Add documentation for integrable representation (#15806) to Lie methods thematic tutorial

[dwbump]

The IntegrableRepresentation code for working with integrable representations of affine Lie algebras is documented in the reference manual but not in the Lie Methods and Related Combinatorics thematic tutorial. This ticket is to add documentation to the thematic tutorial.

CC: @sagetrac-khlee @anneschilling @nthiery @tscrim @bsalisbury1 @kevindilks

Component: documentation

Keywords: sagedays@icerm

Author: Daniel Bump

Branch/Commit: a9119bb

Reviewer: Anne Schilling, Kyu-Hwan Lee, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/25937

[dwbump]

New commits:

506f2ec

Lie thematic tutorial revisions

[dwbump]

Commit: 506f2ec

[dwbump]

Branch: public/tutorial-25937

[dwbump]

Changed author from bump to Daniel Bump

[sagetrac-git]

Changed commit from 506f2ec to 1e8dadf

[sagetrac-git]

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

874e575	writing about weight lattice, integrable representations, etc.
1e8dadf	minor edits

[sagetrac-git]

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

73afeaf

minor fix

[sagetrac-git]

Changed commit from 1e8dadf to 73afeaf

[sagetrac-git]

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

1903175

mention methods of weight lattice

[sagetrac-git]

Changed commit from 73afeaf to 1903175

[sagetrac-git]

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

6b85a92

some writing

[sagetrac-git]

Changed commit from 1903175 to 6b85a92

[sagetrac-git]

Changed commit from 6b85a92 to d54d0f8

[sagetrac-git]

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

d54d0f8

some edits

[sagetrac-git]

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

440d8e2

Coxeter number

[sagetrac-git]

Changed commit from d54d0f8 to 440d8e2

[kevindilks]

comment:10

Once this is done, I can look at it for typos, and see how it looks from the perspective of somebody that's not an expert on this stuff. Would probably still need an expert to at least glance over it to make sure nothing is majorly wrong.

[anneschilling]

comment:11

I would be glad to help review this ticket. Dan, were there sections you wanted me to write? Why have some titles changed from capitals to lower case letters?

[tscrim]

comment:12

I am also willing to help with either writing or reviewing too.

[sagetrac-git]

Changed commit from 440d8e2 to d9066be

[sagetrac-git]

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

d9066be

reorganization: moved weight rings section and created a new section for integrable representations

[sagetrac-git]

Changed commit from d9066be to 83a5de7

[sagetrac-git]

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

83a5de7

integrable.rst

[sagetrac-git]

Changed commit from 83a5de7 to 06d9be6

[sagetrac-git]

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

06d9be6

doc edits and a new method in integrable_representations.py

[sagetrac-git]

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

61c8992

3 comments by Travis

[dwbump]

comment:48

Did you try :mod:~sage.combinat....?

That works. Thanks!

I implemented the last 3 comments from Travis and pushed.

---

New commits:

61c8992

3 comments by Travis

[tscrim]

comment:49

No problem.

Anyone else have any comments? (Kevin?) I am ready to set this to a positive review.

[sagetrac-khlee]

comment:50

I have read the document one more time and found a few typos. After correcting them, I would agree to set this to a positive review. Thanks!!

---

--The support of an integrable highest weight representation

first paragraph: $L(\lambda)$ --> $L(\Lambda)$ (There are two occurrences of this.)

---Sage methods for integrable representations

first paragraph: A period is missing at the end of the last sentence.

second paragraph: The sentence "Then we compute the string function at this weight, which we see agrees with the string function for the corresponding dominant maximal weight:" seems out of place. Could we delete it?

A period is missing at the end of the displayed math in the sentence begin with "Reading what the OEIS..."

The formulas of two string functions are not adequately aligned.

---

[sagetrac-git]

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

b047996

comments by khlee

[sagetrac-git]

Changed commit from 61c8992 to b047996

[dwbump]

comment:52

I made Kyu-Hwan's corrections except this one:

The formulas of two string functions are not adequately aligned.

I don't see the alignment problem.

---

New commits:

b047996

comments by khlee

[anneschilling]

comment:53

In the introduction to "Integrable Highest Weight Representations of Affine Lie algebras", there is still a missing link:

weyl_character_ring

[anneschilling]

comment:54

The link to the last OESIS 'OEIS sequence 128015' seems broken. Other than these last two link problems, I am also happy to set a positive review.

[kevindilks]

comment:55

@tscrim it seems like enough other people have already gotten a chance to read through it.

[sagetrac-git]

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

cb48b6c

two broken links found by Anne

[sagetrac-git]

Changed commit from b047996 to cb48b6c

[sagetrac-khlee]

comment:57

I am not sure what happened to the alignment problem. In any case, it disappeared, and I am happy with the current version.

[sagetrac-git]

Changed commit from cb48b6c to adbc210

[sagetrac-git]

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

adbc210

two more typos

[vbraun]

comment:60

Should be marked as optional internet:

File "src/doc/en/thematic_tutorials/lie/integrable.rst", line 224, in doc.en.thematic_tutorials.lie.integrable
Failed example:
    [oeis(x) for x in V.strings().values()]
Exception raised:
    Traceback (most recent call last):
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 614, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 1025, in compile_and_execute
        exec(compiled, globs)
      File "<doctest doc.en.thematic_tutorials.lie.integrable[12]>", line 1, in <module>
        [oeis(x) for x in V.strings().values()]
      File "sage/misc/lazy_import.pyx", line 354, in sage.misc.lazy_import.LazyImport.__call__ (build/cythonized/sage/misc/lazy_import.c:3759)
        return self.get_object()(*args, **kwds)
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/databases/oeis.py", line 382, in __call__
        return self.find_by_subsequence(query, max_results, first_result)
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/databases/oeis.py", line 510, in find_by_subsequence
        return self.find_by_description(subsequence, max_results, first_result)
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/databases/oeis.py", line 475, in find_by_description
        sequence_list = _fetch(url).split('\n\n')[2:-1]
      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/databases/oeis.py", line 195, in _fetch
        raise IOError("%s\nError fetching %s." % (msg, url))
    IOError: <urlopen error [Errno 60] Operation timed out>
    Error fetching http://oeis.org/search?q=1%2C+1%2C+3%2C+5%2C+10%2C+16%2C+28%2C+43%2C+70%2C+105%2C+161%2C+236&start=0&fmt=text&n=3.
**********************************************************************
1 item had failures:
   1 of  32 in doc.en.thematic_tutorials.lie.integrable
    [31 tests, 1 failure, 131.65 s]
----------------------------------------------------------------------
sage -t --long src/doc/en/thematic_tutorials/lie/integrable.rst  # 1 doctest failed
---------------------------------------------------------------------

[sagetrac-git]

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

a9119bb

oeis test is optional internet

[sagetrac-git]

Changed commit from adbc210 to a9119bb

[dwbump]

comment:62

This had a positive review. Per comment:60 I changed the oeis test to optional -- internet. I was unsure whether it is appropriate for me to put the positive review back so I changed it to needs review.

[vbraun]

Changed branch from public/tutorial-25937 to a9119bb