Dear Edward,
> 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?
For any homalg ZZ-module M you can always use
AbelianGroup( ElementaryDivisors( M ) );
If your interest is just the isomorphism type you can use
ByASmallerPresentation( M );
Display( M );
Best wishes,
Mohamed
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