free Pre-Lie algebras #15635

fchapoton · 2014-01-05T16:07:23Z

one has shuffle algebras, one could have pre-Lie algebras, as soon as one has rooted trees (#11529)

Depends on #11529

CC: @sagetrac-sage-combinat @tscrim @darijgr

Component: combinatorics

Keywords: trees, prelie algebra

Author: Frédéric Chapoton

Branch/Commit: 6fa6d78

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/15635

The text was updated successfully, but these errors were encountered:

fchapoton · 2014-01-05T16:08:22Z

Attachment: prelie_algebra_with_several_gen_try1-fc.patch.gz

fchapoton · 2014-01-05T16:10:02Z

Dependencies: #11529

fchapoton · 2014-06-08T19:00:28Z

comment:5

First step, a git branch that does not look too bad.

New commits:

`83ea133`	`trac #15635 first rough tentative of free Pre-Lie algebras`

fchapoton · 2014-06-08T19:00:28Z

Branch: u/chapoton/15635

fchapoton · 2014-06-08T19:00:28Z

Commit: 83ea133

sagetrac-git · 2014-06-08T20:16:40Z

Changed commit from 83ea133 to a8f683d

sagetrac-git · 2014-06-08T20:16:40Z

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

`a8f683d`	`trac #15635 moving into combinat`

sagetrac-git · 2014-06-09T07:57:36Z

Changed commit from a8f683d to aff5363

sagetrac-git · 2014-06-09T07:57:36Z

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

`aff5363`	`trac #15635 little cleanup`

sagetrac-git · 2014-06-09T08:03:14Z

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

`fe3a8a3`	`trac #15635 two errors corrected`

sagetrac-git · 2014-06-09T08:03:14Z

Changed commit from aff5363 to fe3a8a3

sagetrac-git · 2014-06-09T08:10:17Z

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

`b7a7f57`	`trac #15635 correction in shortcut notation <`

sagetrac-git · 2014-06-09T08:10:17Z

Changed commit from fe3a8a3 to b7a7f57

sagetrac-git · 2015-02-16T16:41:22Z

Changed commit from b7a7f57 to 51eaee8

sagetrac-git · 2015-02-16T16:41:22Z

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

`4e771e4`	`Merge branch 'u/chapoton/15635' into 6.5.rc3`
`51eaee8`	`trac #15635 a few details`

fchapoton · 2015-02-16T17:01:58Z

Changed keywords from trees to trees, prelie algebra

fchapoton · 2015-02-16T17:01:58Z

Author: Frédéric Chapoton

fchapoton · 2015-02-16T17:01:58Z

comment:12

This should be ready, once rooted trees are ok.

sagetrac-git · 2015-04-29T06:25:58Z

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

`db2e59e`	`Merge branch 'u/chapoton/15635' into 6.7.b3`
`30f0ed6`	`trac #15635 no more coerce_impl`

sagetrac-git · 2015-04-29T06:25:58Z

Changed commit from f02c3af to 30f0ed6

sagetrac-git · 2015-05-01T09:28:58Z

Changed commit from 30f0ed6 to c42ba5a

sagetrac-git · 2015-05-01T09:28:58Z

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

`c42ba5a`	`trac #15635 removal of < shortcut, more doc`

fchapoton · 2015-05-01T09:32:50Z

comment:29

Thanks Travis for your comments. I have done something for the first three, but I do not
understand the last one.

I removed the shortcut < alltogether. Using * is almost as good.

I removed coerced_impl and it still works.

I used len(self.algebra_generators()).

tscrim · 2015-05-01T15:05:12Z

comment:30

Thanks! The last one was that line was commented out with a line above it saying about Family not returning a consistent ordering, which is not correct as I understand it.

I plan to do a full review over this weekend.

tscrim · 2015-05-03T06:33:02Z

Reviewer: Travis Scrimshaw

tscrim · 2015-05-03T06:33:02Z

comment:31

I made some review changes:

I added algebras.FreePreLie and made this the standard entry point.
I moved the main explanation doc from the module level to the class. I also made some minor tweaks to the doc overall.
I also renamed the file by removing the s as this is the standard in Sage AFAIK.
I changed the output of algebra_generators as per my previous point. The ordering should be consistent as this was something we changed awhile ago.
Subsequently, I changed around some things so that it works with infinite generating sets.
I changed the some_elements and implemented an an_element method.

If you're happy with my changes, then you can set a positive review.

PS/EDIT - It would be nice to have the trees with specified labels, as this would allow the generic implementation of an_element and removing of the _alphabet parameter (well, pushing it down a level).

New commits:

`da67955`	`Reviewer changes to free pre-Lie algebras.`
`97c3312`	`Changed the output of algebra_generators().`
`c833a23`	`Adding support for infinite indexing sets.`

tscrim · 2015-05-03T06:33:02Z

Changed work issues from coercion to none

tscrim · 2015-05-03T06:33:02Z

Changed branch from u/chapoton/15635 to u/tscrim/free_pre_lie-15635

tscrim · 2015-05-03T06:33:02Z

Changed commit from c42ba5a to c833a23

fchapoton · 2015-05-04T06:53:08Z

comment:32

Thanks a lot for your work on that ticket. I have not yet got time to look at your changes seriously.

I added algebras.FreePreLie and made this the standard entry point.

I do not quite agree. Most people would not call them algebras, because they are NOT associative

I moved the main explanation doc from the module level to the class. I also made some minor tweaks to the doc overall.

I also renamed the file by removing the s as this is the standard in Sage AFAIK.

No problem with removing s

I changed the output of algebra_generators as per my previous point. The ordering should be consistent as this was something we changed awhile ago.

Subsequently, I changed around some things so that it works with infinite generating sets.

Great !

I changed the some_elements and implemented an an_element method.

If you're happy with my changes, then you can set a positive review.

The first point is problematic in my opinion.

PS/EDIT - It would be nice to have the trees with specified labels, as this would allow the generic implementation of an_element and removing of the _alphabet parameter (well, pushing it down a level).

yes, I agree !

fchapoton · 2015-05-04T09:38:33Z

comment:33

Doc does not build, because of the removal of s was forgotten in module_list

fchapoton · 2015-05-05T08:03:00Z

comment:34

corrected the module-list

there remains the problem about the entry in the catalog.

New commits:

`616bace`	`trac #15635 fixing module list`

fchapoton · 2015-05-05T08:03:00Z

Changed commit from c833a23 to 616bace

fchapoton · 2015-05-05T08:03:00Z

Changed branch from u/tscrim/free_pre_lie-15635 to public/ticket/15635

sagetrac-git · 2015-05-05T18:24:25Z

Changed commit from 616bace to 6fa6d78

sagetrac-git · 2015-05-05T18:24:25Z

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

`6fa6d78`	`trac #15635 another s forgotten`

tscrim · 2015-05-06T02:11:53Z

comment:36

Thanks for fixing the module list (I didn't have time until this afternoon to come back to this).

Replying to @fchapoton:

I added algebras.FreePreLie and made this the standard entry point.

I do not quite agree. Most people would not call them algebras, because they are NOT associative

I understand your point, but what would people call them, non-associative algebras? The one of the current thoughts is to rename MagmaticAlgebras to Algebras and add axioms like "associative" (#15043). Also, what do you say about Jordan algebras being in the catalog?

Irregardless of nomenclature, I would say that having this as a global entry point doesn't harm anyone as the name is clear (and there's no danger of confusion), it is documented that it not associative, it makes it discoverable, and FreePreLieAlgebra in the global namespace IMO adds some clutter.

Another option would be to create a (stub) category for pre-Lie algebras, werhich might be bett for the long term, and have a method free similar to:

sage: Groups().free(names='x,y,z')
Free Group on generators {x, y, z}

(and something similar should probably be done for associative unital algebras).

fchapoton · 2015-05-06T08:47:39Z

comment:37

Jordan algebras are not in the catalog, as far as I can see (6.7.beta4)
if J is a Jordan algebra, then J in Algebras returns False

So I really think that the catalog 'algebras' should be kept for associative algebras.

Maybe this should be discussed on sage-devel or sage-combinat-devel ?

tscrim · 2015-05-06T19:13:53Z

comment:38

Replying to @fchapoton:

Jordan algebras are not in the catalog, as far as I can see (6.7.beta4)

I guess I forgot to add them...

if J is a Jordan algebra, then J in Algebras returns False

Hmm...this would definitely create an mild inconsistency in the current state with Algebras being associative and unital (at least in the global namespace; for imports, I would say the implementor should be aware of what assumptions are being made).

Maybe this should be discussed on sage-devel or sage-combinat-devel ?

This is now https://groups.google.com/forum/#!topic/sage-devel/uXN5619Fg54.

tscrim · 2015-05-09T18:16:44Z

comment:39

Given the discussion on sage-devel, would you be okay with letting this stay in the algebras catalog?

fchapoton · 2015-05-11T07:52:45Z

comment:40

Yes, ok to let it go in the algebra catalog.

tscrim · 2015-05-13T04:22:34Z

comment:41

Then positive review.

vbraun · 2015-05-13T20:11:35Z

Changed branch from public/ticket/15635 to 6fa6d78

fchapoton added this to the sage-6.1 milestone Jan 5, 2014

fchapoton added c: combinatorics labels Jan 5, 2014

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.1, sage-6.2 Jan 30, 2014

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.2, sage-6.3 May 6, 2014

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.3, sage-6.4 Aug 10, 2014

fchapoton added the s: needs review label Feb 16, 2015

fchapoton modified the milestones: sage-6.4, sage-6.5 Feb 16, 2015

tscrim added s: positive review and removed s: needs review labels May 13, 2015

vbraun removed the s: positive review label May 13, 2015

vbraun closed this as completed in 41d136b May 13, 2015

fchapoton mentioned this issue Jun 11, 2017

free dendriform algebras #23137

Closed

free Pre-Lie algebras #15635

free Pre-Lie algebras #15635

Comments

fchapoton commented Jan 5, 2014

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