Epsilon:
1,2
1,2
Epsilon:
1,2
1,3
Lead Term of Spoly:
-y(2)(1)*y(2)(3)*x(1)(2)
Divisor:
Epsilon
1,2
2,3
Quotient:
-y(2)(1)
Lead Term of Product:
-y(2)(1)*y(2)(3)*x(1)(2)
Lead term is well behaved
Divisor:
Rho
1,2,2
1,2,3
Quotient:
-1
Lead Term of Product:
y(1)(3)*y(2)(2)*x(2)(1)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(2))*(y(2)(3)*x(1)(1)-y(2)(1)*x(1)(3)-y(1)(3)*x(2)(1)+y(1)(1)*x(2)(3)) - (y(2)(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(2)(3)*x(1)(2)+y(2)(1)*y(2)(2)*x(1)(3)+y(1)(3)*y(2)(2)*x(2)(1)-y(1)(2)*y(2)(3)*x(2)(1)+y(1)(1)*y(2)(3)*x(2)(2)-y(1)(1)*y(2)(2)*x(2)(3)
-----------
TeX output:
S(\eps{1}{2}{1}{2}, \eps{1}{2}{1}{3}) =
(-y_{2, 1})  \eps{1}{2}{2}{3} +(-1)  \pho{1}{2}{2}{1}{2}{3}
----------------------------------
Epsilon:
1,2
1,2
Epsilon:
1,2
2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Epsilon:
1,3
1,2
Lead Term of Spoly:
y(2)(2)*y(3)(1)*x(1)(2)
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(1)(2)
Lead Term of Product:
-y(1)(2)*y(3)(2)*x(2)(1)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,2
Quotient:
-1
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(2)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(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)) - (y(3)(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)(2)*y(3)(1)*x(1)(2)-y(2)(1)*y(3)(2)*x(1)(2)-y(1)(2)*y(3)(2)*x(2)(1)+y(1)(1)*y(3)(2)*x(2)(2)+y(1)(2)*y(2)(2)*x(3)(1)-y(1)(1)*y(2)(2)*x(3)(2)
-----------
TeX output:
S(\eps{1}{2}{1}{2}, \eps{1}{3}{1}{2}) =
(-y_{1, 2})  \eps{2}{3}{1}{2} +(-1)  \lam{1}{2}{3}{1}{2}{2}
----------------------------------
Epsilon:
1,2
1,2
Epsilon:
1,3
1,3
Lead Term of Spoly:
-y(2)(1)*y(3)(3)*x(1)(2)
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(2)(1)
Lead Term of Product:
-y(2)(1)*y(3)(3)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(1)(2)
Lead Term of Product:
-y(1)(2)*y(3)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Epsilon
2,3
2,3
Quotient:
y(1)(1)
Lead Term of Product:
y(1)(1)*y(3)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,2,3
Quotient:
-1
Lead Term of Product:
y(1)(3)*y(2)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-1
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(2)(2))*(y(3)(3)*x(1)(1)-y(3)(1)*x(1)(3)-y(1)(3)*x(3)(1)+y(1)(1)*x(3)(3)) - (y(3)(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)(3)*x(1)(2)+y(2)(2)*y(3)(1)*x(1)(3)-y(1)(2)*y(3)(3)*x(2)(1)+y(1)(1)*y(3)(3)*x(2)(2)+y(1)(3)*y(2)(2)*x(3)(1)-y(1)(1)*y(2)(2)*x(3)(3)
-----------
TeX output:
S(\eps{1}{2}{1}{2}, \eps{1}{3}{1}{3}) =
(-y_{2, 1})  \eps{1}{3}{2}{3} +(-y_{1, 2})  \eps{2}{3}{1}{3} +(y_{1, 1})  \eps{2}{3}{2}{3} +(-1)  \pho{1}{2}{3}{1}{2}{3} +(-1)  \lam{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,2
1,2
Epsilon:
1,3
2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Epsilon:
2,3
1,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Epsilon:
2,3
1,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,2
Epsilon:
2,3
2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Epsilon:
1,2
2,3
Lead Term of Spoly:
y(2)(2)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,2
1,2
Quotient:
y(1)(3)
Lead Term of Product:
-y(1)(3)*x(1)(2)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
1,3
Quotient:
-y(1)(2)
Lead Term of Product:
y(1)(2)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,2
2,3
Quotient:
y(1)(1)
Lead Term of Product:
-y(1)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
x(1)(3)
Lead Term of Product:
y(2)(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)(3)*x(1)(2)-y(2)(2)*x(1)(3)-y(1)(3)*x(2)(2)+y(1)(2)*x(2)(3)) - (x(1)(2))*(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)*x(1)(1)*x(1)(3)-y(2)(1)*x(1)(2)*x(1)(3)-y(1)(3)*x(1)(2)*x(2)(1)+y(1)(3)*x(1)(1)*x(2)(2)-y(1)(2)*x(1)(1)*x(2)(3)+y(1)(1)*x(1)(2)*x(2)(3)
-----------
TeX output:
S(\eps{1}{2}{1}{3}, \eps{1}{2}{2}{3}) =
(y_{1, 3})  \del{1}{2}{1}{2} +(-y_{1, 2})  \del{1}{2}{1}{3} +(y_{1, 1})  \del{1}{2}{2}{3} +(x_{1, 3})  \eps{1}{2}{1}{2}
----------------------------------
Epsilon:
1,2
1,3
Epsilon:
1,3
1,2
Lead Term of Spoly:
y(2)(3)*y(3)(1)*x(1)(2)
Divisor:
Epsilon
1,2
2,3
Quotient:
y(3)(1)
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
-y(1)(3)
Lead Term of Product:
-y(1)(3)*y(3)(2)*x(2)(1)
Lead term is well behaved
Divisor:
Rho
1,2,3
1,2,3
Quotient:
1
Lead Term of Product:
-y(1)(3)*y(2)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,2,3
Quotient:
-1
Lead Term of Product:
y(2)(2)*y(3)(1)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(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)) - (y(3)(2))*(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)(3)*y(3)(1)*x(1)(2)-y(2)(1)*y(3)(2)*x(1)(3)-y(1)(3)*y(3)(2)*x(2)(1)+y(1)(1)*y(3)(2)*x(2)(3)+y(1)(2)*y(2)(3)*x(3)(1)-y(1)(1)*y(2)(3)*x(3)(2)
-----------
TeX output:
S(\eps{1}{2}{1}{3}, \eps{1}{3}{1}{2}) =
(y_{3, 1})  \eps{1}{2}{2}{3} +(-y_{1, 3})  \eps{2}{3}{1}{2} +(1)  \pho{1}{2}{3}{1}{2}{3} +(-1)  \lam{1}{2}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,2
1,3
Epsilon:
1,3
1,3
Lead Term of Spoly:
y(2)(3)*y(3)(1)*x(1)(3)
Divisor:
Epsilon
2,3
1,3
Quotient:
-y(1)(3)
Lead Term of Product:
-y(1)(3)*y(3)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Lam
1,2,3
1,3,3
Quotient:
-1
Lead Term of Product:
y(2)(3)*y(3)(1)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(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)) - (y(3)(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)(3)*y(3)(1)*x(1)(3)-y(2)(1)*y(3)(3)*x(1)(3)-y(1)(3)*y(3)(3)*x(2)(1)+y(1)(1)*y(3)(3)*x(2)(3)+y(1)(3)*y(2)(3)*x(3)(1)-y(1)(1)*y(2)(3)*x(3)(3)
-----------
TeX output:
S(\eps{1}{2}{1}{3}, \eps{1}{3}{1}{3}) =
(-y_{1, 3})  \eps{2}{3}{1}{3} +(-1)  \lam{1}{2}{3}{1}{3}{3}
----------------------------------
Epsilon:
1,2
1,3
Epsilon:
1,3
2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Epsilon:
2,3
1,2
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Epsilon:
2,3
1,3
Relatively Prime
----------------------------------
Epsilon:
1,2
1,3
Epsilon:
2,3
2,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Epsilon:
1,3
1,2
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Epsilon:
1,3
1,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Epsilon:
1,3
2,3
Lead Term of Spoly:
y(2)(3)*y(3)(2)*x(1)(3)
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(1)(3)
Lead Term of Product:
-y(1)(3)*y(3)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Lam
1,2,3
2,3,3
Quotient:
-1
Lead Term of Product:
y(2)(3)*y(3)(2)*x(1)(3)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(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)) - (y(3)(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)(3)*y(3)(2)*x(1)(3)-y(2)(2)*y(3)(3)*x(1)(3)-y(1)(3)*y(3)(3)*x(2)(2)+y(1)(2)*y(3)(3)*x(2)(3)+y(1)(3)*y(2)(3)*x(3)(2)-y(1)(2)*y(2)(3)*x(3)(3)
-----------
TeX output:
S(\eps{1}{2}{2}{3}, \eps{1}{3}{2}{3}) =
(-y_{1, 3})  \eps{2}{3}{2}{3} +(-1)  \lam{1}{2}{3}{2}{3}{3}
----------------------------------
Epsilon:
1,2
2,3
Epsilon:
2,3
1,2
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Epsilon:
2,3
1,3
Relatively Prime
----------------------------------
Epsilon:
1,2
2,3
Epsilon:
2,3
2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Epsilon:
1,3
1,3
Lead Term of Spoly:
-y(3)(1)*y(3)(3)*x(1)(2)
Divisor:
Epsilon
1,3
2,3
Quotient:
-y(3)(1)
Lead Term of Product:
-y(3)(1)*y(3)(3)*x(1)(2)
Lead term is well behaved
Divisor:
Rho
1,3,3
1,2,3
Quotient:
-1
Lead Term of Product:
y(1)(3)*y(3)(2)*x(3)(1)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(2))*(y(3)(3)*x(1)(1)-y(3)(1)*x(1)(3)-y(1)(3)*x(3)(1)+y(1)(1)*x(3)(3)) - (y(3)(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(3)(3)*x(1)(2)+y(3)(1)*y(3)(2)*x(1)(3)+y(1)(3)*y(3)(2)*x(3)(1)-y(1)(2)*y(3)(3)*x(3)(1)+y(1)(1)*y(3)(3)*x(3)(2)-y(1)(1)*y(3)(2)*x(3)(3)
-----------
TeX output:
S(\eps{1}{3}{1}{2}, \eps{1}{3}{1}{3}) =
(-y_{3, 1})  \eps{1}{3}{2}{3} +(-1)  \pho{1}{3}{3}{1}{2}{3}
----------------------------------
Epsilon:
1,3
1,2
Epsilon:
1,3
2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Epsilon:
2,3
1,2
Lead Term of Spoly:
-y(3)(1)*x(1)(2)*x(2)(1)
Divisor:
Delta
1,2
1,2
Quotient:
y(3)(1)
Lead Term of Product:
-y(3)(1)*x(1)(2)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,2
Quotient:
-y(2)(1)
Lead Term of Product:
y(2)(1)*x(1)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
1,2
Quotient:
y(1)(1)
Lead Term of Product:
-y(1)(1)*x(2)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
x(3)(1)
Lead Term of Product:
y(2)(2)*x(1)(1)*x(3)(1)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(y(3)(2)*x(2)(1)-y(3)(1)*x(2)(2)-y(2)(2)*x(3)(1)+y(2)(1)*x(3)(2)) - (x(2)(1))*(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)*x(1)(2)*x(2)(1)+y(3)(1)*x(1)(1)*x(2)(2)+y(2)(2)*x(1)(1)*x(3)(1)-y(1)(2)*x(2)(1)*x(3)(1)-y(2)(1)*x(1)(1)*x(3)(2)+y(1)(1)*x(2)(1)*x(3)(2)
-----------
TeX output:
S(\eps{1}{3}{1}{2}, \eps{2}{3}{1}{2}) =
(y_{3, 1})  \del{1}{2}{1}{2} +(-y_{2, 1})  \del{1}{3}{1}{2} +(y_{1, 1})  \del{2}{3}{1}{2} +(x_{3, 1})  \eps{1}{2}{1}{2}
----------------------------------
Epsilon:
1,3
1,2
Epsilon:
2,3
1,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,2
Epsilon:
2,3
2,3
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Epsilon:
1,3
2,3
Lead Term of Spoly:
y(3)(2)*x(1)(1)*x(1)(3)
Divisor:
Delta
1,3
1,2
Quotient:
y(1)(3)
Lead Term of Product:
-y(1)(3)*x(1)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,3
Quotient:
-y(1)(2)
Lead Term of Product:
y(1)(2)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
y(1)(1)
Lead Term of Product:
-y(1)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
x(1)(3)
Lead Term of Product:
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(3)(3)*x(1)(2)-y(3)(2)*x(1)(3)-y(1)(3)*x(3)(2)+y(1)(2)*x(3)(3)) - (x(1)(2))*(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)*x(1)(1)*x(1)(3)-y(3)(1)*x(1)(2)*x(1)(3)-y(1)(3)*x(1)(2)*x(3)(1)+y(1)(3)*x(1)(1)*x(3)(2)-y(1)(2)*x(1)(1)*x(3)(3)+y(1)(1)*x(1)(2)*x(3)(3)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \eps{1}{3}{2}{3}) =
(y_{1, 3})  \del{1}{3}{1}{2} +(-y_{1, 2})  \del{1}{3}{1}{3} +(y_{1, 1})  \del{1}{3}{2}{3} +(x_{1, 3})  \eps{1}{3}{1}{2}
----------------------------------
Epsilon:
1,3
1,3
Epsilon:
2,3
1,2
Relatively Prime
----------------------------------
Epsilon:
1,3
1,3
Epsilon:
2,3
1,3
Lead Term of Spoly:
-y(3)(1)*x(1)(3)*x(2)(1)
Divisor:
Delta
1,2
1,3
Quotient:
y(3)(1)
Lead Term of Product:
-y(3)(1)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,3
Quotient:
-y(2)(1)
Lead Term of Product:
y(2)(1)*x(1)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
1,3
Quotient:
y(1)(1)
Lead Term of Product:
-y(1)(1)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
x(3)(1)
Lead Term of Product:
y(2)(3)*x(1)(1)*x(3)(1)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(x(1)(1))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3)) - (x(2)(1))*(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)*x(1)(3)*x(2)(1)+y(3)(1)*x(1)(1)*x(2)(3)+y(2)(3)*x(1)(1)*x(3)(1)-y(1)(3)*x(2)(1)*x(3)(1)-y(2)(1)*x(1)(1)*x(3)(3)+y(1)(1)*x(2)(1)*x(3)(3)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \eps{2}{3}{1}{3}) =
(y_{3, 1})  \del{1}{2}{1}{3} +(-y_{2, 1})  \del{1}{3}{1}{3} +(y_{1, 1})  \del{2}{3}{1}{3} +(x_{3, 1})  \eps{1}{2}{1}{3}
----------------------------------
Epsilon:
1,3
1,3
Epsilon:
2,3
2,3
Lead Term of Spoly:
-y(3)(1)*x(1)(3)*x(2)(2)
Divisor:
Delta
1,2
2,3
Quotient:
y(3)(1)
Lead Term of Product:
-y(3)(1)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
-y(2)(1)
Lead Term of Product:
y(2)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,2
Quotient:
y(1)(3)
Lead Term of Product:
-y(1)(3)*x(2)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
1,3
Quotient:
-y(1)(2)
Lead Term of Product:
y(1)(2)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
2*y(1)(1)
Lead Term of Product:
-2*y(1)(1)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,2
Quotient:
-x(3)(3)
Lead Term of Product:
-y(2)(2)*x(1)(1)*x(3)(3)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
x(3)(2)
Lead Term of Product:
y(2)(3)*x(1)(1)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
x(2)(3)
Lead Term of Product:
y(3)(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)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3)) - (x(2)(2))*(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)*x(1)(3)*x(2)(2)+y(3)(2)*x(1)(1)*x(2)(3)-y(1)(3)*x(2)(2)*x(3)(1)+y(2)(3)*x(1)(1)*x(3)(2)-y(2)(2)*x(1)(1)*x(3)(3)+y(1)(1)*x(2)(2)*x(3)(3)
-----------
TeX output:
S(\eps{1}{3}{1}{3}, \eps{2}{3}{2}{3}) =
(y_{3, 1})  \del{1}{2}{2}{3} +(-y_{2, 1})  \del{1}{3}{2}{3} +(y_{1, 3})  \del{2}{3}{1}{2} +(-y_{1, 2})  \del{2}{3}{1}{3} +(2 y_{1, 1})  \del{2}{3}{2}{3} +(-x_{3, 3})  \eps{1}{2}{1}{2} +(x_{3, 2})  \eps{1}{2}{1}{3} +(x_{2, 3})  \eps{1}{3}{1}{2}
----------------------------------
Epsilon:
1,3
2,3
Epsilon:
2,3
1,2
Relatively Prime
----------------------------------
Epsilon:
1,3
2,3
Epsilon:
2,3
1,3
Lead Term of Spoly:
-y(3)(2)*x(1)(3)*x(2)(1)
Divisor:
Delta
1,2
1,3
Quotient:
y(3)(2)
Lead Term of Product:
-y(3)(2)*x(1)(3)*x(2)(1)
Lead term is well behaved
Divisor:
Delta
1,3
1,2
Quotient:
-y(2)(3)
Lead Term of Product:
y(2)(3)*x(1)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
-y(2)(1)
Lead Term of Product:
y(2)(1)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
1,3
Quotient:
y(1)(2)
Lead Term of Product:
-y(1)(2)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Epsilon
1,2
1,3
Quotient:
x(3)(2)
Lead Term of Product:
y(2)(3)*x(1)(1)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,3
1,2
Quotient:
-x(2)(3)
Lead Term of Product:
-y(3)(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)(2))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3)) - (x(2)(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)(2)*x(1)(3)*x(2)(1)+y(3)(1)*x(1)(2)*x(2)(3)+y(2)(3)*x(1)(2)*x(3)(1)-y(1)(3)*x(2)(1)*x(3)(2)-y(2)(1)*x(1)(2)*x(3)(3)+y(1)(2)*x(2)(1)*x(3)(3)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \eps{2}{3}{1}{3}) =
(y_{3, 2})  \del{1}{2}{1}{3} +(-y_{2, 3})  \del{1}{3}{1}{2} +(-y_{2, 1})  \del{1}{3}{2}{3} +(y_{1, 2})  \del{2}{3}{1}{3} +(x_{3, 2})  \eps{1}{2}{1}{3} +(-x_{2, 3})  \eps{1}{3}{1}{2}
----------------------------------
Epsilon:
1,3
2,3
Epsilon:
2,3
2,3
Lead Term of Spoly:
-y(3)(2)*x(1)(3)*x(2)(2)
Divisor:
Delta
1,2
2,3
Quotient:
y(3)(2)
Lead Term of Product:
-y(3)(2)*x(1)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Delta
1,3
2,3
Quotient:
-y(2)(2)
Lead Term of Product:
y(2)(2)*x(1)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
y(1)(2)
Lead Term of Product:
-y(1)(2)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
1,2
2,3
Quotient:
x(3)(2)
Lead Term of Product:
y(2)(3)*x(1)(2)*x(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)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3)) - (x(2)(2))*(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)*x(1)(3)*x(2)(2)+y(3)(2)*x(1)(2)*x(2)(3)+y(2)(3)*x(1)(2)*x(3)(2)-y(1)(3)*x(2)(2)*x(3)(2)-y(2)(2)*x(1)(2)*x(3)(3)+y(1)(2)*x(2)(2)*x(3)(3)
-----------
TeX output:
S(\eps{1}{3}{2}{3}, \eps{2}{3}{2}{3}) =
(y_{3, 2})  \del{1}{2}{2}{3} +(-y_{2, 2})  \del{1}{3}{2}{3} +(y_{1, 2})  \del{2}{3}{2}{3} +(x_{3, 2})  \eps{1}{2}{2}{3}
----------------------------------
Epsilon:
2,3
1,2
Epsilon:
2,3
1,3
Lead Term of Spoly:
-y(3)(1)*y(3)(3)*x(2)(2)
Divisor:
Epsilon
2,3
2,3
Quotient:
-y(3)(1)
Lead Term of Product:
-y(3)(1)*y(3)(3)*x(2)(2)
Lead term is well behaved
Divisor:
Rho
2,3,3
1,2,3
Quotient:
-1
Lead Term of Product:
y(2)(3)*y(3)(2)*x(3)(1)
Lead term is well behaved
test difference:
0
all lead terms worked and remainder was zero
S-poly:
(y(3)(2))*(y(3)(3)*x(2)(1)-y(3)(1)*x(2)(3)-y(2)(3)*x(3)(1)+y(2)(1)*x(3)(3)) - (y(3)(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(3)(3)*x(2)(2)+y(3)(1)*y(3)(2)*x(2)(3)+y(2)(3)*y(3)(2)*x(3)(1)-y(2)(2)*y(3)(3)*x(3)(1)+y(2)(1)*y(3)(3)*x(3)(2)-y(2)(1)*y(3)(2)*x(3)(3)
-----------
TeX output:
S(\eps{2}{3}{1}{2}, \eps{2}{3}{1}{3}) =
(-y_{3, 1})  \eps{2}{3}{2}{3} +(-1)  \pho{2}{3}{3}{1}{2}{3}
----------------------------------
Epsilon:
2,3
1,2
Epsilon:
2,3
2,3
Relatively Prime
----------------------------------
Epsilon:
2,3
1,3
Epsilon:
2,3
2,3
Lead Term of Spoly:
y(3)(2)*x(2)(1)*x(2)(3)
Divisor:
Delta
2,3
1,2
Quotient:
y(2)(3)
Lead Term of Product:
-y(2)(3)*x(2)(2)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
1,3
Quotient:
-y(2)(2)
Lead Term of Product:
y(2)(2)*x(2)(3)*x(3)(1)
Lead term is well behaved
Divisor:
Delta
2,3
2,3
Quotient:
y(2)(1)
Lead Term of Product:
-y(2)(1)*x(2)(3)*x(3)(2)
Lead term is well behaved
Divisor:
Epsilon
2,3
1,2
Quotient:
x(2)(3)
Lead Term of Product:
y(3)(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)(3)*x(2)(2)-y(3)(2)*x(2)(3)-y(2)(3)*x(3)(2)+y(2)(2)*x(3)(3)) - (x(2)(2))*(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)*x(2)(1)*x(2)(3)-y(3)(1)*x(2)(2)*x(2)(3)-y(2)(3)*x(2)(2)*x(3)(1)+y(2)(3)*x(2)(1)*x(3)(2)-y(2)(2)*x(2)(1)*x(3)(3)+y(2)(1)*x(2)(2)*x(3)(3)
-----------
TeX output:
S(\eps{2}{3}{1}{3}, \eps{2}{3}{2}{3}) =
(y_{2, 3})  \del{2}{3}{1}{2} +(-y_{2, 2})  \del{2}{3}{1}{3} +(y_{2, 1})  \del{2}{3}{2}{3} +(x_{2, 3})  \eps{2}{3}{1}{2}
----------------------------------