Collection of miscellaneous small changes ("cleanup")

[wilfwilson]

This is a collection of several 'random' cleanup-style commits that I've made over the last year, but that have never made their way into another PR. I decided to just collect them into one PR here.

This is split into 7 commits with descriptive commit messages to help with reviewing.

[wilfwilson]

Note: if (when) this PR is merged, #4050 will need to be rebased and updated to change this line to

Suggested change

	<partial perm on 1 pts with degree 1, codegree 2>
	<partial perm on 1 pt with degree 1, codegree 2>

[fingolfin]

Perhaps also like this?

Suggested change

	ForAll(GeneratorsOfGroup(G),i->SignPerm(i)=1) and PermgpContainsAn(G)=true);
	ForAll(GeneratorsOfGroup(G),i->SignPerm(i)=1) and PermgpContainsAn(G));

[wilfwilson]

PermgpContainsAn can return either true or false or the return value of PermNatAnTestDetect which can be a set of points, so I can't make that change (as much as I'd like to).

[fingolfin]

Why is this unnecessary?

[wilfwilson]

Perhaps I misunderstand how things work.

Since IsFullTransformationSemigroup is only declared for IsSemigroup, that means anything that could know it satisfies IsFullTransformationSemigroup already knows that it is a semigroup.

Is perhaps the idea that: this InstallTrueMethod is useful because perhaps someone in a package could (for example) do DeclareProperty("IsFullTransformationSemigroup", IsMagma); and then install methods for IsMagma (which would have to somehow test the magma for associativity, but perhaps not directly, and this could therefore mean that IsFullTransformationSemigroup gets set but not IsSemigroup)?

But actually it seems that any magma of transformations already knows that it is associative, and therefore a semigroup:

gap> S := Magma(GeneratorsOfMagma(FullTransformationSemigroup(3)));;
gap> HasIsSemigroup(S);
true

I can't think of any use for this true method, but perhaps I am not imaginative enough 🙂

I notice that there are similar true methods for natural symmetric and alternating groups (e.g. in lib/gpprmsya.gd):

InstallTrueMethod( IsPermGroup, IsNaturalSymmetricGroup );

But things seem to work differently for groups:

gap> G := Semigroup(GeneratorsOfMagma(SymmetricGroup(4)));;
gap> IsGroup(G);
false
gap> SetIsNaturalSymmetricGroup(G, true);
gap> IsGroup(G);
true

[fingolfin]

There is no automatic implication and there cannot be, as indeed GAP cannot predict the future and so can't know whether that property might in the future also be applicable to, say, algebras or strings or graphs or... Sure, as a human you know this is unlikely because of the name, but GAP does not known this (and anyway.

Somewhat related: issue #2336

[wilfwilson]

(and anyway.

Were you going to add something?

Anyway, I'll be happy to remove I have happily removed this commit. I'll read #2336 too.