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D.4.3.7 kernel

Procedure from library homolog.lib (see homolog_lib).

Usage:
kernel(A,M,N);

Compute:
Let M and N be submodules of R^m and R^n presenting M'=R^m/M, N'=R^n/N (R=basering) and let A:R^m-->R^n a matrix inducing a map A':M'-->N'. Compute a presentation K of ker(A') as in the commutative diagram:
 
                       ker(A') --->  M' --A'--> N'
                           |^        |^         |^
                           |         |          |
                          R^r  ---> R^m --A--> R^n
                           |^        |^         |^
                           |K        |M         |N
                           |         |          |
                          R^s  ---> R^p -----> R^q

Return:
module K, a presentation of ker(A')

Example:
 
LIB "homolog.lib";
ring r;
module N=[2x,x],[0,y];
module M=maxideal(1)*freemodule(2);
matrix A[2][2]=2x,0,x,y,z2,y;
module K=kernel(A,M,N);
degree(std(K));
==> // codimension = 3
==> // dimension   = 0
==> // degree      = 2
print(K);
==> z,0,y,0,x,0,
==> 0,z,0,y,0,x 


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