Singular

7.7.20.0. contraHom

Usage:

contraHom(A,k); A matrix, k int

Return:

matrix

Purpose:

compute the matrix of a homomorphism Hom(A,R^k), where R is the basering. Let A be a matrix defining a map F1-->F2 of free R-modules, then the matrix of Hom(F2,R^k)-->Hom(F1,R^k) is computed.

Note:

if A is matrix of a left (resp. right) R-module homomorphism, then Hom(A,R^k) is a right (resp. left) R-module R-module homomorphism

LIB "nchomolog.lib";
ring A=0,(x,y,z),dp;
matrix M[3][3]=1,2,3,
4,5,6,
7,8,9;
module cM = contraHom(M,2);
print(cM);
==> 1,4,7,0,0,0,
==> 2,5,8,0,0,0,
==> 3,6,9,0,0,0,
==> 0,0,0,1,4,7,
==> 0,0,0,2,5,8,
==> 0,0,0,3,6,9