#12141: Implement finite algebras
--------------------------------------------------------------+-------------
Reporter: johanbosman | Owner:
AlexGhitza
Type: enhancement | Status:
needs_review
Priority: major | Milestone:
sage-5.11
Component: algebra | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Johan Bosman, Peter Bruin, Michiel Kosters | Merged in:
Dependencies: | Stopgaps:
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Changes (by pbruin):
* status: new => needs_review
Old description:
> Finite algebras over fields should be implemented. 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`.
>
> Apply: [attachment:trac_12141_finite_algebras.patch]
New description:
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.
Apply: [attachment:trac_12141_finite_algebras.patch],
[attachment:trac_12141_categorify.patch]
--
Comment:
I added the class FiniteAlgebraMorphism and functionality for primary
decomposition, mostly written by Johan Bosman. FiniteAlgebras over a
field ''k'' are now members of the (existing) category
FiniteDimensionalAlgebrasWithBasis(''k''). The code is fully doctest-
covered.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12141#comment:11>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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