Opened 7 years ago

Closed 7 years ago

Last modified 4 years ago

#13724 closed defect (fixed)

Improved support for relabelled Cartan types

Reported by: JesusTorrado Owned by: joyner
Priority: minor Milestone: sage-5.10
Component: combinatorics Keywords: CartanType relabel
Cc: tscrim Merged in: sage-5.10.beta4
Authors: Nicolas M. Thiéry, Jesús Torrado Reviewers: Travis Scrimshaw
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: #4327 Stopgaps:

Description (last modified by nthiery)

This ticket implements features that were missing for relabelled Cartan types and dual cartan types::

sage: A3 = CartanType("A3")          
sage: A3.cartan_matrix()             
[ 2 -1  0]
[-1  2 -1]
[ 0 -1  2]
sage: A3r = A3.relabel({1:2,2:3,3:1})
sage: A3r.cartan_matrix()
...
AttributeError: 'CartanType' object has no attribute 'cartan_matrix'

Here is a similar issue reported by Mark Shimozono:

    sage: ct = CartanType(["D",4,3]).classical(); ct
    ['G', 2]^* relabelled by {1: 2, 2: 1}
    sage: ct.symmetrizer()
    Traceback (most recent call last)
    ...
    AttributeError: 'CartanType' object has no attribute 'symmetrizer'

It does so by adding the appropriate abstract classes to those cartan types, depending on the abstract classes of the original cartan type.

At this occasion, it also implements the ambient space for relabelled Cartan types, and implements the dual of F4 and G2 as relabelled Cartan types. This fixes missing features for those like:

    sage: ct = CartanType(["G",2]).dual()
    sage: ct.affine()
    AttributeError: 'CartanType_with_superclass' object has no attribute 'affine'

WARNING: due to the above change, the ambient space for type G2* and F4* is now constructed by relabelling those for G2 and F4 instead of taking the dual. The end result is isomorphic but not equal to the original one. This shows up in plot pictures. Computations should run as before, except in the (hopefully unlikely case) one is writing input weights for type G2* or F4* as elements of those ambient spaces.

For safety, this ticket also turns on by default the recently added global option latex_relabel for Cartan types.

Related discussion in sage-combinat-devel: https://groups.google.com/forum/?fromgroups=#!topic/sage-combinat-devel/On-VfvxjeDk

Attachments (1)

trac_13724-cartan_type_inheritance-nt.patch (46.3 KB) - added by nthiery 7 years ago.

Download all attachments as: .zip

Change History (14)

comment:1 Changed 7 years ago by JesusTorrado

  • Description modified (diff)

comment:2 Changed 7 years ago by tscrim

  • Cc tscrim added

comment:3 Changed 7 years ago by nthiery

  • Description modified (diff)

I just took over the patch to add similar things for type_dual and finalize. More to come soon.

comment:4 Changed 7 years ago by nthiery

  • Authors changed from Jesus Torrado to Nicolas M. Thiéry, Jesus Torrado
  • Component changed from group theory to combinatorics
  • Dependencies set to #4327
  • Description modified (diff)
  • Status changed from new to needs_review
  • Summary changed from Correct inheritance for relabelled Cartan types to Improved support for relabelled Cartan types
  • Work issues Doctests fail for type_relabel.py deleted

comment:5 Changed 7 years ago by nthiery

There remains to decide whether we want to implemente G_2 dual as a relabelled type. I am exploring this in the queue.

comment:6 Changed 7 years ago by tscrim

  • Reviewers set to Travis Scrimshaw

Looks good. After folding the relabelled patch, you can set this to positive review on my behalf. Thanks.

comment:7 Changed 7 years ago by nthiery

  • Status changed from needs_review to needs_work
  • Work issues set to Handling type F4 dual by relabelling

comment:8 Changed 7 years ago by nthiery

  • Description modified (diff)
  • Status changed from needs_work to needs_review
  • Work issues Handling type F4 dual by relabelling deleted

comment:9 Changed 7 years ago by nthiery

New patch fixes a typo noticed by Travis and fixes on trivial test failure.

comment:10 Changed 7 years ago by nthiery

All long tests passed on sage.math.u-psud.fr.

comment:11 Changed 7 years ago by tscrim

  • Status changed from needs_review to positive_review

Looks good for me as well. Thanks.

Changed 7 years ago by nthiery

comment:12 Changed 7 years ago by jdemeyer

  • Merged in set to sage-5.10.beta4
  • Resolution set to fixed
  • Status changed from positive_review to closed

comment:13 Changed 4 years ago by chapoton

  • Authors changed from Nicolas M. Thiéry, Jesus Torrado to Nicolas M. Thiéry, Jesús Torrado
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