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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
 
    R^k--A-->M'--B-->N'.

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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            User manual for Singular version 3-1-6, Dec 2012, generated by texi2html.