implement ascii art output for Dynkin diagrams

[aghitza]

Dan Bump requested this in his Sage Days 14 talk: have ascii art output a la LiE for Dynkin diagrams (see interfaces/lie.py for some examples of usage).

CC: @sagetrac-sage-combinat

Component: combinatorics

Keywords: dynkin diagram ascii art lie

Issue created by migration from https://trac.sagemath.org/ticket/5502

[dwbump]

comment:2

I uploaded trac_5502.patch for this. It applies to sage-3.4.1.rc2 and there are no errors in sage/combinat/rootsystems/*.py..

I have not tested it against the combinat patchseries because at the moment hg qpush -a fails in sage-combinat.

After the patch, the __repr__ method of class DynkinDiagram returns ascii art for the classical Cartan Types.

A natural extension would be to give the extended Dynkin diagram for the untwisted affine types.

[wdjoyner]

comment:4

Is this related to #2023 ?

[nthiery]

comment:5

Replying to @wdjoyner:

Is this related to #2023 ?

That's indeed the ascii art version of 2023. Thanks for the pointer.

[dwbump]

comment:6

I think the spirit of this patch is the same as #2023.

The idea of this patch is just that if the Cartan type is that
of a classical Lie algebra, you should be able to somehow
access it's Dynkin diagram. The solution here is making it part of the string
returned by the __repr__ method of the class.

We follow the Bourbaki conventions, which is the same as the
programmed-in Cartan types. These diagrams are identical to
those produced by LiE, so you can have them already if you
install that optional package.

sage: CartanType("E6").dynkin_diagram()

        O 2
        |
        |
O---O---O---O---O
1   3   4   5   6   
E6

You want this if you need to be reminded of what labeling
convention is used. If the Cartan type is not recognized, we get the
old behavior. Thus:

sage: CartanType(['E',6,1]).dynkin_diagram()
Dynkin diagram of type ['E', 6, 1]

It might be more convenient if untwisted affine types gave the
extended Dynkin diagram, thus:

sage: CartanType(['E',6,1]).dynkin_diagram()
        O 0 
        |
        |
        O 2
        |
        |
O---O---O---O---O
1   3   4   5   6
E6~

Beyond that, one might implement Dynkin diagrams for twisted
affine types, but that seems less urgent.

[dwbump]

comment:7

The file trac_5502.2.patch add extended Dynkin diagrams as Dynkin diagrams of untwisted affine Cartan types.

Anne Schilling requests twisted affine types, but this is not done.

[dwbump]

comment:8

Attachment: trac_5502-revised.patch.gz

The patch trac_5502-revised.patch corrects some problems and supercedes
the previous patches.

[dwbump]

comment:9

I changed the milestone to 4.0 in hopes this can be merged.

[anneschilling]

comment:10

The patch implements ascii art for all finite and untwisted Cartan types,
which is very useful for visual clues about the numbering of the Dynkin nodes.

All doctests pass.

[sagetrac-mabshoff]

comment:11

There are two new functions without doctests:

• extended_dynkin_diagram_ascii_art
• dynkin_diagram_ascii_art

I know they are tested elsewhere, but the 100% rule still applies. Once the doctests have been added the positive review can be reinstated assuming the doctests in the file modified actually pass ;)

Cheers,

Michael

[dwbump]

comment:12

Attachment: trac_5502-doc.patch.gz

The patch trac_5502-doc.patch goes on top of trac_5502-revised.patch.

It adds doctests to the two ascii art functions.

[sagetrac-mabshoff]

comment:13

Positive review overall.

Dan: Please remember to change the summary back once you updated the patch.

Cheers,

Michael

[sagetrac-mabshoff]

comment:14

Merged both patches in Sage 4.0.alpha0.

Cheers,

Michael