Cubic Braid Groups #27302

soehms · 2019-02-16T08:26:09Z

This ticket implements a new class to work with factor groups of the Artin braid groups having order three on the braid generators.

CC: @tscrim

Component: group theory

Keywords: braid groups, complex reflection groups

Author: Sebastian Oehms

Branch/Commit: 9fdafdd

Reviewer: Travis Scrimshaw, Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/27302

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

soehms · 2019-02-16T08:29:46Z

Branch: u/soehms/cubic_braid_group_27302

soehms · 2019-02-16T08:31:27Z

Commit: 756a7bb

soehms · 2019-02-16T08:31:27Z

New commits:

`0133335`	`implement subgroup / ambient methods for MatrixGroup_base`
`747bc16`	`removed unused keyword`
`d36aeb8`	`Merge branch 'u/soehms/matrix_groups_subgroups-25894' of git://trac.sagemath.org/sage into cubic_braid_group`
`756a7bb`	`27302: initial version`

sagetrac-git · 2019-03-09T17:24:34Z

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`80aabe6`	`25894: implement reviewers suggestions`
`1997ad7`	`25894: missing long-doctest fixed, as well`
`49a04af`	`25894: restore lost changes`
`c7cb49f`	`Merge branch 'u/soehms/matrix_groups_subgroups-25894' of git://trac.sagemath.org/sage into matrix_group_subgroups_25894`
`0aec3cc`	`change representation strings according to reviewers suggestion`
`455bd17`	`fixing further doctests`
`c1280b9`	`25894: corrections on doctest layout`
`ea70462`	`Merge commit 'c1280b9fbd954c5f43be122cafd4606872ed353c' of git://trac.sagemath.org/sage into cubic_braid_group_27302`
`b29a9fc`	`Merge branch 'u/soehms/cubic_braid_group_27302' of git://trac.sagemath.org/sage into cubic_braid_group_27302`
`623e14b`	`PEP8 adaptions`

sagetrac-git · 2019-03-09T17:24:34Z

Changed commit from 756a7bb to 623e14b

embray · 2019-03-25T10:56:15Z

comment:4

Ticket retargeted after milestone closed (if you don't believe this ticket is appropriate for the Sage 8.8 release please retarget manually)

sagetrac-git · 2019-03-29T23:43:01Z

Changed commit from 623e14b to 6b638b4

sagetrac-git · 2019-03-29T23:43:01Z

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

`6b638b4`	`Merge branch 'u/soehms/cubic_braid_group_27302' of git://trac.sagemath.org/sage into cubic_braid_group_27302`

soehms · 2019-03-29T23:45:46Z

comment:6

Fixed merge conflict!

soehms · 2019-03-29T23:45:46Z

Author: Sebastian Oehms

sagetrac-git · 2019-03-30T07:31:00Z

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

`76a845e`	`27302: fixed doctests`

sagetrac-git · 2019-03-30T07:31:00Z

Changed commit from 6b638b4 to 76a845e

sagetrac-git · 2019-03-30T17:03:35Z

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

`3402ba7`	`27302: python3 fixes`

sagetrac-git · 2019-03-30T17:03:35Z

Changed commit from 76a845e to 3402ba7

sagetrac-git · 2019-04-01T18:05:50Z

Changed commit from 3402ba7 to 4b96740

sagetrac-git · 2019-04-01T18:05:50Z

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

`4b96740`	`27302: further corrections according to patchbot hints`

fchapoton · 2019-04-01T18:26:09Z

comment:10

Some random remarks:

typo "refelection"

typo "Vancover"

burau >>> Burau

typo "availlable"

typo "as_permutatopn_group"

Use "Construct" and "Return" in the first lines of doc, not "Constructs" and "Returns"

"len(root_list) == 0" could be "not(root_list)" which is faster

+    TESTS:
+
+        sage: C3 = CubicBraidGroup(3)

is missing a double ::

range(0, n-3) >>> range(n - 3)

In

+            if m % 2  == 0:
+                mhalf = m/2
+            else:
+                mhalf = (m-1)/2

rather use exact division //

sagetrac-git · 2019-04-02T19:03:32Z

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

`1164156`	`27302: typo and style fixes`

sagetrac-git · 2019-04-02T19:03:32Z

Changed commit from 4b96740 to 1164156

soehms · 2019-04-02T19:05:18Z

comment:12

Replying to @fchapoton:

Some random remarks:
...

Thanks for having a look at this!

fchapoton · 2019-04-02T19:08:54Z

comment:13

two more:

typo: hermitain

typo: performace

sagetrac-git · 2019-04-04T20:33:51Z

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

`46a0134`	`27302: spell-check performed`

sagetrac-git · 2019-04-04T20:33:51Z

Changed commit from 1164156 to 46a0134

sagetrac-git · 2019-08-11T08:46:15Z

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

`8375891`	`Merge branch 'u/soehms/cubic_braid_group_27302' of git://trac.sagemath.org/sage into cubic_braid_groups_27302`
`fe4adff`	`27302: comparison for larger groups fixed`

sagetrac-git · 2019-08-11T08:46:15Z

Changed commit from 24c1d06 to fe4adff

soehms · 2019-08-11T08:51:03Z

comment:27

While developing a class for cubic Hecke algebras I observed that comparison for cubic braids on more than 5 strands didn't terminate (since the implementation from the finitely presented groups was used). So, I replaced that comparison for the groups on more than 5 strands by comparison of the corresponding braids resp. the Burau-matrix of the cubic braid.

The default setting for the characteristic of the Burau-matrix was implemented in the as_matrix_group method, which is not the right place. I fixed that, as well.

fchapoton · 2019-08-24T19:33:00Z

comment:28

patchbot's pyflakes-plugin reports an unused import

sagetrac-git · 2019-09-17T18:58:17Z

Changed commit from fe4adff to 4ea9263

sagetrac-git · 2019-09-17T18:58:17Z

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

`4ea9263`	`Merge branch 'u/soehms/cubic_braid_group_27302' of git://trac.sagemath.org/sage into cubic_braid_group_27302`

sagetrac-git · 2019-09-17T18:59:48Z

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

`6663fa7`	27302: add methods `__init__`, `__hash__`,and `_matrix_` to the element class

sagetrac-git · 2019-09-17T18:59:48Z

Changed commit from 4ea9263 to 6663fa7

soehms · 2019-09-17T19:02:52Z

comment:31

I do the following:

fix pyflakes
add method __hash__ to the element class, since the inherited version is not well defined
add method _matrix_ to the element class as an alternative to the default of burau_matrix with better performance properties.
add method __init__ to the element class to perform a reduction on the Tietze-tuple.

sagetrac-git · 2019-10-19T07:52:17Z

Changed commit from 6663fa7 to db5b7a7

sagetrac-git · 2019-10-19T07:52:17Z

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

`2de6f71`	`Merge branch 'u/soehms/cubic_braid_group_27302' of git://trac.sagemath.org/sage into cubic_braid_group_27302`
`db5b7a7`	`27302: some cleaning in burau_matrix`

fchapoton · 2019-11-08T08:06:10Z

comment:34

now the branch is red

fchapoton · 2019-11-08T08:06:10Z

Changed dependencies from #25894 to none

sagetrac-git · 2019-11-09T08:32:35Z

Changed commit from db5b7a7 to 9fdafdd

sagetrac-git · 2019-11-09T08:32:35Z

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

`9fdafdd`	`Merge branch 'u/soehms/cubic_braid_group_27302' of git://trac.sagemath.org/sage into cubic_braid_group_27302`

soehms · 2019-11-09T08:37:05Z

comment:36

Merge error in references index.rst fixed

fchapoton · 2019-11-13T08:06:12Z

comment:37

ok, let it be. One can keep further enhancement for later tickets.

fchapoton · 2019-11-13T08:06:12Z

Reviewer: Travis Scrimshaw, Frédéric Chapoton

soehms · 2019-11-13T20:39:02Z

comment:38

Thanks!

vbraun · 2019-11-16T20:15:50Z

Changed branch from u/soehms/cubic_braid_group_27302 to 9fdafdd

soehms added this to the sage-8.7 milestone Feb 16, 2019

soehms added c: group theory labels Feb 16, 2019

soehms added the s: needs review label Feb 16, 2019

embray modified the milestones: sage-8.7, sage-8.8 Mar 25, 2019

soehms modified the milestones: sage-8.9, sage-9.0 Oct 19, 2019

fchapoton added s: needs work and removed s: needs review labels Nov 8, 2019

soehms added s: needs review and removed s: needs work labels Nov 9, 2019

fchapoton added s: positive review and removed s: needs review labels Nov 13, 2019

vbraun removed the s: positive review label Nov 16, 2019

vbraun closed this as completed in 133435b Nov 16, 2019

Cubic Braid Groups #27302

Cubic Braid Groups #27302

Comments

soehms commented Feb 16, 2019

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