Adding the zero element to the generating set for graph inverse semigroups with at most one vertex.

[joe-dw]

Fixing issue #1211

[joe-dw]

There are some tests that currently fail as they expect the old behavior, where
GraphInverseSemigroup(Digraph([ [] ]))
is isomorphic to the trivial group

[joe-dw]

@james-d-mitchell this now passes the standard tests on my end, AssignGeneratorVariables still works and warns the user when the generating set includes zero

[james-d-mitchell]

This'd be more compact as (a properly formatted, and working version of):

  SetGraphOfGraphInverseSemigroup(S, graph);
  inv_gens := [];
  for i in [1 .. DigraphNrVertices(graph) + DigraphNrEdges(graph)] do
    Add(inv_gens, Objectify(fam!.type, [[i], graph]));
  od;
  gens := Concatenation(inv_gens, List([1 .. DigraphNrEdges(graph)], x -> gens[x] ^ -1));
  if DigraphNrVertices(graph) < 2 then
     Add(gens, MultiplicativeZero(S));
     Add(inv_gens, MultiplicativeZero(S));
  fi;
  SetGeneratorsOfInverseSemigroup(inv_gens);
  SetGeneratorsOfSemigroup(gens);

if the order of the generators is not important, then you could conditionally add the zero to inv_gens before populating gens. I haven't checked that this actually works.

[joe-dw]

I've added it at the end as there are test cases that use the fact that, for any i less than the number of edges,

S.i = e_i

And this way it shouldn't break anything

[james-d-mitchell]

I think that makes sense

[joe-dw]

Will implement your changes and add some comments

[james-d-mitchell]

Thanks @joe-dw this looks mostly good, a little refactoring required please. Also can you please add a comment to the code indicating why these changes are being made (something like "if the number of vertices is 1 or 0, then the multiplicative zero element of a gis is not a product of any vertices or edges, and so must be added to both generating sets).