Inconsistent behavior with generator ordering in free Lie algebras

[ehaka]

This is an issue discovered due to #27018. Giving a free Lie algebra a set of generators that are not in lexicographic order causes graded_basis to output elements which are not recognized as basis elements of the Lie algebra due to different ordering behavior.

sage: Lxyz = LieAlgebra(QQ, ['x','y','z']).Lyndon()
sage: Lzxy = LieAlgebra(QQ, ['z','x','y']).Lyndon()
sage: Lxyz.graded_basis(2)
([x, y], [x, z], [y, z])
sage: Lzxy.graded_basis(2)
([z, x], [z, y], [x, y])
sage: x,y,z = Lxyz.gens()
sage: a,b,c = Lzxy.gens()
sage: a,b,c
(z, x, y)
sage: b.bracket(a)
[x, z]
sage: x.bracket(z)
[x, z]
sage: Lzxy._is_basis_element(b.leading_support(),a.leading_support())
True
sage: Lzxy._is_basis_element(a.leading_support(),b.leading_support())
False

Trying to compute brackets with these elements leads to unhelpful tracebacks, e.g.

sage: Lzxy[Lzxy.graded_basis(2)[0],Lzxy.graded_basis(1)[0]]
Traceback (most recent call last)
...
AttributeError: 'sage.algebras.lie_algebras.lie_algebra_element.Lie' object has no attribute '_right'

Component: algebra

Keywords: Lie algebras

Author: Eero Hakavuori, Travis Scrimshaw

Branch/Commit: a3f59d3

Reviewer: Travis Scrimshaw, Eero Hakavuori

Issue created by migration from https://trac.sagemath.org/ticket/27069

[sagetrac-git]

Changed commit from 4e27c06 to 45b4506

[sagetrac-git]

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

af8cac3	Merge branch 'public/lie_elem_indexing-27018' of git://trac.sagemath.org/sage into public/lie_elem_indexing-27018
45b4506	Using the word given by elements \NN to generate the free Lie algebra basis elements.

[tscrim]

Author: Eero Hakavuori, Travis Scrimshaw

[tscrim]

Reviewer: Travis Scrimshaw, Eero Hakavuori

[tscrim]

comment:2

Okay, this should fix it, as well as #27018.

[sagetrac-git]

Changed commit from 45b4506 to a3f59d3

[sagetrac-git]

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

a3f59d3

Small tweak to the documentation.

[ehaka]

comment:4

Everything seems to be working as it should now, thanks for the fix!

[vbraun]

Changed branch from public/lie_elem_indexing-27018 to a3f59d3