Tensor product of crystals does not handle -inf for epsilon/phi correctly

[tscrim]

This does not work:

sage: E1 = crystals.elementary.B(['A',2], 1)
sage: E2 = crystals.elementary.B(['A',2], 2)
sage: T = crystals.TensorProduct(E1, E2)
sage: x = T(E1.module_generators[0], E2.module_generators[0]); x
[0, 0]
sage: x.f(1)
[-1, 0]
sage: x.e(1)
[1, 0]

The reason is because we try and be clever with how we compute the _sig and do an epsilon_(k) - phi_i(k-1). If one of these (in particular, the phi) is -inf, then the computation breaks down. Instead, we have to bite the bullet and do the partial sums of the weight pairings to make sure we cover these cases.

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

Component: combinatorics

Keywords: crystals, tensor product

Author: Travis Scrimshaw

Branch/Commit: 9a24ea0

Reviewer: Ben Salisbury

Issue created by migration from https://trac.sagemath.org/ticket/18469

[tscrim]

Commit: 211f611

[tscrim]

Branch: public/crystals/fix_tensor_product-18469

[tscrim]

New commits:

211f611

Fixing _sig for epsilon/phi returning -inf.

[sagetrac-git]

Changed commit from 211f611 to 9a24ea0

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

9a24ea0

Fixing _sig for epsilon/phi returning -inf.

[bsalisbury1]

comment:3

Thanks, Travis.

[bsalisbury1]

Reviewer: Ben Salisbury

[vbraun]

Changed branch from public/crystals/fix_tensor_product-18469 to 9a24ea0