[GAP Forum] Homalg Homology result as GAP group

[Mohamed Barakat]

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