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D.4.7.10 homology
Procedure from library homolog.lib (see homolog_lib).
- Usage:
- homology(A,B,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,B matrices inducing maps
| R^k --A--> R^m --B--> R^n.
| Compute a presentation of the module
| ker(B)/im(A) := ker(M'/im(A) --B--> N'/im(BM)+im(BA)).
| If B induces a map M'-->N' (i.e BM=0) and if im(A) is contained in
ker(B) (that is, BA=0) then ker(B)/im(A) is the homology of the
complex
- Return:
- module H, a presentation of ker(B)/im(A).
- Note:
- homology returns a free module of rank m if ker(B)=im(A).
Example:
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