Add Lie bracket operation in Rings()

[nthiery]

From the documentation:

    sage: F = AlgebrasWithBasis(QQ).example(); F
    An example of an algebra with basis: the free algebra on the generators ('a', 'b', 'c') over Rational Field
    sage: a,b,c = F.algebra_generators()
    sage: F.bracket(a,b)
    B[word: ab] - B[word: ba]

Apply trac_10961-lie_bracket_in_rings-nt.patch

Component: algebra

Author: Nicolas M. Thiéry

Reviewer: Anne Schilling

Merged: sage-4.7.1.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/10961

[anneschilling]

comment:1

The patch implements the Lie bracket and it would be good to merge it into sage soon. However, the tests in /categories/rings.py line 70 do not pass due to the misprint
{{
sage: a,b,c = FF.algebra_generators()
}}
should be
{{
sage: a,b,c = F.algebra_generators()
}}

[anneschilling]

Reviewer: Anne Schilling

[nthiery]

comment:2

Replying to @anneschilling:

The patch implements the Lie bracket and it would be good to merge it into sage soon. However, the tests in /categories/rings.py line 70 do not pass due to the misprint
{{
sage: a,b,c = FF.algebra_generators()
}}
should be
{{
sage: a,b,c = F.algebra_generators()
}}

Shoot; I had noticed this, and got distracted. Thanks for the reminder! Fixed!

[nthiery]

Attachment: wifi.gz

Please delete this file!

[nthiery]

Attachment: trac_10961-lie_bracket_in_rings-nt.patch.gz

Final version

[anneschilling]

comment:4

Looks good!

[nthiery]

comment:5

Thanks for the review!

[jdemeyer]

Merged: sage-4.7.1.alpha0