Dear forum,
I'm using the homalg package to compute the homology of a chain complex, as
follows:
> ZZ := HomalgRingOfIntegers( );;
> C2 := 1 * ZZ;;
> C1 := 1 * ZZ;;
> C0 := 1 * ZZ;;
> d2 := HomalgMap(HomalgMatrix("[2]", 1, 1, ZZ), C2, C1);;
> d1 := HomalgMap(HomalgMatrix("[0]", 1, 1, ZZ), C1, C0);;
> C := HomalgComplex(C0);;
> Add(C, d1);;
> Add(C, d2);;
> Display(Homology(C,1));
Z/< 2 >
However, this isn't an actual GAP group; for example running
> IsIsomorphicGroup(Homology(C,1), CyclicGroup(2));
yields an error saying it can't find a suitable method.
Is there any way of coercing the result of this computation into an actual
abelian group? If not, is there another package that will allow me to calculate
the homology of a chain complex of abelian groups, which is specified by the
(integral) matrices determining the differentials, and gives me an answer that
is a GAP group? As far as I can tell from the docs, HAP doesn't support this
method of constructing chain complexes.
Thanks,
Josh
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