New and better methods for Natural Alternating and Symmetric Groups

[stevelinton]

as already existed for Natural Symmetric Groups.

There might be more similar ommissions so don't merge yet.

[frankluebeck]

Looks good to me so far.

[stevelinton]

Looking at the code for natural symmetric and alternating groups more closely, it was a bit of a mess. There was a StabilizerOp method that could never be called, for instance. The latest version of this includes effective StabilizerOp methods for natural Sn for some basic actions. Still WIP.

[stevelinton]

As far as I know this is now good to merge.

[ChrisJefferson]

Only found one small issue:

gap> g := Group([()]);;
gap> IsAlternatingGroup(g);
true
gap> Size(g);
1/2

[olexandr-konovalov]

Thanks - let's merge this. I'd only update the title of this PR to reflect that is also contains some further improvements,not only Size and Random.

[olexandr-konovalov]

@stevelinton while loading the library, SYMGP_STABILIZER causes "unbound global variable" warning for gens and size. This does not crash testinstall, but but hits the test of Tutorial examples and seemingly teststandard. Shall I just add them to local ?

[stevelinton]

Yes, please.

[olexandr-konovalov]

Finally, something less trivial: this input, based on the doc/tut/group.xml leads to an error:

s8 := Group( (1,2), (1,2,3,4,5,6,7,8) );
a8 := DerivedSubgroup( s8 );
IsNaturalAlternatingGroup(a8);
pairs := Tuples( [1..8], 2 );;
IsTransitive( a8, pairs, OnPairs );
orbs := Orbits( a8, pairs, OnPairs );; Length( orbs );
u56 := Stabilizer( a8, orbs[2][1], OnPairs );; Index( a8, u56 );

and the error is

gap> u56 := Stabilizer( a8, orbs[2][1], OnPairs );; Index( a8, u56 );
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `AlternatingSubgroup' on 1 arguments called from
AlternatingSubgroup( CallFuncList( SYMGP_STABILIZER, Concatenation( [ SymmetricParentGroup( g ) ], arg 
     ) ) ) at /Users/alexk/GITREPS/gap/lib/gpprmsya.gi:1007 called from
orbish( G, pnt, gens, acts, act ) at /Users/alexk/GITREPS/gap/lib/oprt.gd:863 called from
CallFuncList( StabilizerFunc, arg ) at /Users/alexk/GITREPS/gap/lib/oprt.gi:2829 called from
<function "Stabilizer">( <arguments> )
 called from read-eval loop at line 30 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> 

If one removes the call of IsNaturalAlternatingGroup(a8); then everything works.

[stevelinton]

Fixed now in a commit on the master branch.

[olexandr-konovalov]

Thanks - 4485002 fixed all.