Implement the blob algebra

[tscrim]

Also known as the Temperley-Lieb algebra of type B. This is an important algebra appearing in mathematical physics and the blob vs Soergel conjecture.

CC: @sagetrac-sage-combinat @AndrewAtLarge

Component: combinatorics

Author: Travis Scrimshaw

Branch: 8061aa2

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/29696

[tscrim]

New commits:

5e02fc6

Initial implementation of blob algebras.

[tscrim]

Commit: 5e02fc6

[tscrim]

Branch: public/combinat/blob_algebra-29696

[sagetrac-git]

Changed commit from 5e02fc6 to fb4cb46

[sagetrac-git]

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

fb4cb46

Slightly abstracting the latex code for diagrams to use in blob algebra.

[fchapoton]

comment:4

• Typo in:

+.. [ILZ2018] \K. Iohara, G. Gehrer, and R. Zhang.

second author should be G. Lehrer

• unicode art ? (ok, not really needed...)

[sagetrac-git]

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

1039ed0

Adding ascii/unicode art for Temperley-Lieb/blob diagrams.

[sagetrac-git]

Changed commit from fb4cb46 to 1039ed0

[tscrim]

comment:6

Fixed for the first. As for the second, it took some work, but I implemented an ascii/unicode art and it looks beautiful IMO. Now the question becomes will someone figure out a better way to do it or to generalize it in some way to general partition diagrams. Anyways, it works for now.

[fchapoton]

comment:7

patchbot plugin is not happy with invalid espace sequences, some missing r""" ?

[sagetrac-git]

Changed commit from 1039ed0 to 7dd76f6

[sagetrac-git]

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

2d64558	Merge branch 'public/combinat/blob_algebra-29696' of git://trac.sagemath.org/sage into public/combinat/blob_algebra-29696
7dd76f6	Added an r""" to TL_diagram_ascii_art().

[tscrim]

comment:9

Replying to @fchapoton:

patchbot plugin is not happy with invalid espace sequences, some missing r""" ?

Indeed I was missing a necessary one on TL_diagram_ascii_art(). Fixed.

[fchapoton]

comment:10

ok, looks good. But I suspect that the bullet ⚫ will break the unicode display alignment in many fonts. Maybe the letter "capital O" would do a better job, even if not as nice.

[sagetrac-git]

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

e5e91e7

Better unicode object for the blob.

[sagetrac-git]

Changed commit from 7dd76f6 to e5e91e7

[tscrim]

comment:12

I agree. Here is another attempted. What do you think?

[fchapoton]

Reviewer: Frédéric Chapoton

[fchapoton]

comment:13

Much better !

Say hello to the

   __         __
 /"  "\     /"  "\
(  (\  )___(  /)  )
 \               /
 /               \
/    () ___ ()    \
|      (   )      |
 \      \_/      /
   \...__!__.../
         "

[tscrim]

comment:14

<3

Thank you.

[vbraun]

comment:15

PDF docs don't build

[sagetrac-git]

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

85dbe35	Merge branch 'public/combinat/blob_algebra-29696' of git://trac.sagemath.org/sage into public/combinat/blob_algebra-29696
57bc9f6	Attempt to fix pdf build, plus other misc fixes.

[sagetrac-git]

Changed commit from e5e91e7 to 57bc9f6

[tscrim]

comment:17

Okay, I have tried to fix the pdf docbuild. At least, this is the only thing that I could see that would break it. I will try to test it later today.

[fchapoton]

comment:18

unicode may be another source of latex issues, alas

[tscrim]

comment:19

Replying to @fchapoton:

unicode may be another source of latex issues, alas

Well, if that is indeed the problem, we can just remove that output (well, the ones with the blobs on them).

[sagetrac-git]

Changed commit from 57bc9f6 to 8061aa2

[sagetrac-git]

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

8061aa2

Fixing the pdf docbuild.

[tscrim]

comment:21

So it was that in part, and because I forgot to add the blob algebra to the BLOC (big list of combinatorics) modules. The html and pdf docs now builds for me.

[fchapoton]

comment:22

ok, looks good. Let us try again

[vbraun]

Changed branch from public/combinat/blob_algebra-29696 to 8061aa2

[mkoeppe]

Changed commit from 8061aa2 to none

[mkoeppe]

comment:24

Looking at https://wiki.sagemath.org/ReleaseTours/sage-9.2#Unicode_art,
unfortunately the "⚬" does not align well with the line art when viewed in the Chrome browser on macOS (it's fine, of course, in Emacs and in the terminal)

[tscrim]

comment:25

Same for me using Firefox on Ubuntu, but it might just be something we have to live with.