# Weird behaviour of SemigroupIdeal (?)

Issue #127 resolved
Markus Pfeiffer
created an issue

I just tried creating some ideals of matrix semigroups like so:

```gap> S := RandomMatrixSemigroup(GF(4), 2, 4, [1,2]);
<monoid of 4x4 s-matrices over GF(2^2) with 2 generators>
gap> Size(S);
21
gap> I := SemigroupIdeal(S, Idempotents(S));
<ideal of semigroup of 4x4 s-matrices over GF(2^2) with 8 generators>
gap> Size(I);
57
```

This strikes me as rather odd, so I thought it's a problem with the matrix code, but the transformations code behaves the same:

```gap> T := AsTransformationSemigroup(S);
<transformation monoid on 256 pts with 2 generators>
gap> Size(T);
21
gap> I := SemigroupIdeal(T, Idempotents(T));
<regular transformation semigroup ideal on 256 pts with 8 generators>
gap> Size(I);
57
```

The generators for the matrix semigroup are the following:

```[ NewSMatrix(IsPlistSMatrixRep, GF(2^2), 4, [ [ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ], [ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ] ]), NewSMatrix(IsPlistSMatrixRep, GF(2^2), 4,
[ [ Z(2^2), Z(2)^0, Z(2^2), Z(2)^0 ], [ Z(2^2)^2, Z(2^2), Z(2^2)^2, Z(2^2) ],
[ Z(2)^0, Z(2^2)^2, Z(2)^0, Z(2^2)^2 ], [ Z(2)^0, Z(2^2)^2, Z(2)^0, Z(2^2)^2 ] ]),
NewSMatrix(IsPlistSMatrixRep, GF(2^2), 4, [ [ 0*Z(2), Z(2^2)^2, 0*Z(2), Z(2)^0 ],
[ Z(2^2)^2, Z(2)^0, 0*Z(2), Z(2)^0 ], [ Z(2^2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ Z(2^2)^2, Z(2)^0, 0*Z(2), Z(2)^0 ] ]) ]
```

Sorry if this is a known issue on the main branch, I didn't dare merging yet.

1. repo owner

This exists in other branches too, I wasn't aware of it. Something is wrong in the main algorithm for regular acting semigroup ideals. I will investigate and update.

2. repo owner

I fixed it, and I grafted the changes onto the tip of matrix-semigroups (so you don't have to merge to get it). Please let me know if something still doesn't work.

3. repo owner
• removed milestone

Removing milestone: 2.5 (automated comment)