Improvements to root systems #15384

tscrim · 2013-11-08T20:46:03Z

Implement various things for affine root systems:

The symmetric form ( | ).
Methods for checking the short/long/imaginary roots.
Modelling the positive roots roots in affine types.
Basic untwisted types (so type A_2n⁽²⁾ would give A_2n).
(Dual) Coxeter numbers for finite types.

CC: @sagetrac-sage-combinat @anneschilling @nthiery @darijgr @bsalisbury1 @dwbump

Component: combinatorics

Keywords: root systems, days54

Author: Travis Scrimshaw

Branch/Commit: 7285940

Reviewer: Daniel Bump

Issue created by migration from https://trac.sagemath.org/ticket/15384

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

tscrim · 2013-11-08T20:50:05Z

New commits:

`[0fa598a](https://github.com/sagemath/sagetrac-mirror/commit/0fa598a)`	`imported patch root_system_data-ts.patch`
`[870837f](https://github.com/sagemath/sagetrac-mirror/commit/870837f)`	`imported patch root_systems-ts.patch`

tscrim · 2013-11-08T20:50:05Z

Commit: 0fa598a

tscrim · 2013-11-08T20:50:05Z

Branch: public/combinat/root_systems/improvements-15384

tscrim · 2013-11-09T00:12:25Z

Changed keywords from root systems to root systems, days54

sagetrac-git · 2013-11-15T03:45:48Z

Changed commit from 0fa598a to e40f892

sagetrac-git · 2013-11-15T03:45:48Z

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

`[e40f892](https://github.com/sagemath/sagetrac-mirror/commit/e40f892)`	`Changed horizontal to basic_untwisted.`
`[930782b](https://github.com/sagemath/sagetrac-mirror/commit/930782b)`	`Fixed indentation error.`
`[f87789d](https://github.com/sagemath/sagetrac-mirror/commit/f87789d)`	`Merge branch 'master' into public/combinat/root_systems/improvements-15384`

sagetrac-git · 2013-11-18T07:27:31Z

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

`[b4c7865](https://github.com/sagemath/sagetrac-mirror/commit/b4c7865)`	`Merge branch 'master' into public/combinat/root_systems/improvements-15384`

sagetrac-git · 2013-11-18T07:27:31Z

Changed commit from e40f892 to b4c7865

sagetrac-git · 2014-03-04T18:14:28Z

Changed commit from b4c7865 to dd976c7

sagetrac-git · 2014-03-04T18:14:28Z

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

`6100a4b`	`Merge branch 'public/combinat/root_systems/improvements-15384' of trac.sagemath.org:sage into public/combinat/root_systems/improvements-15384`
`a5a6b1c`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`f802ae1`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`d83982c`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`ecf8f76`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`c52545c`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`14c367e`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`fe68bf6`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`896e682`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`dd976c7`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`

sagetrac-git · 2014-03-13T05:21:56Z

Changed commit from dd976c7 to 2c7f793

sagetrac-git · 2014-03-13T05:21:56Z

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

`2c7f793`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`

sagetrac-git · 2014-04-15T02:20:36Z

Changed commit from 2c7f793 to 122ca6e

sagetrac-git · 2014-04-15T02:20:36Z

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

`ea1641f`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`054b37c`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`30de9e8`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`122ca6e`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`

sagetrac-git · 2014-05-06T21:26:02Z

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

`87cf9ed`	`Merge branch 'public/combinat/root_systems/improvements-15384' of trac.sagemath.org:sage into public/combinat/root_systems/improvements-15384`
`c5f9747`	`Added placeholder for symmetric_form in WLR.`
`64ac7a5`	`Fixed doctests.`

sagetrac-git · 2014-05-06T21:26:02Z

Changed commit from 122ca6e to 64ac7a5

dwbump · 2014-05-06T23:40:43Z

Reviewer: bump

sagetrac-git · 2014-05-07T00:30:09Z

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

`1817877`	`Almost there.`

sagetrac-git · 2014-05-07T00:30:09Z

Changed commit from 64ac7a5 to 1817877

sagetrac-git · 2014-05-07T03:57:13Z

Changed commit from 1817877 to 18fd094

sagetrac-git · 2014-05-07T03:57:13Z

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

`18fd094`	`Fixed affine weight lattice symmetric form.`

sagetrac-git · 2014-05-10T16:56:24Z

Changed commit from eab1afe to 66f5674

tscrim · 2014-05-10T16:58:00Z

comment:27

That was an error. Fixed now.

dwbump · 2014-05-10T19:03:36Z

comment:28

What about this?

sage: RootSystem(['D',4,2]).root_lattice().positive_roots()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-11-ea364fc7aada> in <module>()
----> 1 RootSystem(['D',Integer(4),Integer(2)]).root_lattice().positive_roots()

-snip -

AttributeError: 'NoneType' object has no attribute 'dual'

BTW Sage reports this root system as Root lattice of the Root system of type ['C', 3, 1]^*

If I have my facts straight Macdonald introduced a classification of affine root systems in his
paper "Affine root systems and the Dedekind eta function" Inventiones 1972 but
Kac didn't follow Macdonald. He introduced his own classification. So we are
entering root systems in Kac' notation and they are getting converted automatically
to Macdonald's notation. Of course that policy was not introduced by this patch but
I mention that I've personally found it a little confusing.

sagetrac-git · 2014-05-10T22:43:04Z

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

`e17ce53`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`7e83910`	`Fixes for other twisted root systems.`

sagetrac-git · 2014-05-10T22:43:04Z

Changed commit from 66f5674 to 7e83910

tscrim · 2014-05-10T22:46:27Z

comment:30

Another (stupid) error on my part. Fixed.

Also if you want to display in Kac's notation, you can do the following (it's somewhat hidden at the bottom of CatanType?):

sage: CartanType.global_options(notation='Kac')
sage: CartanType(['D',4,2])
['D', 4, 2]

sagetrac-git · 2014-05-21T00:26:08Z

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

`c91754d`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`82c6257`	`Fixed doctest.`
`1ffb4bb`	`Fixed doctest and for the weight lattice.`

sagetrac-git · 2014-05-21T00:26:08Z

Changed commit from 7e83910 to 1ffb4bb

dwbump · 2014-05-23T18:45:33Z

comment:32

The following returns an error:

sage: sr=RootSystem(['A',6,2]).weight_lattice().simple_roots()
sage: sr[0].symmetric_form(sr[1])
...
TypeError: no conversion of this rational to integer

There is no error if we use the root_lattice.

sagetrac-git · 2014-05-26T02:58:00Z

Changed commit from 1ffb4bb to bccea25

sagetrac-git · 2014-05-26T02:58:00Z

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

`bccea25`	`Worked around a minor coercion issue and added doctests.`

tscrim · 2014-05-26T03:06:20Z

comment:34

Hey Dan,

I've fixed the issue; the matrix stack() command doesn't coerce (well, it's more of I've worked around it and is now #16399). I've added some more doctests about this. I'll merge in the latest beta later tonight.

sagetrac-git · 2014-05-26T04:07:03Z

Changed commit from bccea25 to f4cee52

sagetrac-git · 2014-05-26T04:07:03Z

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

`f4cee52`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`

dwbump · 2014-05-29T02:09:01Z

Changed reviewer from Dan Bump to Daniel Bump

dwbump · 2014-05-29T02:09:01Z

comment:36

This patch implements some important things from Chapter 6 of Kac' book for both twisted and untwisted affine Lie algebras, as methods of the root_lattice_realization or the weight_lattice_realization. These include a method of enumerating the positive roots (both real and imaginary), the invariant bilinear form, and a few other things. I tested with Kac' book in front of me, and all the problems I found have been addressed.

tscrim · 2014-05-29T05:47:08Z

comment:37

Thank you for doing the review Dan.

vbraun · 2014-05-29T14:52:53Z

comment:38

Doctests fail

sagetrac-git · 2014-05-29T16:48:12Z

Changed commit from f4cee52 to 7285940

sagetrac-git · 2014-05-29T16:48:12Z

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

`7285940`	`Fixed bad merging in simple_roots_tilde.`

tscrim · 2014-05-29T16:50:10Z

comment:40

Bad merging on my part; ended up overwriting simple_roots_tilde().

vbraun · 2014-05-30T11:35:42Z

Changed branch from public/combinat/root_systems/improvements-15384 to 7285940

tscrim added this to the sage-6.1 milestone Nov 8, 2013

tscrim added c: combinatorics labels Nov 8, 2013

tscrim assigned sagetrac-sage-combinat Nov 8, 2013

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

dwbump mannequin added s: positive review and removed s: needs review labels May 29, 2014

vbraun added s: needs work and removed s: positive review labels May 29, 2014

tscrim added s: positive review and removed s: needs work labels May 29, 2014

vbraun removed the s: positive review label May 30, 2014

vbraun closed this as completed in 0eec83c May 30, 2014

Improvements to root systems #15384

Improvements to root systems #15384

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