Add support for general c_{ij} for Nakajima monomials and some cleanup

[tscrim]

The definition allows a choice of a general c_ij matrix such that c_ij + c_ji = 1 for all i != j.

We also perform some cleanup:

• Remove the trailing whitespace at the end of the monomial printing.
• Only needing to input the dominant weight.
• Better handling of dictionaries in monomial methods.

CC: @sagetrac-sage-combinat @bsalisbury1

Component: combinatorics

Keywords: crystals, nakajima monomials

Author: Travis Scrimshaw

Branch/Commit: 5da5f89

Reviewer: Ben Salisbury

Issue created by migration from https://trac.sagemath.org/ticket/18895

[tscrim]

comment:1

I am recycling this ticket because I couldn't improve the weight function.

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New commits:

aab22d3

Adding support for general c_{ij} and some cleanup.

[tscrim]

Branch: public/crystals/general_c_monomial-18895

[tscrim]

Commit: aab22d3

[sagetrac-git]

Changed commit from aab22d3 to 2ef42bc

[sagetrac-git]

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

2ef42bc

Needing to do a transpose and adding an extra input check.

[sagetrac-git]

Changed commit from 2ef42bc to 825bf35

[sagetrac-git]

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

53891f2	Added some more documentation and input checking.
825bf35	Making the choice of monomial a global option.

[sagetrac-git]

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

b87cc0a	Merge branch 'develop' into public/crystals/general_c_monomial-18895
fd09f2a	Some last little fixes for the global_options option.

[sagetrac-git]

Changed commit from 825bf35 to fd09f2a

[tscrim]

Changed commit from fd09f2a to 58ffd2c

[tscrim]

comment:5

Variant which uses an instance option rather than global option for setting the display output.

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New commits:

58ffd2c

A variant using an instance option.

[tscrim]

Changed branch from public/crystals/general_c_monomial-18895 to public/crystals/general_c_monomial_v2-18895

[sagetrac-git]

Changed commit from 58ffd2c to fd4af09

[sagetrac-git]

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

4b7a2a4	Merge branch 'public/crystals/general_c_monomial-18895' of git://trac.sagemath.org/sage into monomials
b8ed79d	Merge branch 'public/crystals/general_c_monomial_v2-18895' of git://trac.sagemath.org/sage into monomials
3c2fa2b	Merge branch 'develop' into monomials
fd4af09	documentation fixes and changed _monomial to _variable

[sagetrac-git]

Changed commit from fd4af09 to e010047

[sagetrac-git]

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

e010047

fixed doctest error

[bsalisbury1]

comment:8

Hey Travis,

Thanks for doing this! I made a bunch of documentation fixes and improvements. Also, I changed ._monomial, .get_monomials, and .set_monomials to _.variable, .get_variables, and .set_variables, respectively. If you agree with these changes, then it can get a positive review from me.

[bsalisbury1]

Reviewer: Ben Salisbury

[sagetrac-git]

Changed commit from e010047 to 5da5f89

[sagetrac-git]

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

5da5f89

Fixing the handling of (deprecated) use_Y.

[tscrim]

comment:10

I noticed that we aren't properly using the use_Y, and I fixed that on my last commit. I'm okay with your changes. So if you agree with mine, then it is a positive review.

[vbraun]

Changed branch from public/crystals/general_c_monomial_v2-18895 to 5da5f89