Implement finite algebras

[sagetrac-johanbosman]

Implementation of finite algebras over fields. A finite algebra A is simply given by means of a basis and for each basis element e a matrix that describes (right) multiplication of A by e.

The basic set-up is for algebras that are not necessarily unitary, commutative, or associative. Only algebras that satisfy all these conditions are fully supported.

CC: @koffie

Component: algebra

Keywords: sd51

Author: Johan Bosman, Peter Bruin, Michiel Kosters, Travis Scrimshaw

Branch/Commit: b629254

Reviewer: Travis Scrimshaw, Peter Bruin

Issue created by migration from https://trac.sagemath.org/ticket/12141

[sagetrac-johanbosman]

Changed keywords from none to sd35

[sagetrac-johanbosman]

comment:2

Attachment: 12141_basic_setup.patch.gz

Lots of things to do still:

• Properly put it in a Category.
• Implement ideals and morphisms.

[sagetrac-mkosters]

Attachment: 12141_2_basic_setup.patch.gz

Added an associativity check.

[sagetrac-johanbosman]

Attachment: 12141_improve_repr.patch.gz

[sagetrac-mkosters]

Many new functions

[sagetrac-johanbosman]

Attachment: 12141_4.patch.gz

[sagetrac-johanbosman]

comment:3

Attachment: 12141_improve_associativity.patch.gz

I've uploaded an improvement of the associativity check, but it does need further improvement.

[sagetrac-johanbosman]

Dependencies: #11068

[sagetrac-johanbosman]

comment:4

Attachment: 12141_fix_random_docstring.patch.gz

[sagetrac-johanbosman]

Don't apply this yet; it contains bugs, but I messed up my hg.