Incorrect behaviour for a monoid created by MonoidByAdjoiningIdentity

[wilfwilson]

In the GAP lib/adjoin.gd file, MonoidByAdjoiningIdentity is declared as an attribute that adjoins an identity to a semigroup (even if it already has one). Without the Semigroups package loaded, this is the following correct behaviour:

gap> R := ReesMatrixSemigroup(Group(()), [[()]]);;
gap> S := MonoidByAdjoiningIdentity(R);
gap> Size(S);
2
gap> Elements(S);
[ ONE, (1,(),1) ]

With the Semigroups package loaded, this is what we get:

gap> R := ReesMatrixSemigroup(Group(()), [[()]]);;
gap> S := MonoidByAdjoiningIdentity(R);
<commutative monoid with 1 generator>
gap> Size(S);
1
gap> Elements(S);
[ (1,(),1) ]

I've not dug into what's going on.

[wilfwilson]

Additional information. Without Semigroups package:

gap> R := ReesMatrixSemigroup(Group(()), [[()]]);
gap> S := MonoidByAdjoiningIdentity(R);
gap> GeneratorsOfSemigroup(S);
[ ONE, (1,(),1) ]

With Semigroups:

gap> R := ReesMatrixSemigroup(Group(()), [[()]]);;
gap> S := MonoidByAdjoiningIdentity(R);
gap> GeneratorsOfSemigroup(S);
[ (1,(),1) ]

[wilfwilson]

Line 280-284 in gap/semigroups/semigrp.gi:

  if CanEasilyCompareElements(gens) and not One(gens) in gens then
    SetGeneratorsOfMagma(S, Concatenation([One(gens)], gens));
  else
    SetGeneratorsOfMagma(S, AsList(gens));
  fi;

In this example, gens is basically [ (1,(),1) ], i.e. it doesn't contain ONE, and moreover, the remaining generator does not generate (using *) this adjoined identity. So really we should be adding ONE at this point too.

[wilfwilson]

@james-d-mitchell shall I just change this code block to:

if not One(gens) in gens then
  SetGeneratorsOfMagma(S, Concatenation([One(gens)], gens));
else
  SetGeneratorsOfMagma(S, AsList(gens));
fi;

?