Wrong degree for trivial transformation monoids

[james-d-mitchell]

Originally reported by: Attila Egri-Nagy (Bitbucket: egri-nagy, GitHub: egri-nagy)

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#!python

gap> DegreeOfTransformationSemigroup(FullTransformationSemigroup(1));
0
gap> S := Semigroup(Transformation([1,2,3]));
<trivial transformation group>
gap> AsList(S);
[ IdentityTransformation ]
gap> DegreeOfTransformationSemigroup(S);
0

Workaround: setting the degree for the semigroup explicitly by SetDegreeOfTransformationSemigroup

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• Bitbucket: https://bitbucket.org/james-d-mitchell/semigroups/issue/100

[james-d-mitchell]

Original comment by James Mitchell (Bitbucket: james-d-mitchell, GitHub: james-d-mitchell):

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Removing milestone: 2.1 (automated comment)

[james-d-mitchell]

Original comment by James Mitchell (Bitbucket: james-d-mitchell, GitHub: james-d-mitchell):

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Just for keeping track, I'm marking this as invalid.

[james-d-mitchell]

Original comment by Attila Egri-Nagy (Bitbucket: egri-nagy, GitHub: egri-nagy):

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the problem is elsewhere

[james-d-mitchell]

Original comment by Attila Egri-Nagy (Bitbucket: egri-nagy, GitHub: egri-nagy):

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The problem originated from here:

#!python

gap> GroupOfUnits(FullTransformationSemigroup(1));
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `DegreeOfTransformationCollection' on 1 arguments called from
DegreeOfTransformationCollection( GeneratorsOfGroup( s ) ) called from
DegreeOfTransformationSemigroup( S ) called from
LambdaFunc( s ) called from
GradedLambdaOrb( s, f, false ) called from
GreensRClassOfElementNC( s, MultiplicativeNeutralElement( s ) ) called from
...  at line 1 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> 

I have no problem with the definition (except that difficult to forget the old habits), but it seems that that some code also thinks in terms of the old fixed size families of transformations. So I will report it for GroupOfUnits.

[james-d-mitchell]

Original comment by James Mitchell (Bitbucket: james-d-mitchell, GitHub: james-d-mitchell):

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I'm not sure what you think is wrong here? This behaviour is consistent with what I would expect and with the documentation: the degree of transformation semigroup is the maximum of the degrees of its elements. The degree of a transformation f is the largest value such that n^f<>n or i^f=n for some i<>n. The degree is an invariant of the transformation, i.e. since IdentityTransformation=Transformation([1,2,3]) the degrees of the lefthand side and the righthand side are equal (to 0). Hence the semigroup generated by the identity transformation (however you have defined it) is 0.

You must not use SetDegreeOfTransformationSemigroup in this way, this could cause incorrect results or even cause GAP to crash.