Fix weight of Nakajima monomials

[tscrim]

With #18453, all weights are computed as the difference of the highest weight to what should be the weight. In particular, any highest weight element has weight 0.

sage: La = RootSystem(['A',2]).weight_lattice().fundamental_weights()
sage: M = crystals.NakajimaMonomials(['A',2], La[1])
sage: M.module_generators[0].weight()
(0, 0, 0)

I also make Nakajima monomials as classical crystals for the finite types.

CC: @sagetrac-sage-combinat @bsalisbury1 @anneschilling

Component: combinatorics

Keywords: crystals, nakajima monomials

Author: Travis Scrimshaw

Branch/Commit: 4eb38e2

Reviewer: Ben Salisbury

Issue created by migration from https://trac.sagemath.org/ticket/18722

[tscrim]

Last 10 new commits:

c8fd060	Alcove paths weights are up to snuff.
495fa98	documentation updates
42ed2f2	Merge branch 'public/crystal/18453' of git://trac.sagemath.org/sage into public/crystal/18453
f4955c5	Fixing RC crystals for extended and non-extended weight input.
f156803	18453: small edits
9b5b9d5	Merge branch 'develop' into public/crystal/18453
d120397	18453: updated thematic tutorial on affine crystals
8e5c4cd	18453: some more additions to the thematic tutorial
ee398ef	18453: fixed one_dimensional_configuration sum issue
f02f80c	Fixing weight of Nakajima monomials.

[tscrim]

Commit: f02f80c

[tscrim]

Branch: public/crystals/fix_nakajima_monomials-18722

[bsalisbury1]

comment:3

The following example failed with the original commit:

sage: M = crystals.NakajimaMonomials(['A',2,1], RootSystem(['A',2,1]).weight_lattice(extended=True).fundamental_weight(0))
sage: m = M.module_generators[0]
sage: m.weight()
Lambda[0]

A conditional was added to __classcall_private__ of CrystalsOfNakajimaMonomials to ensure the weight lattice being used is the extended weight lattice with the underlying Cartan type is affine.

Some doctests needed to be updated so that the input used the extended weight lattice in affine examples.

Doctests passed on my machine, so if you agree with these changes, then you may set the ticket to positive review on my behalf.

[sagetrac-git]

Changed commit from f02f80c to 4eb38e2

[sagetrac-git]

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

4eb38e2

made input from extended weight lattice for highest weight Nakajima monomial crystals

[tscrim]

comment:5

Works for me. Thanks!

[tscrim]

Reviewer: Ben Salisbury

[vbraun]

Changed branch from public/crystals/fix_nakajima_monomials-18722 to 4eb38e2