Using ranges for seeds in Orbits

[rfmorse]

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Observed behaviour

gap> act := function(omega,g) return PowerModInt(omega,Int(g),15); end;
gap> ugrp := Units(ZmodnZ(Phi(15)));
gap> orbs := Orbits(ugrp,[1..5],act);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `[]:=' on 3 arguments
The 2nd argument is 'fail' which might point to an earlier problem
 at /Users/morse/gap-4.12.0/lib/methsel2.g:249 called from
PositionCanonical( D, o ) at /Users/morse/gap-4.12.0/lib/oprt.gi:1694 called from
op( G, D, gens, gens, act ) at /Users/morse/gap-4.12.0/lib/oprt.gd:654 called from
<function "Orbits for a group, a domain or list, and a function">( <arguments> )
 called from read-eval loop at *stdin*:3
type 'quit;' to quit to outer loop

Expected behaviour

#Same as

gap> orbs := Orbits(ugrp,[1,2,3,4,5],act);
[ [ 1 ], [ 2, 8 ], [ 3, 12 ], [ 4 ], [ 5 ] ]

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[fingolfin]

Thanks for the report!

In this case, the Orbits method from lib/oprt.gi line 1665 is invoked, which starts like this:

InstallMethod( Orbits, "for arbitrary domains", true, OrbitsishReq, 0,
function( G, D, gens, acts, act )

The info string is revealing: it suggests D is a domain (in the GAP sense) which is counter to what the documentation says (we have OrbitsDomain for this case). Rather, D should be called seeds to match the documentation.

This Orbits method then has a special case for when D / seeds is a plist. If it is not, it kinda assumed that D is a domain (i.e., closed under the action, i.e., a union of orbits).

Anyway, should be fixed by PR #5057

[rfmorse]

I was thinking of how to make the example simpler and made "act" the trivial action. However in this case the error does not occur.

gap> act := function(omega,g) return omega; end;
gap> orbs := Orbits(ugrp,[1..5],act);
[ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ] ]

gap> act := function(omega,g) return PowerModInt(omega,Int(g),15); end;
gap> orbs := Orbits(ugrp,[1..5],act);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound . . .

Surprised that the action definition made a difference.