XClassReps

[ChristopherRussell]

gap> S := SymmetricInverseMonoid(4);;
gap> H := HClass(S, PartialPerm([1,2,3],[1,2,3]));;
gap> R := RClass(S, H);
<Green's R-class: <Green's H-class: <identity partial perm on [ 1, 2, 3 ]>>>
gap> HClassReps(R);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
The 1st argument is 'fail' which might point to an earlier problem
Error, no 1st choice method found for `GreensHClasses' on 1 arguments at /Users/crussell/gap/lib/methsel2.g:241 called from
GreensHClasses( CanonicalGreensClass( x ) ) at /Users/crussell/gap/lib/semirel.gi:721 called from
GreensHClasses( C ) at /Users/crussell/gap/pkg/semigroups/gap/greens/gree.gi:380 called from
<function "unknown">( <arguments> )
 called from read-eval loop at *stdin*:361
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue

[wilfwilson]

According to the documentation, implicitly the line gap> R := RClass(S, H); should not have worked:

Note that GreensXClassOfElement and XClass are synonyms and have identical output. The shorter command is provided for the sake of convenience.

Looking at the documentation, the correct command is gap> R := RClassOfHClass(H); or gap> R := RClass(H);, which gives:

gap> S := SymmetricInverseMonoid(4);;
gap> H := HClass(S, PartialPerm([1,2,3],[1,2,3]));;
gap> R := RClassOfHClass(H);
<Green's R-class: <identity partial perm on [ 1, 2, 3 ]>>
gap> HClassReps(R);
[ <identity partial perm on [ 1, 2, 3 ]>, [1,2,3,4], [2,4](1,3), [3,2,1,4] ]

Either we actually want to be able to do RClass(S, H), and so the code should be updated to allow it, or the code should be updated so that RClass(S, H) gives 'no method found'. The documentation should be updated in either case, to emphasise the behaviour.

[james-d-mitchell]

RClass(S, H) should definitely not work, this is the bug.

[james-d-mitchell]

I think I fixed this in GAP PR 1771. This prevents RClass(S, H) from working and hence prevents the other errors in this issue.