id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
26750,"Use GroupHomset_libgap for permutation groups, as well",soehms,,"At the moment the construction of group homomorphisms between groups implemented under the classes `ParentLibGAP` and `PermutationGroup_generic` (and vice versa) is not possible in sage using the method `hom`. For example, it isn't possible to construct the natural projection from symplectic groups onto the corresponding projective group although this is possible using GAP:
{{{
sage: Sp43 = Sp(4,3)
sage: PSp43 = PSp(4,3)
sage: natProj = Sp43.hom(PSp43.gens())
Traceback (most recent call last):
...
TypeError: unable to convert [(3,4)(6,7)(9,10)(12,13)(17,20)(18,21)(19,22)(23,32)(24,33)(25,34)(26,38)(27,39)(28,40)(29,35)(30,36)(31,37), (1,5,14,17,27,22,19,36,3)(2,6,32)(4,7,23,20,37,13,16,26,40)(8,24,29,30,39,10,33,11,34)(9,15,35)(12,25,38)(21,28,31)] to an element of Set of Morphisms from Symplectic Group of degree 4 over Finite Field of size 3 to The projective symplectic linear group of degree 4 over Finite Field of size 3 in Category of finite groups
}}}
The reason for this is that the constructor of the class `GroupHomset_libgap` explicitly checks both groups to be instances of `ParentLibGAP`. So an easy way to have `hom` work in such cases, as well, would be to allow `PermutationGroup_generic` additionally.
An alternative option is to shift `PermutationGroup_generic` into the `ParentLibGAP` framework. But this would cause a lot of work to have all doctests pass through. The main problem here is that the element class of PermutationGroup_generic still has `parent` as second (optional) argument (in opposite to `ParentLibGAP`).
Therefore, this ticket will follow the first option!",enhancement,closed,major,sage-8.6,group theory,fixed,"permutation group, homomorphism, libgap",tscrim sbrandhorst,,Sebastian Oehms,Simon Brandhorst,N/A,,66ceb94036041b2bf05e1f4abf91ea8bdeac862a,,#26420,