D.4.3.18 tensorMod

Procedure from library homolog.lib (see homolog_lib).

Usage:

tensorMod(M,N); M,N modules

Compute:

presentation matrix A of the tensor product T of the modules M’=coker(M), N’=coker(N): if matrix(M) defines a map M: R^r–>R^s and matrix(N) defines a map N: R^p–>R^q, then A defines a presentation

R^(sp+rq) --A-> R^(sq) --> T --> 0 .

Return:

matrix A satisfying coker(A) = tensorprod(coker(M),coker(N)) .

Example:

LIB "homolog.lib";
ring A=0,(x,y,z),dp;
matrix M[3][3]=1,2,3,4,5,6,7,8,9;
matrix N[2][2]=x,y,0,z;
print(M);
→ 1,2,3,
→ 4,5,6,
→ 7,8,9 
print(N);
→ x,y,
→ 0,z 
print(tensorMod(M,N));
→ x,y,0,0,0,0,1,0,2,0,3,0,
→ 0,z,0,0,0,0,0,1,0,2,0,3,
→ 0,0,x,y,0,0,4,0,5,0,6,0,
→ 0,0,0,z,0,0,0,4,0,5,0,6,
→ 0,0,0,0,x,y,7,0,8,0,9,0,
→ 0,0,0,0,0,z,0,7,0,8,0,9