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D.15.11.38 tensorModule
Procedure from library modules.lib (see modules_lib).
- Return:
- Tensorprodukt of M,N
Example:
| | LIB "modules.lib";
ring R = 0,(x,y,z),dp;
matrix a[1][2] = x,y;
Matrix A = a;
matrix b[1][2] = x2,y2;
Matrix B = b;
Module M = subquotient(A,B);
M;
==> subquotient (| x y |, | x2 y2 |)
==>
==>
matrix c[2][2]=x,y2,z,xz;
Matrix C=c;
matrix d[2][3]=z2,xyz,x2y2,xy,x3,y4;
Matrix D=d;
Module N = subquotient(C,D);
N;
==> subquotient (| x y2 |, | z2 xyz x2y2 |)
==> | z xz | | xy x3 y4 |
==>
==>
tensorModule(M,N);
==> cokernel | 0 x -y 0 0 0 -xyz+y2 0 x2z-xyz 0 y4-xyz2-x2z+xyz+\
y2z-y2 0 -xy2z-y3z+xy2+y3+x2z-xyz+xz2+y2 0 \
-y3z+xz2 0 xy2z2-xy2z-y3z+y3 0 \
y4z-y4-x2z2+xyz2+x2z-xyz-y2z+y2 0 xy3z-xy\
3+xy2z+y3z-xy2-y3-x2z+xyz-xz2-y2 0 \
0 0 x2y2z-x2y2+xy2z+y3z-xy2-y3-x2z+xyz-xz2-y2 0 \
|
==> | y 0 x 0 0 0 0 -xyz+y2 0 x2z-xyz 0 \
y4-xyz2-x2z+xyz+y2z-y2 0 -xy2z-y3z+x\
y2+y3+x2z-xyz+xz2+y2 0 -y3z+xz2 0 xy2z2-xy2z-y3z+y\
3 0 y4z-y4-x2z2+xyz2+x2z-xyz-y2z+y2 0 \
xy3z-xy3+xy2z+y3z-xy2-y3-x2z+xyz-xz2-y2 \
0 0 0 x2y2z-x2y2+xy2z\
+y3z-xy2-y3-x2z+xyz-xz2-y2 |
==> | 0 0 0 0 x -y z2-x 0 0 0 -xy2+z3-z2+x \
0 -y2z+yz2-x2-xy-xz+z2-x 0 \
0 0 -yz3+x2z+yz2-xy 0 \
xy2-z3+z2-x 0 -y2z2+x\
2y+y2z-yz2+x2+xy+xz-z2+x 0 \
xyz-y2z 0 -xyz2+x3+y2z-yz2+x2+xy+xz-z2+x 0 \
|
==> | 0 0 0 y 0 x 0 z2-x 0 0 0 \
-xy2+z3-z2+x 0 -y2z+yz2-x2\
-xy-xz+z2-x 0 0 0 -yz3+x2z+yz2-xy \
0 xy2-z3+z2-x 0 \
-y2z2+x2y+y2z-yz2+x2+xy+xz-z2+x \
0 xyz-y2z 0 -xyz2+x3+y2z-yz\
2+x2+xy+xz-z2+x |
==>
==>
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