)*x(2)(4)+y(2)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(2)(1)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
y(4)(1)*x(2)(4)-y(2)(1)*x(4)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(2)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,3
Quotient:
-y(2)(4)*x(3)(4)
Lead Term of Product:
-y(2)(4)*y(4)(3)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(1)*x(2)(4)+y(2)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(2)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(2)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(1))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(2)(4))*(y(4)(3)*x(2)(1)-y(4)(1)*x(2)(3)-y(2)(3)*x(4)(1)+y(2)(1)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(2)(1)*x(2)(4)+y(3)(4)*y(4)(1)*x(2)(3)*x(2)(4)-y(2)(4)*y(4)(3)*x(2)(1)*x(3)(4)+y(2)(3)*y(4)(4)*x(2)(1)*x(3)(4)+y(2)(3)*y(3)(4)*x(2)(4)*x(4)(1)-y(2)(1)*y(3)(4)*x(2)(4)*x(4)(3)+y(2)(4)*y(3)(3)*x(2)(1)*x(4)(4)-y(2)(3)*y(3)(4)*x(2)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{1}{3}, \lam{2}{3}{4}{3}{4}{4}) =
(y_{2, 3} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{2, 4} y_{4, 1}-y_{2, 1} y_{4, 4})  \del{2}{3}{3}{4} +(-y_{2, 3} y_{3, 4})  \del{2}{4}{1}{4} +(y_{2, 4} y_{3, 1}+y_{2, 1} y_{3, 4})  \del{2}{4}{3}{4} +(y_{2, 3} y_{2, 4})  \del{3}{4}{1}{4} +(-2 y_{2, 1} y_{2, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{2, 4}+y_{2, 4} x_{4, 4})  \eps{2}{3}{1}{3} +(y_{4, 1} x_{2, 4}-y_{2, 1} x_{4, 4})  \eps{2}{3}{3}{4} +(-y_{2, 4} x_{3, 4})  \eps{2}{4}{1}{3} +(-y_{3, 1} x_{2, 4}+y_{2, 1} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{2, 4})  \lam{2}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
1,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,2,4
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(4)(4)*x(1)(4)*x(2)(2)
Divisor:
Delta
1,2
2,4
Quotient:
y(2)(3)*y(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(2)(4)*y(4)(2)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
-y(2)(3)*y(2)(4)
Lead Term of Product:
y(2)(3)*y(2)(4)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(2)(2)*y(2)(4)
Lead Term of Product:
-y(2)(2)*y(2)(4)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
-y(1)(2)*y(2)(4)
Lead Term of Product:
y(1)(2)*y(2)(4)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(4)(4)*x(2)(4)+y(2)(4)*x(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(4)(2)*x(2)(4)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(2)*x(2)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(1)(4)*x(2)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
y(1)(2)*x(2)(4)
Lead Term of Product:
y(1)(2)*y(4)(4)*x(2)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
2,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(2)(4)*y(4)(3)*x(1)(4)+y(2)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(2)(4)-y(1)(3)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(4)(4)+y(1)(3)*y(2)(4)*x(4)(4)) - (-y(2)(4)*x(1)(4))*(y(4)(3)*x(2)(2)-y(4)(2)*x(2)(3)-y(2)(3)*x(4)(2)+y(2)(2)*x(4)(3))
-------
Rewrite:
-y(2)(3)*y(4)(4)*x(1)(4)*x(2)(2)+y(2)(4)*y(4)(2)*x(1)(4)*x(2)(3)-y(1)(4)*y(4)(3)*x(2)(2)*x(2)(4)+y(1)(3)*y(4)(4)*x(2)(2)*x(2)(4)+y(2)(3)*y(2)(4)*x(1)(4)*x(4)(2)-y(2)(2)*y(2)(4)*x(1)(4)*x(4)(3)+y(1)(4)*y(2)(3)*x(2)(2)*x(4)(4)-y(1)(3)*y(2)(4)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{2}{3}, \lam{1}{2}{4}{3}{4}{4}) =
(y_{2, 3} y_{4, 4})  \del{1}{2}{2}{4} +(-y_{2, 4} y_{4, 2})  \del{1}{2}{3}{4} +(-y_{2, 3} y_{2, 4})  \del{1}{4}{2}{4} +(y_{2, 2} y_{2, 4})  \del{1}{4}{3}{4} +(y_{1, 4} y_{2, 3})  \del{2}{4}{2}{4} +(-y_{1, 2} y_{2, 4})  \del{2}{4}{3}{4} +(-y_{4, 4} x_{2, 4}+y_{2, 4} x_{4, 4})  \eps{1}{2}{2}{3} +(y_{4, 2} x_{2, 4})  \eps{1}{2}{3}{4} +(-y_{2, 2} x_{2, 4})  \eps{1}{4}{3}{4} +(-y_{1, 4} x_{2, 4})  \eps{2}{4}{2}{3} +(y_{1, 2} x_{2, 4})  \eps{2}{4}{3}{4} +(-x_{2, 4})  \lam{1}{2}{4}{2}{3}{4}
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(2)
Divisor:
Delta
1,2
2,4
Quotient:
y(3)(3)*y(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,2
3,4
Quotient:
-y(3)(4)*y(4)(2)
Lead Term of Product:
y(3)(4)*y(4)(2)*x(1)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
-y(2)(3)*y(3)(4)
Lead Term of Product:
y(2)(3)*y(3)(4)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(2)(2)*y(3)(4)
Lead Term of Product:
-y(2)(2)*y(3)(4)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(3)*y(4)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(1)(4)*y(4)(2)-y(1)(2)*y(4)(4)
Lead Term of Product:
y(1)(4)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(1)(4)*y(3)(2)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(4)*y(2)(2)-y(1)(2)*y(2)(4)
Lead Term of Product:
y(1)(4)*y(2)(2)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(3)(4)*x(4)(4)
Lead Term of Product:
y(2)(3)*y(3)(4)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(4)(4)*x(2)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
y(4)(2)*x(2)(4)
Lead Term of Product:
y(3)(4)*y(4)(2)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(2)*x(2)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
-y(1)(2)*x(4)(4)
Lead Term of Product:
-y(1)(2)*y(3)(4)*x(2)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
y(1)(2)*x(3)(4)
Lead Term of Product:
y(1)(2)*y(4)(4)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
2,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(2)*x(1)(4)*x(2)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(1)(4))*(y(4)(3)*x(2)(2)-y(4)(2)*x(2)(3)-y(2)(3)*x(4)(2)+y(2)(2)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(4)*x(2)(2)+y(3)(4)*y(4)(2)*x(1)(4)*x(2)(3)-y(1)(4)*y(4)(3)*x(2)(2)*x(3)(4)+y(1)(3)*y(4)(4)*x(2)(2)*x(3)(4)+y(2)(3)*y(3)(4)*x(1)(4)*x(4)(2)-y(2)(2)*y(3)(4)*x(1)(4)*x(4)(3)+y(1)(4)*y(3)(3)*x(2)(2)*x(4)(4)-y(1)(3)*y(3)(4)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{2}{3}, \lam{1}{3}{4}{3}{4}{4}) =
(y_{3, 3} y_{4, 4})  \del{1}{2}{2}{4} +(-y_{3, 4} y_{4, 2})  \del{1}{2}{3}{4} +(-y_{2, 3} y_{3, 4})  \del{1}{4}{2}{4} +(y_{2, 2} y_{3, 4})  \del{1}{4}{3}{4} +(y_{1, 3} y_{4, 4})  \del{2}{3}{2}{4} +(-y_{1, 4} y_{4, 2}-y_{1, 2} y_{4, 4})  \del{2}{3}{3}{4} +(y_{1, 4} y_{3, 2})  \del{2}{4}{3}{4} +(y_{1, 4} y_{2, 3})  \del{3}{4}{2}{4} +(-y_{1, 4} y_{2, 2}-y_{1, 2} y_{2, 4})  \del{3}{4}{3}{4} +(y_{3, 4} x_{4, 4})  \eps{1}{2}{2}{3} +(-y_{4, 4} x_{2, 4})  \eps{1}{3}{2}{3} +(y_{4, 2} x_{2, 4})  \eps{1}{3}{3}{4} +(-y_{3, 2} x_{2, 4})  \eps{1}{4}{3}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{2}{3} +(-y_{1, 2} x_{4, 4})  \eps{2}{3}{3}{4} +(-y_{1, 4} x_{3, 4})  \eps{2}{4}{2}{3} +(y_{1, 2} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{2, 4})  \lam{1}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
2,4
2,3
Lam:
2,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*y(4)(3)*x(2)(2)
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*y(4)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
-y(2)(2)*y(4)(1)+y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(2)*y(4)(1)*y(4)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,3
Quotient:
-y(4)(2)
Lead Term of Product:
y(3)(2)*y(4)(1)*y(4)(2)*x(2)(3)
Lead term is well behaved
Divisor:
Psi
2,3,4
1,2,3
Quotient:
-x(4)(2)
Lead Term of Product:
y(2)(3)*y(3)(2)*y(4)(1)*x(4)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(3))*(-y(3)(2)*y(4)(1)*x(2)(2)+y(3)(1)*y(4)(2)*x(2)(2)+y(2)(2)*y(4)(1)*x(3)(2)-y(2)(1)*y(4)(2)*x(3)(2)-y(2)(2)*y(3)(1)*x(4)(2)+y(2)(1)*y(3)(2)*x(4)(2)) - (-y(3)(2)*y(4)(1))*(y(4)(3)*x(2)(2)-y(4)(2)*x(2)(3)-y(2)(3)*x(4)(2)+y(2)(2)*x(4)(3))
-------
Rewrite:
-y(3)(1)*y(4)(2)*y(4)(3)*x(2)(2)+y(3)(2)*y(4)(1)*y(4)(2)*x(2)(3)-y(2)(2)*y(4)(1)*y(4)(3)*x(3)(2)+y(2)(1)*y(4)(2)*y(4)(3)*x(3)(2)+y(2)(3)*y(3)(2)*y(4)(1)*x(4)(2)+y(2)(2)*y(3)(1)*y(4)(3)*x(4)(2)-y(2)(1)*y(3)(2)*y(4)(3)*x(4)(2)-y(2)(2)*y(3)(2)*y(4)(1)*x(4)(3)
-----------
TeX output:
S(\eps{2}{4}{2}{3}, \lam{2}{3}{4}{1}{2}{2}) =
(-y_{3, 1} y_{4, 2})  \eps{2}{4}{2}{3} +(-y_{2, 2} y_{4, 1}+y_{2, 1} y_{4, 2})  \eps{3}{4}{2}{3} +(-y_{4, 2})  \lam{2}{3}{4}{1}{2}{3} +(-x_{4, 2})  \psi{2}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
2,4
2,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,3
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(2)(2)*x(2)(4)
Divisor:
Delta
2,3
2,4
Quotient:
y(2)(3)*y(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(2)(4)*y(4)(2)-y(2)(2)*y(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(2)(3)*y(3)(4)
Lead Term of Product:
y(2)(3)*y(3)(4)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(2)(4)*y(3)(2)+y(2)(2)*y(3)(4)
Lead Term of Product:
-y(2)(4)*y(3)(2)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
y(2)(3)*y(2)(4)
Lead Term of Product:
-y(2)(3)*y(2)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-2*y(2)(2)*y(2)(4)
Lead Term of Product:
2*y(2)(2)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(4)(4)*x(2)(4)+y(2)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(2)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
y(4)(2)*x(2)(4)-y(2)(2)*x(4)(4)
Lead Term of Product:
y(3)(4)*y(4)(2)*x(2)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(2)(4)*x(3)(4)
Lead Term of Product:
-y(2)(4)*y(4)(3)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(2)*x(2)(4)+y(2)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(2)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
2,3,4
Quotient:
-x(2)(4)
Lead Term of Product:
y(3)(3)*y(4)(2)*x(2)(4)^2
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(2)(2))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(2)(4))*(y(4)(3)*x(2)(2)-y(4)(2)*x(2)(3)-y(2)(3)*x(4)(2)+y(2)(2)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(2)(2)*x(2)(4)+y(3)(4)*y(4)(2)*x(2)(3)*x(2)(4)-y(2)(4)*y(4)(3)*x(2)(2)*x(3)(4)+y(2)(3)*y(4)(4)*x(2)(2)*x(3)(4)+y(2)(3)*y(3)(4)*x(2)(4)*x(4)(2)-y(2)(2)*y(3)(4)*x(2)(4)*x(4)(3)+y(2)(4)*y(3)(3)*x(2)(2)*x(4)(4)-y(2)(3)*y(3)(4)*x(2)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{2}{3}, \lam{2}{3}{4}{3}{4}{4}) =
(y_{2, 3} y_{4, 4})  \del{2}{3}{2}{4} +(-y_{2, 4} y_{4, 2}-y_{2, 2} y_{4, 4})  \del{2}{3}{3}{4} +(-y_{2, 3} y_{3, 4})  \del{2}{4}{2}{4} +(y_{2, 4} y_{3, 2}+y_{2, 2} y_{3, 4})  \del{2}{4}{3}{4} +(y_{2, 3} y_{2, 4})  \del{3}{4}{2}{4} +(-2 y_{2, 2} y_{2, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{2, 4}+y_{2, 4} x_{4, 4})  \eps{2}{3}{2}{3} +(y_{4, 2} x_{2, 4}-y_{2, 2} x_{4, 4})  \eps{2}{3}{3}{4} +(-y_{2, 4} x_{3, 4})  \eps{2}{4}{2}{3} +(-y_{3, 2} x_{2, 4}+y_{2, 2} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{2, 4})  \lam{2}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
2,3,4
1,2,2
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*y(4)(4)*x(2)(2)
Divisor:
Epsilon
2,4
2,4
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*y(4)(4)*x(2)(2)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,4
Quotient:
-y(2)(2)*y(4)(1)+y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(2)*y(4)(1)*y(4)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,4
Quotient:
-y(4)(2)
Lead Term of Product:
y(3)(2)*y(4)(1)*y(4)(2)*x(2)(4)
Lead term is well behaved
Divisor:
Psi
2,3,4
1,2,4
Quotient:
-x(4)(2)
Lead Term of Product:
y(2)(4)*y(3)(2)*y(4)(1)*x(4)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(3)(2)*y(4)(1)*x(2)(2)+y(3)(1)*y(4)(2)*x(2)(2)+y(2)(2)*y(4)(1)*x(3)(2)-y(2)(1)*y(4)(2)*x(3)(2)-y(2)(2)*y(3)(1)*x(4)(2)+y(2)(1)*y(3)(2)*x(4)(2)) - (-y(3)(2)*y(4)(1))*(y(4)(4)*x(2)(2)-y(4)(2)*x(2)(4)-y(2)(4)*x(4)(2)+y(2)(2)*x(4)(4))
-------
Rewrite:
-y(3)(1)*y(4)(2)*y(4)(4)*x(2)(2)+y(3)(2)*y(4)(1)*y(4)(2)*x(2)(4)-y(2)(2)*y(4)(1)*y(4)(4)*x(3)(2)+y(2)(1)*y(4)(2)*y(4)(4)*x(3)(2)+y(2)(4)*y(3)(2)*y(4)(1)*x(4)(2)+y(2)(2)*y(3)(1)*y(4)(4)*x(4)(2)-y(2)(1)*y(3)(2)*y(4)(4)*x(4)(2)-y(2)(2)*y(3)(2)*y(4)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{2}{4}, \lam{2}{3}{4}{1}{2}{2}) =
(-y_{3, 1} y_{4, 2})  \eps{2}{4}{2}{4} +(-y_{2, 2} y_{4, 1}+y_{2, 1} y_{4, 2})  \eps{3}{4}{2}{4} +(-y_{4, 2})  \lam{2}{3}{4}{1}{2}{4} +(-x_{4, 2})  \psi{2}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
2,4
2,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
2,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
2,3,4
1,2,3
Lead Term of Spoly:
-y(3)(1)*y(4)(2)*y(4)(4)*x(2)(3)
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(1)*y(4)(2)
Lead Term of Product:
-y(3)(1)*y(4)(2)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(2)(2)*y(4)(1)+y(2)(1)*y(4)(2)
Lead Term of Product:
-y(2)(2)*y(4)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*y(4)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Psi
2,3,4
1,2,3
Quotient:
x(4)(4)
Lead Term of Product:
-y(2)(3)*y(3)(2)*y(4)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Psi
2,3,4
1,2,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(2)(4)*y(3)(2)*y(4)(1)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(3)(2)*y(4)(1)*x(2)(3)+y(3)(1)*y(4)(2)*x(2)(3)+y(2)(2)*y(4)(1)*x(3)(3)-y(2)(1)*y(4)(2)*x(3)(3)-y(2)(2)*y(3)(1)*x(4)(3)+y(2)(1)*y(3)(2)*x(4)(3)) - (-y(3)(2)*y(4)(1))*(y(4)(4)*x(2)(3)-y(4)(3)*x(2)(4)-y(2)(4)*x(4)(3)+y(2)(3)*x(4)(4))
-------
Rewrite:
-y(3)(1)*y(4)(2)*y(4)(4)*x(2)(3)+y(3)(2)*y(4)(1)*y(4)(3)*x(2)(4)-y(2)(2)*y(4)(1)*y(4)(4)*x(3)(3)+y(2)(1)*y(4)(2)*y(4)(4)*x(3)(3)+y(2)(4)*y(3)(2)*y(4)(1)*x(4)(3)+y(2)(2)*y(3)(1)*y(4)(4)*x(4)(3)-y(2)(1)*y(3)(2)*y(4)(4)*x(4)(3)-y(2)(3)*y(3)(2)*y(4)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{3}{4}, \lam{2}{3}{4}{1}{2}{3}) =
(-y_{3, 1} y_{4, 2})  \eps{2}{4}{3}{4} +(-y_{2, 2} y_{4, 1}+y_{2, 1} y_{4, 2})  \eps{3}{4}{3}{4} +(-y_{4, 3})  \lam{2}{3}{4}{1}{2}{4} +(x_{4, 4})  \psi{2}{3}{4}{1}{2}{3} +(-x_{4, 3})  \psi{2}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
2,4
3,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
2,3,4
1,3,3
Lead Term of Spoly:
-y(3)(1)*y(4)(3)*y(4)(4)*x(2)(3)
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(1)*y(4)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(2)(3)*y(4)(1)+y(2)(1)*y(4)(3)
Lead Term of Product:
-y(2)(3)*y(4)(1)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,3,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(3)(3)*y(4)(1)*y(4)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Psi
2,3,4
1,3,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(2)(4)*y(3)(3)*y(4)(1)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(3)(3)*y(4)(1)*x(2)(3)+y(3)(1)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(1)*x(3)(3)-y(2)(1)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(1)*x(4)(3)+y(2)(1)*y(3)(3)*x(4)(3)) - (-y(3)(3)*y(4)(1))*(y(4)(4)*x(2)(3)-y(4)(3)*x(2)(4)-y(2)(4)*x(4)(3)+y(2)(3)*x(4)(4))
-------
Rewrite:
-y(3)(1)*y(4)(3)*y(4)(4)*x(2)(3)+y(3)(3)*y(4)(1)*y(4)(3)*x(2)(4)-y(2)(3)*y(4)(1)*y(4)(4)*x(3)(3)+y(2)(1)*y(4)(3)*y(4)(4)*x(3)(3)+y(2)(4)*y(3)(3)*y(4)(1)*x(4)(3)+y(2)(3)*y(3)(1)*y(4)(4)*x(4)(3)-y(2)(1)*y(3)(3)*y(4)(4)*x(4)(3)-y(2)(3)*y(3)(3)*y(4)(1)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{3}{4}, \lam{2}{3}{4}{1}{3}{3}) =
(-y_{3, 1} y_{4, 3})  \eps{2}{4}{3}{4} +(-y_{2, 3} y_{4, 1}+y_{2, 1} y_{4, 3})  \eps{3}{4}{3}{4} +(-y_{4, 3})  \lam{2}{3}{4}{1}{3}{4} +(-x_{4, 3})  \psi{2}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
2,4
3,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
2,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*y(4)(4)*x(2)(3)
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*y(4)(4)*x(2)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
-y(2)(3)*y(4)(2)+y(2)(2)*y(4)(3)
Lead Term of Product:
-y(2)(3)*y(4)(2)*y(4)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
2,3,4
2,3,4
Quotient:
-y(4)(3)
Lead Term of Product:
y(3)(3)*y(4)(2)*y(4)(3)*x(2)(4)
Lead term is well behaved
Divisor:
Psi
2,3,4
2,3,4
Quotient:
-x(4)(3)
Lead Term of Product:
y(2)(4)*y(3)(3)*y(4)(2)*x(4)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(4)(4))*(-y(3)(3)*y(4)(2)*x(2)(3)+y(3)(2)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(2)*x(3)(3)-y(2)(2)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(2)*x(4)(3)+y(2)(2)*y(3)(3)*x(4)(3)) - (-y(3)(3)*y(4)(2))*(y(4)(4)*x(2)(3)-y(4)(3)*x(2)(4)-y(2)(4)*x(4)(3)+y(2)(3)*x(4)(4))
-------
Rewrite:
-y(3)(2)*y(4)(3)*y(4)(4)*x(2)(3)+y(3)(3)*y(4)(2)*y(4)(3)*x(2)(4)-y(2)(3)*y(4)(2)*y(4)(4)*x(3)(3)+y(2)(2)*y(4)(3)*y(4)(4)*x(3)(3)+y(2)(4)*y(3)(3)*y(4)(2)*x(4)(3)+y(2)(3)*y(3)(2)*y(4)(4)*x(4)(3)-y(2)(2)*y(3)(3)*y(4)(4)*x(4)(3)-y(2)(3)*y(3)(3)*y(4)(2)*x(4)(4)
-----------
TeX output:
S(\eps{2}{4}{3}{4}, \lam{2}{3}{4}{2}{3}{3}) =
(-y_{3, 2} y_{4, 3})  \eps{2}{4}{3}{4} +(-y_{2, 3} y_{4, 2}+y_{2, 2} y_{4, 3})  \eps{3}{4}{3}{4} +(-y_{4, 3})  \lam{2}{3}{4}{2}{3}{4} +(-x_{4, 3})  \psi{2}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
2,4
3,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
2,4
3,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,4
2,3,3
Lead Term of Spoly:
-y(2)(2)*y(4)(3)*x(1)(3)*x(3)(1)
Divisor:
Delta
1,3
1,3
Quotient:
y(2)(2)*y(4)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,3
Quotient:
-y(2)(3)*y(3)(2)
Lead Term of Product:
y(2)(3)*y(3)(2)*x(1)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(2)(3)*y(3)(1)
Lead Term of Product:
-y(2)(3)*y(3)(1)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,3
Quotient:
y(1)(3)*y(4)(2)-y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(3)*x(3)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
y(3)(2)*x(4)(3)
Lead Term of Product:
y(2)(3)*y(3)(2)*x(1)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(1)*x(3)(3)-y(3)(1)*x(4)(3)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*x(3)(3)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(3)*x(4)(3)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(2)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(3)*x(3)(3)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(2)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(1)*x(3)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,2,3
Quotient:
-x(4)(3)
Lead Term of Product:
y(1)(3)*y(2)(2)*x(3)(1)*x(4)(3)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
x(4)(3)
Lead Term of Product:
-y(2)(2)*y(3)(1)*x(1)(3)*x(4)(3)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-x(3)(3)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(3)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(2)(3)*y(4)(2)*x(1)(3)+y(2)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(2)(3)-y(1)(2)*y(4)(3)*x(2)(3)-y(1)(3)*y(2)(2)*x(4)(3)+y(1)(2)*y(2)(3)*x(4)(3)) - (-y(2)(3)*x(1)(3))*(y(4)(2)*x(3)(1)-y(4)(1)*x(3)(2)-y(3)(2)*x(4)(1)+y(3)(1)*x(4)(2))
-------
Rewrite:
-y(2)(2)*y(4)(3)*x(1)(3)*x(3)(1)-y(1)(3)*y(4)(2)*x(2)(3)*x(3)(1)+y(1)(2)*y(4)(3)*x(2)(3)*x(3)(1)+y(2)(3)*y(4)(1)*x(1)(3)*x(3)(2)+y(2)(3)*y(3)(2)*x(1)(3)*x(4)(1)-y(2)(3)*y(3)(1)*x(1)(3)*x(4)(2)+y(1)(3)*y(2)(2)*x(3)(1)*x(4)(3)-y(1)(2)*y(2)(3)*x(3)(1)*x(4)(3)
-----------
TeX output:
S(\eps{3}{4}{1}{2}, \lam{1}{2}{4}{2}{3}{3}) =
(y_{2, 2} y_{4, 3})  \del{1}{3}{1}{3} +(-y_{2, 3} y_{4, 1})  \del{1}{3}{2}{3} +(-y_{2, 3} y_{3, 2})  \del{1}{4}{1}{3} +(y_{2, 3} y_{3, 1})  \del{1}{4}{2}{3} +(y_{1, 3} y_{4, 2}-y_{1, 2} y_{4, 3})  \del{2}{3}{1}{3} +(y_{1, 3} y_{2, 2})  \del{3}{4}{1}{3} +(-y_{1, 1} y_{2, 3})  \del{3}{4}{2}{3} +(-y_{4, 3} x_{3, 3})  \eps{1}{2}{1}{2} +(y_{3, 2} x_{4, 3})  \eps{1}{2}{1}{3} +(y_{4, 1} x_{3, 3}-y_{3, 1} x_{4, 3})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{3, 3})  \eps{1}{4}{2}{3} +(y_{1, 3} x_{4, 3})  \eps{2}{3}{1}{2} +(-y_{1, 3} x_{3, 3})  \eps{2}{4}{1}{2} +(y_{1, 1} x_{3, 3})  \eps{2}{4}{2}{3} +(-x_{4, 3})  \pho{1}{2}{3}{1}{2}{3} +(x_{4, 3})  \lam{1}{2}{3}{1}{2}{3} +(-x_{3, 3})  \lam{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,4
2,3,4
Lead Term of Spoly:
-y(2)(2)*y(4)(3)*x(1)(4)*x(3)(1)
Divisor:
Delta
1,3
1,4
Quotient:
y(2)(2)*y(4)(3)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(2)(3)*y(4)(1)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(2)(3)*y(3)(2)
Lead Term of Product:
y(2)(3)*y(3)(2)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(2)(3)*y(3)(1)
Lead Term of Product:
-y(2)(3)*y(3)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(3)*y(4)(2)-y(1)(2)*y(4)(3)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(3)*y(2)(2)
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(2)(3)
Lead Term of Product:
y(1)(1)*y(2)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(3)*x(3)(4)
Lead Term of Product:
-y(2)(2)*y(4)(3)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
y(3)(2)*x(4)(4)
Lead Term of Product:
y(2)(3)*y(3)(2)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
y(4)(1)*x(3)(4)-y(3)(1)*x(4)(4)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(2)(1)*x(3)(4)
Lead Term of Product:
-y(2)(1)*y(4)(3)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(3)*x(4)(4)
Lead Term of Product:
y(1)(3)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(3)*x(3)(4)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,2,3
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(3)*y(2)(2)*x(3)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
x(4)(4)
Lead Term of Product:
-y(2)(2)*y(3)(1)*x(1)(3)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,3
Quotient:
-x(3)(4)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(3)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(2)(3)*y(4)(2)*x(1)(4)+y(2)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(2)(4)-y(1)(2)*y(4)(3)*x(2)(4)-y(1)(3)*y(2)(2)*x(4)(4)+y(1)(2)*y(2)(3)*x(4)(4)) - (-y(2)(3)*x(1)(4))*(y(4)(2)*x(3)(1)-y(4)(1)*x(3)(2)-y(3)(2)*x(4)(1)+y(3)(1)*x(4)(2))
-------
Rewrite:
-y(2)(2)*y(4)(3)*x(1)(4)*x(3)(1)-y(1)(3)*y(4)(2)*x(2)(4)*x(3)(1)+y(1)(2)*y(4)(3)*x(2)(4)*x(3)(1)+y(2)(3)*y(4)(1)*x(1)(4)*x(3)(2)+y(2)(3)*y(3)(2)*x(1)(4)*x(4)(1)-y(2)(3)*y(3)(1)*x(1)(4)*x(4)(2)+y(1)(3)*y(2)(2)*x(3)(1)*x(4)(4)-y(1)(2)*y(2)(3)*x(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{1}{2}, \lam{1}{2}{4}{2}{3}{4}) =
(y_{2, 2} y_{4, 3})  \del{1}{3}{1}{4} +(-y_{2, 3} y_{4, 1})  \del{1}{3}{2}{4} +(-y_{2, 3} y_{3, 2})  \del{1}{4}{1}{4} +(y_{2, 3} y_{3, 1})  \del{1}{4}{2}{4} +(y_{1, 3} y_{4, 2}-y_{1, 2} y_{4, 3})  \del{2}{3}{1}{4} +(y_{1, 3} y_{2, 2})  \del{3}{4}{1}{4} +(-y_{1, 1} y_{2, 3})  \del{3}{4}{2}{4} +(-y_{4, 3} x_{3, 4})  \eps{1}{2}{1}{2} +(y_{3, 2} x_{4, 4})  \eps{1}{2}{1}{3} +(y_{4, 1} x_{3, 4}-y_{3, 1} x_{4, 4})  \eps{1}{2}{2}{3} +(-y_{2, 1} x_{3, 4})  \eps{1}{4}{2}{3} +(y_{1, 3} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{1, 3} x_{3, 4})  \eps{2}{4}{1}{2} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{2}{3} +(-x_{4, 4})  \pho{1}{2}{3}{1}{2}{3} +(x_{4, 4})  \lam{1}{2}{3}{1}{2}{3} +(-x_{3, 4})  \lam{1}{2}{4}{1}{2}{3}
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,4
2,4,4
Lead Term of Spoly:
-y(2)(2)*y(4)(4)*x(1)(4)*x(3)(1)
Divisor:
Delta
1,3
1,4
Quotient:
y(2)(2)*y(4)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(2)(4)*y(4)(1)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(2)(4)*y(3)(2)
Lead Term of Product:
y(2)(4)*y(3)(2)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(2)(4)*y(3)(1)
Lead Term of Product:
-y(2)(4)*y(3)(1)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(4)*y(4)(2)-y(1)(2)*y(4)(4)
Lead Term of Product:
-y(1)(4)*y(4)(2)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(4)*y(2)(2)
Lead Term of Product:
-y(1)(4)*y(2)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(1)*y(2)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-y(4)(4)*x(3)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
y(3)(2)*x(4)(4)
Lead Term of Product:
y(2)(4)*y(3)(2)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
y(4)(1)*x(3)(4)-y(3)(1)*x(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(2)(1)*x(3)(4)
Lead Term of Product:
-y(2)(1)*y(4)(4)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(2)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,2
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(2)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,2,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(4)*y(2)(2)*x(3)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,4
Quotient:
x(4)(4)
Lead Term of Product:
-y(2)(2)*y(3)(1)*x(1)(4)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,2,4
Quotient:
-x(3)(4)
Lead Term of Product:
y(2)(2)*y(4)(1)*x(1)(4)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(2)(4)*y(4)(2)*x(1)(4)+y(2)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(2)(4)-y(1)(2)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(2)*x(4)(4)+y(1)(2)*y(2)(4)*x(4)(4)) - (-y(2)(4)*x(1)(4))*(y(4)(2)*x(3)(1)-y(4)(1)*x(3)(2)-y(3)(2)*x(4)(1)+y(3)(1)*x(4)(2))
-------
Rewrite:
-y(2)(2)*y(4)(4)*x(1)(4)*x(3)(1)-y(1)(4)*y(4)(2)*x(2)(4)*x(3)(1)+y(1)(2)*y(4)(4)*x(2)(4)*x(3)(1)+y(2)(4)*y(4)(1)*x(1)(4)*x(3)(2)+y(2)(4)*y(3)(2)*x(1)(4)*x(4)(1)-y(2)(4)*y(3)(1)*x(1)(4)*x(4)(2)+y(1)(4)*y(2)(2)*x(3)(1)*x(4)(4)-y(1)(2)*y(2)(4)*x(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{1}{2}, \lam{1}{2}{4}{2}{4}{4}) =
(y_{2, 2} y_{4, 4})  \del{1}{3}{1}{4} +(-y_{2, 4} y_{4, 1})  \del{1}{3}{2}{4} +(-y_{2, 4} y_{3, 2})  \del{1}{4}{1}{4} +(y_{2, 4} y_{3, 1})  \del{1}{4}{2}{4} +(y_{1, 4} y_{4, 2}-y_{1, 2} y_{4, 4})  \del{2}{3}{1}{4} +(y_{1, 4} y_{2, 2})  \del{3}{4}{1}{4} +(-y_{1, 1} y_{2, 4})  \del{3}{4}{2}{4} +(-y_{4, 4} x_{3, 4})  \eps{1}{2}{1}{2} +(y_{3, 2} x_{4, 4})  \eps{1}{2}{1}{4} +(y_{4, 1} x_{3, 4}-y_{3, 1} x_{4, 4})  \eps{1}{2}{2}{4} +(-y_{2, 1} x_{3, 4})  \eps{1}{4}{2}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{1}{2} +(-y_{1, 4} x_{3, 4})  \eps{2}{4}{1}{2} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{2}{4} +(-x_{4, 4})  \pho{1}{2}{3}{1}{2}{4} +(x_{4, 4})  \lam{1}{2}{3}{1}{2}{4} +(-x_{3, 4})  \lam{1}{2}{4}{1}{2}{4}
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(3)*x(3)(1)
Divisor:
Delta
1,3
1,3
Quotient:
y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
-y(3)(3)*y(4)(1)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,3
Quotient:
-y(3)(2)*y(3)(3)
Lead Term of Product:
y(3)(2)*y(3)(3)*x(1)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,3
Quotient:
y(3)(1)*y(3)(3)
Lead Term of Product:
-y(3)(1)*y(3)(3)*x(1)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
y(1)(3)*y(3)(2)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(1)(1)*y(3)(3)
Lead Term of Product:
y(1)(1)*y(3)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(3)(3)+y(3)(3)*x(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
y(4)(1)*x(3)(3)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
1,2
Quotient:
-y(1)(3)*x(3)(3)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(3)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
y(1)(1)*x(3)(3)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(3)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(3)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(3)(3)*y(4)(2)*x(1)(3)+y(3)(2)*y(4)(3)*x(1)(3)+y(1)(3)*y(4)(2)*x(3)(3)-y(1)(2)*y(4)(3)*x(3)(3)-y(1)(3)*y(3)(2)*x(4)(3)+y(1)(2)*y(3)(3)*x(4)(3)) - (-y(3)(3)*x(1)(3))*(y(4)(2)*x(3)(1)-y(4)(1)*x(3)(2)-y(3)(2)*x(4)(1)+y(3)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(3)*x(3)(1)+y(3)(3)*y(4)(1)*x(1)(3)*x(3)(2)-y(1)(3)*y(4)(2)*x(3)(1)*x(3)(3)+y(1)(2)*y(4)(3)*x(3)(1)*x(3)(3)+y(3)(2)*y(3)(3)*x(1)(3)*x(4)(1)-y(3)(1)*y(3)(3)*x(1)(3)*x(4)(2)+y(1)(3)*y(3)(2)*x(3)(1)*x(4)(3)-y(1)(2)*y(3)(3)*x(3)(1)*x(4)(3)
-----------
TeX output:
S(\eps{3}{4}{1}{2}, \lam{1}{3}{4}{2}{3}{3}) =
(y_{3, 2} y_{4, 3})  \del{1}{3}{1}{3} +(-y_{3, 3} y_{4, 1})  \del{1}{3}{2}{3} +(-y_{3, 2} y_{3, 3})  \del{1}{4}{1}{3} +(y_{3, 1} y_{3, 3})  \del{1}{4}{2}{3} +(y_{1, 3} y_{3, 2})  \del{3}{4}{1}{3} +(-y_{1, 1} y_{3, 3})  \del{3}{4}{2}{3} +(-y_{4, 3} x_{3, 3}+y_{3, 3} x_{4, 3})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{3, 3})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{3, 3})  \eps{1}{4}{2}{3} +(-y_{1, 3} x_{3, 3})  \eps{3}{4}{1}{2} +(y_{1, 1} x_{3, 3})  \eps{3}{4}{2}{3} +(-x_{3, 3})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(1)(4)*x(3)(1)
Divisor:
Delta
1,3
1,4
Quotient:
y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(3)(3)*y(4)(1)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(3)(2)*y(3)(3)
Lead Term of Product:
y(3)(2)*y(3)(3)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(3)(1)*y(3)(3)
Lead Term of Product:
-y(3)(1)*y(3)(3)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(3)*y(3)(2)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(3)(3)
Lead Term of Product:
y(1)(1)*y(3)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(3)*x(3)(4)+y(3)(3)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,3
Quotient:
-y(3)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
1,2
Quotient:
-y(1)(3)*x(3)(4)
Lead Term of Product:
-y(1)(3)*y(4)(2)*x(3)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(3)*x(3)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,3
Quotient:
-x(3)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(3)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(3)(3)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(3)*x(1)(4)+y(1)(3)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(3)*x(3)(4)-y(1)(3)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(3)*x(4)(4)) - (-y(3)(3)*x(1)(4))*(y(4)(2)*x(3)(1)-y(4)(1)*x(3)(2)-y(3)(2)*x(4)(1)+y(3)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(1)(4)*x(3)(1)+y(3)(3)*y(4)(1)*x(1)(4)*x(3)(2)-y(1)(3)*y(4)(2)*x(3)(1)*x(3)(4)+y(1)(2)*y(4)(3)*x(3)(1)*x(3)(4)+y(3)(2)*y(3)(3)*x(1)(4)*x(4)(1)-y(3)(1)*y(3)(3)*x(1)(4)*x(4)(2)+y(1)(3)*y(3)(2)*x(3)(1)*x(4)(4)-y(1)(2)*y(3)(3)*x(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{1}{2}, \lam{1}{3}{4}{2}{3}{4}) =
(y_{3, 2} y_{4, 3})  \del{1}{3}{1}{4} +(-y_{3, 3} y_{4, 1})  \del{1}{3}{2}{4} +(-y_{3, 2} y_{3, 3})  \del{1}{4}{1}{4} +(y_{3, 1} y_{3, 3})  \del{1}{4}{2}{4} +(y_{1, 3} y_{3, 2})  \del{3}{4}{1}{4} +(-y_{1, 1} y_{3, 3})  \del{3}{4}{2}{4} +(-y_{4, 3} x_{3, 4}+y_{3, 3} x_{4, 4})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{3, 4})  \eps{1}{3}{2}{3} +(-y_{3, 1} x_{3, 4})  \eps{1}{4}{2}{3} +(-y_{1, 3} x_{3, 4})  \eps{3}{4}{1}{2} +(y_{1, 1} x_{3, 4})  \eps{3}{4}{2}{3} +(-x_{3, 4})  \lam{1}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(1)(4)*x(3)(1)
Divisor:
Delta
1,3
1,4
Quotient:
y(3)(2)*y(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,4
Quotient:
-y(3)(4)*y(4)(1)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(3)(2)*y(3)(4)
Lead Term of Product:
y(3)(2)*y(3)(4)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
y(3)(1)*y(3)(4)
Lead Term of Product:
-y(3)(1)*y(3)(4)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(4)*y(3)(2)
Lead Term of Product:
-y(1)(4)*y(3)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(1)(1)*y(3)(4)
Lead Term of Product:
y(1)(1)*y(3)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-y(4)(4)*x(3)(4)+y(3)(4)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,4
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
2,4
Quotient:
-y(3)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
1,2
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(2)*x(3)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,4
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(3)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,2,4
Quotient:
-x(3)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(1)(4)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(3)(4)*y(4)(2)*x(1)(4)+y(3)(2)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(2)*x(3)(4)-y(1)(2)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(2)*x(4)(4)+y(1)(2)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(1)(4))*(y(4)(2)*x(3)(1)-y(4)(1)*x(3)(2)-y(3)(2)*x(4)(1)+y(3)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(1)(4)*x(3)(1)+y(3)(4)*y(4)(1)*x(1)(4)*x(3)(2)-y(1)(4)*y(4)(2)*x(3)(1)*x(3)(4)+y(1)(2)*y(4)(4)*x(3)(1)*x(3)(4)+y(3)(2)*y(3)(4)*x(1)(4)*x(4)(1)-y(3)(1)*y(3)(4)*x(1)(4)*x(4)(2)+y(1)(4)*y(3)(2)*x(3)(1)*x(4)(4)-y(1)(2)*y(3)(4)*x(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{1}{2}, \lam{1}{3}{4}{2}{4}{4}) =
(y_{3, 2} y_{4, 4})  \del{1}{3}{1}{4} +(-y_{3, 4} y_{4, 1})  \del{1}{3}{2}{4} +(-y_{3, 2} y_{3, 4})  \del{1}{4}{1}{4} +(y_{3, 1} y_{3, 4})  \del{1}{4}{2}{4} +(y_{1, 4} y_{3, 2})  \del{3}{4}{1}{4} +(-y_{1, 1} y_{3, 4})  \del{3}{4}{2}{4} +(-y_{4, 4} x_{3, 4}+y_{3, 4} x_{4, 4})  \eps{1}{3}{1}{2} +(y_{4, 1} x_{3, 4})  \eps{1}{3}{2}{4} +(-y_{3, 1} x_{3, 4})  \eps{1}{4}{2}{4} +(-y_{1, 4} x_{3, 4})  \eps{3}{4}{1}{2} +(y_{1, 1} x_{3, 4})  \eps{3}{4}{2}{4} +(-x_{3, 4})  \lam{1}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
3,4
1,2
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,2
Lam:
2,3,4
2,3,3
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(2)(3)*x(3)(1)
Divisor:
Delta
2,3
1,3
Quotient:
y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
-y(3)(3)*y(4)(1)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,3
Quotient:
-y(3)(2)*y(3)(3)
Lead Term of Product:
y(3)(2)*y(3)(3)*x(2)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,3
Quotient:
y(3)(1)*y(3)(3)
Lead Term of Product:
-y(3)(1)*y(3)(3)*x(2)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,3
Quotient:
y(2)(3)*y(3)(2)
Lead Term of Product:
-y(2)(3)*y(3)(2)*x(3)(3)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,3
Quotient:
-y(2)(1)*y(3)(3)
Lead Term of Product:
y(2)(1)*y(3)(3)*x(3)(3)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(4)(3)*x(3)(3)+y(3)(3)*x(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(2)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(4)(1)*x(3)(3)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(2)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(3)(1)*x(3)(3)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(2)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
1,2
Quotient:
-y(2)(3)*x(3)(3)
Lead Term of Product:
-y(2)(3)*y(4)(2)*x(3)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
y(2)(1)*x(3)(3)
Lead Term of Product:
y(2)(1)*y(4)(3)*x(3)(2)*x(3)(3)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,3
Quotient:
-x(3)(3)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(2)(3)*x(3)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(3)(3)*y(4)(2)*x(2)(3)+y(3)(2)*y(4)(3)*x(2)(3)+y(2)(3)*y(4)(2)*x(3)(3)-y(2)(2)*y(4)(3)*x(3)(3)-y(2)(3)*y(3)(2)*x(4)(3)+y(2)(2)*y(3)(3)*x(4)(3)) - (-y(3)(3)*x(2)(3))*(y(4)(2)*x(3)(1)-y(4)(1)*x(3)(2)-y(3)(2)*x(4)(1)+y(3)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(2)(3)*x(3)(1)+y(3)(3)*y(4)(1)*x(2)(3)*x(3)(2)-y(2)(3)*y(4)(2)*x(3)(1)*x(3)(3)+y(2)(2)*y(4)(3)*x(3)(1)*x(3)(3)+y(3)(2)*y(3)(3)*x(2)(3)*x(4)(1)-y(3)(1)*y(3)(3)*x(2)(3)*x(4)(2)+y(2)(3)*y(3)(2)*x(3)(1)*x(4)(3)-y(2)(2)*y(3)(3)*x(3)(1)*x(4)(3)
-----------
TeX output:
S(\eps{3}{4}{1}{2}, \lam{2}{3}{4}{2}{3}{3}) =
(y_{3, 2} y_{4, 3})  \del{2}{3}{1}{3} +(-y_{3, 3} y_{4, 1})  \del{2}{3}{2}{3} +(-y_{3, 2} y_{3, 3})  \del{2}{4}{1}{3} +(y_{3, 1} y_{3, 3})  \del{2}{4}{2}{3} +(y_{2, 3} y_{3, 2})  \del{3}{4}{1}{3} +(-y_{2, 1} y_{3, 3})  \del{3}{4}{2}{3} +(-y_{4, 3} x_{3, 3}+y_{3, 3} x_{4, 3})  \eps{2}{3}{1}{2} +(y_{4, 1} x_{3, 3})  \eps{2}{3}{2}{3} +(-y_{3, 1} x_{3, 3})  \eps{2}{4}{2}{3} +(-y_{2, 3} x_{3, 3})  \eps{3}{4}{1}{2} +(y_{2, 1} x_{3, 3})  \eps{3}{4}{2}{3} +(-x_{3, 3})  \lam{2}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
3,4
1,2
Lam:
2,3,4
2,3,4
Lead Term of Spoly:
-y(3)(2)*y(4)(3)*x(2)(4)*x(3)(1)
Divisor:
Delta
2,3
1,4
Quotient:
y(3)(2)*y(4)(3)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(3)(3)*y(4)(1)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(3)(2)*y(3)(3)
Lead Term of Product:
y(3)(2)*y(3)(3)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(3)(1)*y(3)(3)
Lead Term of Product:
-y(3)(1)*y(3)(3)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(2)(3)*y(3)(2)
Lead Term of Product:
-y(2)(3)*y(3)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(2)(1)*y(3)(3)
Lead Term of Product:
y(2)(1)*y(3)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(4)(3)*x(3)(4)+y(3)(3)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(3)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(3)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(3)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
1,2
Quotient:
-y(2)(3)*x(3)(4)
Lead Term of Product:
-y(2)(3)*y(4)(2)*x(3)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
y(2)(1)*x(3)(4)
Lead Term of Product:
y(2)(1)*y(4)(3)*x(3)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,3
Quotient:
-x(3)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(2)(3)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(3)(3)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(3)*x(2)(4)+y(2)(3)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(3)*x(3)(4)-y(2)(3)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(3)*x(4)(4)) - (-y(3)(3)*x(2)(4))*(y(4)(2)*x(3)(1)-y(4)(1)*x(3)(2)-y(3)(2)*x(4)(1)+y(3)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(3)*x(2)(4)*x(3)(1)+y(3)(3)*y(4)(1)*x(2)(4)*x(3)(2)-y(2)(3)*y(4)(2)*x(3)(1)*x(3)(4)+y(2)(2)*y(4)(3)*x(3)(1)*x(3)(4)+y(3)(2)*y(3)(3)*x(2)(4)*x(4)(1)-y(3)(1)*y(3)(3)*x(2)(4)*x(4)(2)+y(2)(3)*y(3)(2)*x(3)(1)*x(4)(4)-y(2)(2)*y(3)(3)*x(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{1}{2}, \lam{2}{3}{4}{2}{3}{4}) =
(y_{3, 2} y_{4, 3})  \del{2}{3}{1}{4} +(-y_{3, 3} y_{4, 1})  \del{2}{3}{2}{4} +(-y_{3, 2} y_{3, 3})  \del{2}{4}{1}{4} +(y_{3, 1} y_{3, 3})  \del{2}{4}{2}{4} +(y_{2, 3} y_{3, 2})  \del{3}{4}{1}{4} +(-y_{2, 1} y_{3, 3})  \del{3}{4}{2}{4} +(-y_{4, 3} x_{3, 4}+y_{3, 3} x_{4, 4})  \eps{2}{3}{1}{2} +(y_{4, 1} x_{3, 4})  \eps{2}{3}{2}{3} +(-y_{3, 1} x_{3, 4})  \eps{2}{4}{2}{3} +(-y_{2, 3} x_{3, 4})  \eps{3}{4}{1}{2} +(y_{2, 1} x_{3, 4})  \eps{3}{4}{2}{3} +(-x_{3, 4})  \lam{2}{3}{4}{1}{2}{3}
----------------------------------
Epsilon:
3,4
1,2
Lam:
2,3,4
2,4,4
Lead Term of Spoly:
-y(3)(2)*y(4)(4)*x(2)(4)*x(3)(1)
Divisor:
Delta
2,3
1,4
Quotient:
y(3)(2)*y(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
-y(3)(4)*y(4)(1)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(3)(2)*y(3)(4)
Lead Term of Product:
y(3)(2)*y(3)(4)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
y(3)(1)*y(3)(4)
Lead Term of Product:
-y(3)(1)*y(3)(4)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(2)(4)*y(3)(2)
Lead Term of Product:
-y(2)(4)*y(3)(2)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
-y(2)(1)*y(3)(4)
Lead Term of Product:
y(2)(1)*y(3)(4)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(4)(4)*x(3)(4)+y(3)(4)*x(4)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,4
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,4
Quotient:
-y(3)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
1,2
Quotient:
-y(2)(4)*x(3)(4)
Lead Term of Product:
-y(2)(4)*y(4)(2)*x(3)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,4
Quotient:
y(2)(1)*x(3)(4)
Lead Term of Product:
y(2)(1)*y(4)(4)*x(3)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,2,4
Quotient:
-x(3)(4)
Lead Term of Product:
y(3)(2)*y(4)(1)*x(2)(4)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(3)(4)*y(4)(2)*x(2)(4)+y(3)(2)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(2)*x(3)(4)-y(2)(2)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(2)*x(4)(4)+y(2)(2)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(2)(4))*(y(4)(2)*x(3)(1)-y(4)(1)*x(3)(2)-y(3)(2)*x(4)(1)+y(3)(1)*x(4)(2))
-------
Rewrite:
-y(3)(2)*y(4)(4)*x(2)(4)*x(3)(1)+y(3)(4)*y(4)(1)*x(2)(4)*x(3)(2)-y(2)(4)*y(4)(2)*x(3)(1)*x(3)(4)+y(2)(2)*y(4)(4)*x(3)(1)*x(3)(4)+y(3)(2)*y(3)(4)*x(2)(4)*x(4)(1)-y(3)(1)*y(3)(4)*x(2)(4)*x(4)(2)+y(2)(4)*y(3)(2)*x(3)(1)*x(4)(4)-y(2)(2)*y(3)(4)*x(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{1}{2}, \lam{2}{3}{4}{2}{4}{4}) =
(y_{3, 2} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{3, 4} y_{4, 1})  \del{2}{3}{2}{4} +(-y_{3, 2} y_{3, 4})  \del{2}{4}{1}{4} +(y_{3, 1} y_{3, 4})  \del{2}{4}{2}{4} +(y_{2, 4} y_{3, 2})  \del{3}{4}{1}{4} +(-y_{2, 1} y_{3, 4})  \del{3}{4}{2}{4} +(-y_{4, 4} x_{3, 4}+y_{3, 4} x_{4, 4})  \eps{2}{3}{1}{2} +(y_{4, 1} x_{3, 4})  \eps{2}{3}{2}{4} +(-y_{3, 1} x_{3, 4})  \eps{2}{4}{2}{4} +(-y_{2, 4} x_{3, 4})  \eps{3}{4}{1}{2} +(y_{2, 1} x_{3, 4})  \eps{3}{4}{2}{4} +(-x_{3, 4})  \lam{2}{3}{4}{1}{2}{4}
----------------------------------
Epsilon:
3,4
1,2
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,2,4
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(4)(4)*x(1)(4)*x(3)(1)
Divisor:
Delta
1,3
1,4
Quotient:
y(2)(3)*y(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(2)(4)*y(4)(1)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(2)(4)*y(3)(3)
Lead Term of Product:
y(2)(4)*y(3)(3)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(2)(4)*y(3)(1)
Lead Term of Product:
-y(2)(4)*y(3)(1)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,3
1,4
Quotient:
y(1)(4)*y(4)(3)-y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(1)*y(2)(4)
Lead Term of Product:
y(1)(1)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
-y(4)(4)*x(3)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,4
Quotient:
y(3)(3)*x(4)(4)
Lead Term of Product:
y(2)(4)*y(3)(3)*x(1)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(4)(1)*x(3)(4)-y(3)(1)*x(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(1)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(1)*x(3)(4)
Lead Term of Product:
-y(2)(1)*y(4)(4)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(2)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
1,3
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,3,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(4)*y(2)(3)*x(3)(1)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,3,4
Quotient:
x(4)(4)
Lead Term of Product:
-y(2)(3)*y(3)(1)*x(1)(4)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
1,3,4
Quotient:
-x(3)(4)
Lead Term of Product:
y(2)(3)*y(4)(1)*x(1)(4)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(2)(4)*y(4)(3)*x(1)(4)+y(2)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(2)(4)-y(1)(3)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(4)(4)+y(1)(3)*y(2)(4)*x(4)(4)) - (-y(2)(4)*x(1)(4))*(y(4)(3)*x(3)(1)-y(4)(1)*x(3)(3)-y(3)(3)*x(4)(1)+y(3)(1)*x(4)(3))
-------
Rewrite:
-y(2)(3)*y(4)(4)*x(1)(4)*x(3)(1)-y(1)(4)*y(4)(3)*x(2)(4)*x(3)(1)+y(1)(3)*y(4)(4)*x(2)(4)*x(3)(1)+y(2)(4)*y(4)(1)*x(1)(4)*x(3)(3)+y(2)(4)*y(3)(3)*x(1)(4)*x(4)(1)-y(2)(4)*y(3)(1)*x(1)(4)*x(4)(3)+y(1)(4)*y(2)(3)*x(3)(1)*x(4)(4)-y(1)(3)*y(2)(4)*x(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{1}{3}, \lam{1}{2}{4}{3}{4}{4}) =
(y_{2, 3} y_{4, 4})  \del{1}{3}{1}{4} +(-y_{2, 4} y_{4, 1})  \del{1}{3}{3}{4} +(-y_{2, 4} y_{3, 3})  \del{1}{4}{1}{4} +(y_{2, 4} y_{3, 1})  \del{1}{4}{3}{4} +(y_{1, 4} y_{4, 3}-y_{1, 3} y_{4, 4})  \del{2}{3}{1}{4} +(y_{1, 4} y_{2, 3})  \del{3}{4}{1}{4} +(-y_{1, 1} y_{2, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{3, 4})  \eps{1}{2}{1}{3} +(y_{3, 3} x_{4, 4})  \eps{1}{2}{1}{4} +(y_{4, 1} x_{3, 4}-y_{3, 1} x_{4, 4})  \eps{1}{2}{3}{4} +(-y_{2, 1} x_{3, 4})  \eps{1}{4}{3}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{1}{3} +(-y_{1, 4} x_{3, 4})  \eps{2}{4}{1}{3} +(y_{1, 1} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{4, 4})  \pho{1}{2}{3}{1}{3}{4} +(x_{4, 4})  \lam{1}{2}{3}{1}{3}{4} +(-x_{3, 4})  \lam{1}{2}{4}{1}{3}{4}
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(4)*x(3)(1)
Divisor:
Delta
1,3
1,4
Quotient:
y(3)(3)*y(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(3)(4)*y(4)(1)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
1,4
Quotient:
-y(3)(3)*y(3)(4)
Lead Term of Product:
y(3)(3)*y(3)(4)*x(1)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(3)(1)*y(3)(4)
Lead Term of Product:
-y(3)(1)*y(3)(4)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(1)(4)*y(3)(3)
Lead Term of Product:
-y(1)(4)*y(3)(3)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(1)*y(3)(4)
Lead Term of Product:
y(1)(1)*y(3)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,3
Quotient:
-y(4)(4)*x(3)(4)+y(3)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
1,3
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(3)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
y(1)(1)*x(3)(4)
Lead Term of Product:
y(1)(1)*y(4)(4)*x(3)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
1,3,4
Quotient:
-x(3)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(1)(4)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(1)(4))*(y(4)(3)*x(3)(1)-y(4)(1)*x(3)(3)-y(3)(3)*x(4)(1)+y(3)(1)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(4)*x(3)(1)+y(3)(4)*y(4)(1)*x(1)(4)*x(3)(3)-y(1)(4)*y(4)(3)*x(3)(1)*x(3)(4)+y(1)(3)*y(4)(4)*x(3)(1)*x(3)(4)+y(3)(3)*y(3)(4)*x(1)(4)*x(4)(1)-y(3)(1)*y(3)(4)*x(1)(4)*x(4)(3)+y(1)(4)*y(3)(3)*x(3)(1)*x(4)(4)-y(1)(3)*y(3)(4)*x(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{1}{3}, \lam{1}{3}{4}{3}{4}{4}) =
(y_{3, 3} y_{4, 4})  \del{1}{3}{1}{4} +(-y_{3, 4} y_{4, 1})  \del{1}{3}{3}{4} +(-y_{3, 3} y_{3, 4})  \del{1}{4}{1}{4} +(y_{3, 1} y_{3, 4})  \del{1}{4}{3}{4} +(y_{1, 4} y_{3, 3})  \del{3}{4}{1}{4} +(-y_{1, 1} y_{3, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{3, 4}+y_{3, 4} x_{4, 4})  \eps{1}{3}{1}{3} +(y_{4, 1} x_{3, 4})  \eps{1}{3}{3}{4} +(-y_{3, 1} x_{3, 4})  \eps{1}{4}{3}{4} +(-y_{1, 4} x_{3, 4})  \eps{3}{4}{1}{3} +(y_{1, 1} x_{3, 4})  \eps{3}{4}{3}{4} +(-x_{3, 4})  \lam{1}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
3,4
1,3
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,3
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(2)(4)*x(3)(1)
Divisor:
Delta
2,3
1,4
Quotient:
y(3)(3)*y(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(2)(4)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(3)(4)*y(4)(1)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
1,4
Quotient:
-y(3)(3)*y(3)(4)
Lead Term of Product:
y(3)(3)*y(3)(4)*x(2)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(3)(1)*y(3)(4)
Lead Term of Product:
-y(3)(1)*y(3)(4)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
1,4
Quotient:
y(2)(4)*y(3)(3)
Lead Term of Product:
-y(2)(4)*y(3)(3)*x(3)(4)*x(4)(1)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(2)(1)*y(3)(4)
Lead Term of Product:
y(2)(1)*y(3)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(4)(4)*x(3)(4)+y(3)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(2)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
y(4)(1)*x(3)(4)
Lead Term of Product:
y(3)(4)*y(4)(1)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(1)*x(3)(4)
Lead Term of Product:
-y(3)(1)*y(4)(4)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
1,3
Quotient:
-y(2)(4)*x(3)(4)
Lead Term of Product:
-y(2)(4)*y(4)(3)*x(3)(1)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
y(2)(1)*x(3)(4)
Lead Term of Product:
y(2)(1)*y(4)(4)*x(3)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
1,3,4
Quotient:
-x(3)(4)
Lead Term of Product:
y(3)(3)*y(4)(1)*x(2)(4)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(1))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(2)(4))*(y(4)(3)*x(3)(1)-y(4)(1)*x(3)(3)-y(3)(3)*x(4)(1)+y(3)(1)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(2)(4)*x(3)(1)+y(3)(4)*y(4)(1)*x(2)(4)*x(3)(3)-y(2)(4)*y(4)(3)*x(3)(1)*x(3)(4)+y(2)(3)*y(4)(4)*x(3)(1)*x(3)(4)+y(3)(3)*y(3)(4)*x(2)(4)*x(4)(1)-y(3)(1)*y(3)(4)*x(2)(4)*x(4)(3)+y(2)(4)*y(3)(3)*x(3)(1)*x(4)(4)-y(2)(3)*y(3)(4)*x(3)(1)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{1}{3}, \lam{2}{3}{4}{3}{4}{4}) =
(y_{3, 3} y_{4, 4})  \del{2}{3}{1}{4} +(-y_{3, 4} y_{4, 1})  \del{2}{3}{3}{4} +(-y_{3, 3} y_{3, 4})  \del{2}{4}{1}{4} +(y_{3, 1} y_{3, 4})  \del{2}{4}{3}{4} +(y_{2, 4} y_{3, 3})  \del{3}{4}{1}{4} +(-y_{2, 1} y_{3, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{3, 4}+y_{3, 4} x_{4, 4})  \eps{2}{3}{1}{3} +(y_{4, 1} x_{3, 4})  \eps{2}{3}{3}{4} +(-y_{3, 1} x_{3, 4})  \eps{2}{4}{3}{4} +(-y_{2, 4} x_{3, 4})  \eps{3}{4}{1}{3} +(y_{2, 1} x_{3, 4})  \eps{3}{4}{3}{4} +(-x_{3, 4})  \lam{2}{3}{4}{1}{3}{4}
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
1,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,2,4
3,4,4
Lead Term of Spoly:
-y(2)(3)*y(4)(4)*x(1)(4)*x(3)(2)
Divisor:
Delta
1,3
2,4
Quotient:
y(2)(3)*y(4)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(2)(4)*y(4)(2)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
-y(2)(4)*y(3)(3)
Lead Term of Product:
y(2)(4)*y(3)(3)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(2)(4)*y(3)(2)
Lead Term of Product:
-y(2)(4)*y(3)(2)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
2,3
2,4
Quotient:
y(1)(4)*y(4)(3)-y(1)(3)*y(4)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
y(1)(4)*y(2)(3)
Lead Term of Product:
-y(1)(4)*y(2)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(2)*y(2)(4)
Lead Term of Product:
y(1)(2)*y(2)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(4)(4)*x(3)(4)
Lead Term of Product:
-y(2)(3)*y(4)(4)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,4
Quotient:
y(3)(3)*x(4)(4)
Lead Term of Product:
y(2)(4)*y(3)(3)*x(1)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
1,2
3,4
Quotient:
y(4)(2)*x(3)(4)-y(3)(2)*x(4)(4)
Lead Term of Product:
y(2)(4)*y(4)(2)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(2)(2)*x(3)(4)
Lead Term of Product:
-y(2)(2)*y(4)(4)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(1)(4)*x(4)(4)
Lead Term of Product:
y(1)(4)*y(3)(3)*x(2)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
2,3
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
y(1)(2)*x(3)(4)
Lead Term of Product:
y(1)(2)*y(4)(4)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Rho
1,2,3
2,3,4
Quotient:
-x(4)(4)
Lead Term of Product:
y(1)(4)*y(2)(3)*x(3)(2)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,3
2,3,4
Quotient:
x(4)(4)
Lead Term of Product:
-y(2)(3)*y(3)(2)*x(1)(4)*x(4)(4)
Lead term is well behaved
Divisor:
Lam
1,2,4
2,3,4
Quotient:
-x(3)(4)
Lead Term of Product:
y(2)(3)*y(4)(2)*x(1)(4)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(2))*(-y(2)(4)*y(4)(3)*x(1)(4)+y(2)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(2)(4)-y(1)(3)*y(4)(4)*x(2)(4)-y(1)(4)*y(2)(3)*x(4)(4)+y(1)(3)*y(2)(4)*x(4)(4)) - (-y(2)(4)*x(1)(4))*(y(4)(3)*x(3)(2)-y(4)(2)*x(3)(3)-y(3)(3)*x(4)(2)+y(3)(2)*x(4)(3))
-------
Rewrite:
-y(2)(3)*y(4)(4)*x(1)(4)*x(3)(2)-y(1)(4)*y(4)(3)*x(2)(4)*x(3)(2)+y(1)(3)*y(4)(4)*x(2)(4)*x(3)(2)+y(2)(4)*y(4)(2)*x(1)(4)*x(3)(3)+y(2)(4)*y(3)(3)*x(1)(4)*x(4)(2)-y(2)(4)*y(3)(2)*x(1)(4)*x(4)(3)+y(1)(4)*y(2)(3)*x(3)(2)*x(4)(4)-y(1)(3)*y(2)(4)*x(3)(2)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{2}{3}, \lam{1}{2}{4}{3}{4}{4}) =
(y_{2, 3} y_{4, 4})  \del{1}{3}{2}{4} +(-y_{2, 4} y_{4, 2})  \del{1}{3}{3}{4} +(-y_{2, 4} y_{3, 3})  \del{1}{4}{2}{4} +(y_{2, 4} y_{3, 2})  \del{1}{4}{3}{4} +(y_{1, 4} y_{4, 3}-y_{1, 3} y_{4, 4})  \del{2}{3}{2}{4} +(y_{1, 4} y_{2, 3})  \del{3}{4}{2}{4} +(-y_{1, 2} y_{2, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{3, 4})  \eps{1}{2}{2}{3} +(y_{3, 3} x_{4, 4})  \eps{1}{2}{2}{4} +(y_{4, 2} x_{3, 4}-y_{3, 2} x_{4, 4})  \eps{1}{2}{3}{4} +(-y_{2, 2} x_{3, 4})  \eps{1}{4}{3}{4} +(y_{1, 4} x_{4, 4})  \eps{2}{3}{2}{3} +(-y_{1, 4} x_{3, 4})  \eps{2}{4}{2}{3} +(y_{1, 2} x_{3, 4})  \eps{2}{4}{3}{4} +(-x_{4, 4})  \pho{1}{2}{3}{2}{3}{4} +(x_{4, 4})  \lam{1}{2}{3}{2}{3}{4} +(-x_{3, 4})  \lam{1}{2}{4}{2}{3}{4}
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
1,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(1)(4)*x(3)(2)
Divisor:
Delta
1,3
2,4
Quotient:
y(3)(3)*y(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
1,3
3,4
Quotient:
-y(3)(4)*y(4)(2)
Lead Term of Product:
y(3)(4)*y(4)(2)*x(1)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
1,4
2,4
Quotient:
-y(3)(3)*y(3)(4)
Lead Term of Product:
y(3)(3)*y(3)(4)*x(1)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
1,4
3,4
Quotient:
y(3)(2)*y(3)(4)
Lead Term of Product:
-y(3)(2)*y(3)(4)*x(1)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
y(1)(4)*y(3)(3)
Lead Term of Product:
-y(1)(4)*y(3)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(1)(2)*y(3)(4)
Lead Term of Product:
y(1)(2)*y(3)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(4)(4)*x(3)(4)+y(3)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(1)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,3
3,4
Quotient:
y(4)(2)*x(3)(4)
Lead Term of Product:
y(3)(4)*y(4)(2)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
1,4
3,4
Quotient:
-y(3)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(1)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
-y(1)(4)*x(3)(4)
Lead Term of Product:
-y(1)(4)*y(4)(3)*x(3)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
y(1)(2)*x(3)(4)
Lead Term of Product:
y(1)(2)*y(4)(4)*x(3)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
1,3,4
2,3,4
Quotient:
-x(3)(4)
Lead Term of Product:
y(3)(3)*y(4)(2)*x(1)(4)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(2))*(-y(3)(4)*y(4)(3)*x(1)(4)+y(3)(3)*y(4)(4)*x(1)(4)+y(1)(4)*y(4)(3)*x(3)(4)-y(1)(3)*y(4)(4)*x(3)(4)-y(1)(4)*y(3)(3)*x(4)(4)+y(1)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(1)(4))*(y(4)(3)*x(3)(2)-y(4)(2)*x(3)(3)-y(3)(3)*x(4)(2)+y(3)(2)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(1)(4)*x(3)(2)+y(3)(4)*y(4)(2)*x(1)(4)*x(3)(3)-y(1)(4)*y(4)(3)*x(3)(2)*x(3)(4)+y(1)(3)*y(4)(4)*x(3)(2)*x(3)(4)+y(3)(3)*y(3)(4)*x(1)(4)*x(4)(2)-y(3)(2)*y(3)(4)*x(1)(4)*x(4)(3)+y(1)(4)*y(3)(3)*x(3)(2)*x(4)(4)-y(1)(3)*y(3)(4)*x(3)(2)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{2}{3}, \lam{1}{3}{4}{3}{4}{4}) =
(y_{3, 3} y_{4, 4})  \del{1}{3}{2}{4} +(-y_{3, 4} y_{4, 2})  \del{1}{3}{3}{4} +(-y_{3, 3} y_{3, 4})  \del{1}{4}{2}{4} +(y_{3, 2} y_{3, 4})  \del{1}{4}{3}{4} +(y_{1, 4} y_{3, 3})  \del{3}{4}{2}{4} +(-y_{1, 2} y_{3, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{3, 4}+y_{3, 4} x_{4, 4})  \eps{1}{3}{2}{3} +(y_{4, 2} x_{3, 4})  \eps{1}{3}{3}{4} +(-y_{3, 2} x_{3, 4})  \eps{1}{4}{3}{4} +(-y_{1, 4} x_{3, 4})  \eps{3}{4}{2}{3} +(y_{1, 2} x_{3, 4})  \eps{3}{4}{3}{4} +(-x_{3, 4})  \lam{1}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
3,4
2,3
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,3
Lam:
2,3,4
3,4,4
Lead Term of Spoly:
-y(3)(3)*y(4)(4)*x(2)(4)*x(3)(2)
Divisor:
Delta
2,3
2,4
Quotient:
y(3)(3)*y(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(2)(4)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
3,4
Quotient:
-y(3)(4)*y(4)(2)
Lead Term of Product:
y(3)(4)*y(4)(2)*x(2)(4)*x(3)(3)
Lead term is well behaved
Divisor:
Delta
2,4
2,4
Quotient:
-y(3)(3)*y(3)(4)
Lead Term of Product:
y(3)(3)*y(3)(4)*x(2)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
2,4
3,4
Quotient:
y(3)(2)*y(3)(4)
Lead Term of Product:
-y(3)(2)*y(3)(4)*x(2)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Delta
3,4
2,4
Quotient:
y(2)(4)*y(3)(3)
Lead Term of Product:
-y(2)(4)*y(3)(3)*x(3)(4)*x(4)(2)
Lead term is well behaved
Divisor:
Delta
3,4
3,4
Quotient:
-y(2)(2)*y(3)(4)
Lead Term of Product:
y(2)(2)*y(3)(4)*x(3)(4)*x(4)(3)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(4)(4)*x(3)(4)+y(3)(4)*x(4)(4)
Lead Term of Product:
-y(3)(3)*y(4)(4)*x(2)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,3
3,4
Quotient:
y(4)(2)*x(3)(4)
Lead Term of Product:
y(3)(4)*y(4)(2)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
2,4
3,4
Quotient:
-y(3)(2)*x(3)(4)
Lead Term of Product:
-y(3)(2)*y(4)(4)*x(2)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
2,3
Quotient:
-y(2)(4)*x(3)(4)
Lead Term of Product:
-y(2)(4)*y(4)(3)*x(3)(2)*x(3)(4)
Lead term is well behaved
Divisor:
Epsilon
3,4
3,4
Quotient:
y(2)(2)*x(3)(4)
Lead Term of Product:
y(2)(2)*y(4)(4)*x(3)(3)*x(3)(4)
Lead term is well behaved
Divisor:
Lam
2,3,4
2,3,4
Quotient:
-x(3)(4)
Lead Term of Product:
y(3)(3)*y(4)(2)*x(2)(4)*x(3)(4)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(3)(2))*(-y(3)(4)*y(4)(3)*x(2)(4)+y(3)(3)*y(4)(4)*x(2)(4)+y(2)(4)*y(4)(3)*x(3)(4)-y(2)(3)*y(4)(4)*x(3)(4)-y(2)(4)*y(3)(3)*x(4)(4)+y(2)(3)*y(3)(4)*x(4)(4)) - (-y(3)(4)*x(2)(4))*(y(4)(3)*x(3)(2)-y(4)(2)*x(3)(3)-y(3)(3)*x(4)(2)+y(3)(2)*x(4)(3))
-------
Rewrite:
-y(3)(3)*y(4)(4)*x(2)(4)*x(3)(2)+y(3)(4)*y(4)(2)*x(2)(4)*x(3)(3)-y(2)(4)*y(4)(3)*x(3)(2)*x(3)(4)+y(2)(3)*y(4)(4)*x(3)(2)*x(3)(4)+y(3)(3)*y(3)(4)*x(2)(4)*x(4)(2)-y(3)(2)*y(3)(4)*x(2)(4)*x(4)(3)+y(2)(4)*y(3)(3)*x(3)(2)*x(4)(4)-y(2)(3)*y(3)(4)*x(3)(2)*x(4)(4)
-----------
TeX output:
S(\eps{3}{4}{2}{3}, \lam{2}{3}{4}{3}{4}{4}) =
(y_{3, 3} y_{4, 4})  \del{2}{3}{2}{4} +(-y_{3, 4} y_{4, 2})  \del{2}{3}{3}{4} +(-y_{3, 3} y_{3, 4})  \del{2}{4}{2}{4} +(y_{3, 2} y_{3, 4})  \del{2}{4}{3}{4} +(y_{2, 4} y_{3, 3})  \del{3}{4}{2}{4} +(-y_{2, 2} y_{3, 4})  \del{3}{4}{3}{4} +(-y_{4, 4} x_{3, 4}+y_{3, 4} x_{4, 4})  \eps{2}{3}{2}{3} +(y_{4, 2} x_{3, 4})  \eps{2}{3}{3}{4} +(-y_{3, 2} x_{3, 4})  \eps{2}{4}{3}{4} +(-y_{2, 4} x_{3, 4})  \eps{3}{4}{2}{3} +(y_{2, 2} x_{3, 4})  \eps{3}{4}{3}{4} +(-x_{3, 4})  \lam{2}{3}{4}{2}{3}{4}
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
2,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,3
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,3
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,3
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,3
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,3
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,3
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,3
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,3
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,3
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,3
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,2,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
1,3,4
3,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
2,3,4
1,2,2
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
2,3,4
1,2,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
2,3,4
1,2,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
2,3,4
1,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
2,3,4
1,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
2,3,4
1,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
2,3,4
2,3,3
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
2,3,4
2,3,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
2,3,4
2,4,4
Relatively Prime
----------------------------------
Epsilon:
3,4
3,4
Lam:
2,3,4
3,4,4
Relatively Prime
----------------------------------