DirectProduct incorrectly adding identity

[mtorpey]

DirectProduct is not behaving correctly. It appears to be appending the identity transformation when it shouldn't. Consider the following example (found by @ffloresbrito):

gap> S := Semigroup([Transformation([1, 2, 3, 3, 3])]);;
gap> CC := Semigroup([Transformation([2, 1])]);;
gap> Size(S); Size(CC);
1
2
gap> DP := DirectProduct(S, CC);;
gap> Elements(DP);
[ Transformation( [ 1, 2, 3, 3, 3 ] ), 
  Transformation( [ 1, 2, 3, 3, 3, 7, 6 ] ), IdentityTransformation, 
  Transformation( [ 1, 2, 3, 4, 5, 7, 6 ] ) ]
gap> Size(DP);
2

As you can see, the function seems to be treating S as though it contains IdentityTransformation, which it doesn't. Hence two extra elements are ending up in the direct product, even though the size is being calculated correctly.

While I was at it, I noticed that DirectProduct for semigroups is not documented, meaning that the only manual entry for it is in the GAP manual, where it just talks about groups. This should be rectified as well (I'll add it to Issue #298).

[james-d-mitchell]

Hmm, something is for sure not right here...

[ChrisJefferson]

What was the error?

[james-d-mitchell]

Don't know but a semigroup of size 2 shouldn't have 4 elements

[james-d-mitchell]

I've fixed this in PR #343

[mtorpey]

Merged and fixed!