[GAP Forum] efficient factorisation of integers in computing Abelianisation

[Jean RAIMBAULT]

Hello all,

I am currently trying to use GAP to compute the first homology of some 
large-index congruence subgroups in arithmetic Kleinian groups. Large 
primes often occur in the order of the torsion subgroup of such homology 
and this causes the computation to be stalled by the inefficiency of the 
factoring method ("FactorsInt") use in the function "AbelianInvariants".

For example a computation lasted for more than three hours (after the 
group presentation was obtained) because of the failure to factor the 
integer

105023714400084996151549919196232398687915731 = 8882788338909318083641 * 
11823282329046290928491

(the number of "RhoTrials" kept augmenting but the algorithm failed to 
terminate). On the other hand the factorisation above was almost 
immediately computed by the function "Factors" after loading the package 
"FactInt".

So I was wondering whether there is a simple way to force the function 
AbelianInvariants to use the latter method of factorisation, or a 
package with a function computing abelianisation of a group when large 
primes occur in the invariants.

Cheers,

Jean Raimbault.