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D.4.7.15 hom_kernel
Procedure from library homolog.lib (see homolog_lib).
- Usage:
- hom_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 be a matrix inducing a
map A':M'-->N'. Then ker(A,M,N); computes 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':coker(M)->coker(N)).
Example:
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