Ensure Comm for group automorphisms does not trigger a coset enumeration

[fingolfin]

This used to run into a coset enumeration.

Resolves #3898
Resolves #5910

[ThomasBreuer]

Yes, this is a solution.

Besides that (something for another pull request), I think that it would be desirable that special (partial) methods for composition mappings are preferred to other methods.
In the current example, the IsInjective method for composition mappings is what one expects to be checked, but it has a lower rank than the method for group homomorphisms.

[hulpke]

Yes, this fixes the problem at hand. But doesn't it push the coset enumeration to the bit when the homomorphism gets evaluated on elements?

[fingolfin]

Evaluation on elements seems to work fine:

gap> hom(x1);
(x2*x3^-1)^4*x1*(x3^-1*x2)^4
gap> hom(x2);
(x2*x3^-1)^8*x2

[fingolfin]

That said, this does indeed "only" solve part of the issue; one may argue it "papers over the real issue" -- I guess that's why nobody applied this fix despite it being suggested 5 years ago... Since nobody fixed the "real" issue in 5 years, I thought it is a bit silly to refuse to apply the immediate fix. We can still track the "real" issue afterwards if we want to, and perhaps one day someone will address it :-)

[fingolfin]

I've revised this now to instead uprank IsInjective and other methods specific for IsCompositionMappingRep. I've also extended and refined the test case a bit.

[fingolfin]

@ThomasBreuer does this look reasonable to you?

[ThomasBreuer]

Yes, this looks reasonable.

I think that in general, an available method that is installed for composition mappings should be called first for a composition mapping, because delegating to the maps which define the composition is the most natural strategy --other methods have less information. In particular, in situations where the defining maps (or perhaps all of them except one) store already that they are bijective, the question ends up in the right place.

If this change should cause problems in certain situations then I expect that a solution will be not to construct a composition mapping but something better in that situation.

The same strategy should be used also for computing images and preimages. As far as I see, this is not a problem because we have essentially the methods for the different representations of mappings, and these methods are not competing for applicability.

[fingolfin]

Backported to stable-4.14 in 6611874