Iterator through magma elements

[stumpc5]

CC: @nthiery @sagetrac-vpilaud @saliola

Component: combinatorics

Keywords: sagedays64.5

Work Issues: document

Author: Christian Stump

Branch/Commit: u/stumpc5/iterator_through_magma_elements @ 154e2ea

Issue created by migration from https://trac.sagemath.org/ticket/18584

[stumpc5]

Branch: u/stumpc5/iterator_through_magma_elements

[stumpc5]

New commits:

a2f0f31

first implementation of the iterator through magma elements

[stumpc5]

Commit: a2f0f31

[stumpc5]

Author: Christian Stump

[stumpc5]

Work Issues: document

[stumpc5]

comment:3

Hi Nicolas and Franco -

I found this code on my computer (in my favourite sage-6.5 with parts of the combinat queue applied and the only computer where a proper chevie interface for reflection groups is running). It does not appear to be in Sage, so I wonder whether that's needed, or whether there is something better than that.

Thanks, Christian

[stumpc5]

Changed keywords from none to sagedays64.5

[stumpc5]

comment:5

It appears that finitely_generated_semigroups have a succ_generators and an {{iter}} defined. Is there a reason why that code is not in finitely_generated_magmas?

@Nicolas: should I move that code there, and delete my code for magmas?

[stumpc5]

comment:6

And do you know what that # TODO: update transitive ideal in the source of finitely_generated_semigroups mean?

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from a2f0f31 to 47efd39

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

ac813a4	some documentation
47efd39	moved the magma iterator from semigroups to magmas

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 47efd39 to c63a09f

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

c63a09f

again removed my obsolete trivial iterator

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

154e2ea

fixed typo and documentation

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from c63a09f to 154e2ea

[stumpc5]

comment:10

Okay, this breaks a few things, but I leave the ticket open until someone says whether or not the iterator should stay in semigroups or should go to finitely generated magmas...

[stumpc5]

comment:11

Is there an implementation of this iterator that not only iters through the elements, but also keeps track of the words in the generators to get to an element?

[tscrim]

comment:12

I believe there is an issue with needing associativity. Specifically, I don't believe that iterator could get (a * b) * (a * b). However, I think a default iterator could be described by using all previously encountered elements.

[nthiery]

comment:13

Hi Christian, Travis!

Replying to @tscrim:

I believe there is an issue with needing associativity. Specifically, I don't believe that iterator could get (a * b) * (a * b). However, I think a default iterator could be described by using all previously encountered elements.

Indeed this is why I had put this iterator in Semigroups.

Which raises a good question: could we implement this with the current RecursivelyEnumeratedSet? It essentially allows only for univariate functions which is presumably not enough.

Christian: what's your use case?

Cheers,

[stumpc5]

comment:14

Christian: what's your use case?

I wanted (back when writing the never-finished-coxeter-group-stuff) to use an iterator through the reflection group, keeping track of the used word along the way.

Which raises a good question: could we implement this with the current RecursivelyEnumeratedSet?

Sorry, could you point to which question you refer? The way the iterator is implemented, or implementing a flag to attach the used word to the output?

Thanks, Christian

[nthiery]

comment:15

Replying to @stumpc5:

Christian: what's your use case?

I wanted (back when writing the never-finished-coxeter-group-stuff) to use an iterator through the reflection group, keeping track of the used word along the way.

Ok; so having it on a semigroup is enough for you.

Which raises a good question: could we implement this with the current RecursivelyEnumeratedSet?

Sorry, could you point to which question you refer? The way the iterator is implemented, or implementing a flag to attach the used word to the output?

My question was about the implementation of an iterator over a finitely generated magma using only RecursivelyEnumeratedSet. But if there is no explicit need for this feature right now, we might as well not worry about it.

Cheers, Nicolas