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D.15.23.38 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            |
==> 
==>