Install specific IsIdempotentGenerated methods for RMS/RZMS #325
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wilfwilson
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mtorpey
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gap/attributes/attr.gi
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| od; | ||
| od; | ||
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| out := RegularSemigroup(gens); |
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I think you decided to stop using this - certainly you replaced it in the RMS case. Is this safe?
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I changed it over.
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I'm happy. Will merge once the tests pass. |
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For a regular Rees (0-)matrix semigroup over a group, it's easy to say write down a fairly small generating set for the idempotent generated subsemigroup. For Rees matrix semigroups, I think the method gives a minimal generating set (it's certainly irredundant). For Rees 0-matrix semigroups, the code now makes use of my recent addition to Digraphs called
UndirectedSpanningForest. A spanning forest of theRZMSDigraphcorresponds to a generating set for the idempotent generated subsemigroup. Whilst this certainly does not return a irredundant generating set in general, it has the potential to return a much smaller generating set that was obtained previously.Additionally, this PR allows me to address a long-standing TODO from my maximal subsemigroups code. At a certain part in those algorithms, to specify the generating set of a maximal subsemigroup, we require the set of idempotents of a particular Rees (0-)matrix semigroup. However, we only actually require a generating set for these idempotents. Since there is a special method installed for this now, we may as well use this.