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Issue 20586: Allow T and R crystals to take a weight

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For tensor products, it is more natural to allow the weight to belong in any weight lattice realization. Moreover, we should extract the Cartan type from the weight.

CC: @sagetrac-sage-combinat @bsalisbury1

Component: combinatorics

Keywords: crystals, elementary crystals

Author: Travis Scrimshaw

Branch/Commit: 511c1a8

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/20586


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Commit: abc779b


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comment:1

The current behavior causes me some problems with tensor products with affine types whose weight lattice realization is not the ambient space.


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

cdf2d39Changing input to keep track of the weight lattice realization.

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comment:3

failing doctests, see bot


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511c1a8Adding option for different weight lattice realizations for the component crystal.

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comment:6

ok, looks good to me.


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Reviewer: Frédéric Chapoton


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