|  |  D.4.8.10 homology Procedure from libraryhomolog.lib(see  homolog_lib).
 
Example: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
Compute a presentation of the module|  |     R^k --A--> R^m --B--> R^n.
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 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|  |     ker(B)/im(A) := ker(M'/im(A) --B--> N'/im(BM)+im(BA)).
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Return:
module H, a presentation of ker(B)/im(A).
Note:
homology returns a free module of rank m if ker(B)=im(A).
 |  | LIB "homolog.lib";
ring r;
ideal id=maxideal(4);
qring qr=std(id);
module N=maxideal(3)*freemodule(2);
module M=maxideal(2)*freemodule(2);
module B=[2x,0],[x,y],[z2,y];
module A=M;
module H=homology(A,B,M,N);
H=std(H);
// dimension of homology:
dim(H);
==> 0
// vector space dimension:
vdim(H);
==> 19
ring s=0,x,ds;
qring qs=std(x4);
module A=[x];
module B=A;
module M=[x3];
module N=M;
homology(A,B,M,N);
==> _[1]=gen(1)
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