#11068: Basic implementation of one- and twosided ideals of non-commutative
rings,
and quotients by twosided ideals
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Reporter: SimonKing | Owner:
AlexGhitza
Type: enhancement | Status:
needs_work
Priority: major | Milestone:
sage-4.7
Component: algebra | Keywords:
onesided twosided ideal noncommutative ring
Author: | Upstream:
N/A
Reviewer: | Merged:
Work_issues: Add examples; move code from ring.py to rings.py |
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Changes (by SimonKing):
* status: new => needs_work
* work_issues: => Add examples; move code from ring.py to rings.py
Old description:
> It was suggested that my patch for #7797 be split into several parts.
>
> The first part shall be about ideals in non-commutative rings. Aim, for
> example:
> {{{
> sage: A = SteenrodAlgebra(2)
> sage: A*[A.0,A.1^2]
> Left Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
> sage: [A.0,A.1^2]*A
> Right Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
> sage: A*[A.0,A.1^2]*A
> Twosided Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
> }}}
>
> It was suggested to also add quotients by twosided ideals, although it
> will be difficult to provide examples before having letterplace ideals.
New description:
It was suggested that my patch for #7797 be split into several parts.
The first part shall be about ideals in non-commutative rings. Aim, for
example:
{{{
sage: A = SteenrodAlgebra(2)
sage: A*[A.0,A.1^2]
Left Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
sage: [A.0,A.1^2]*A
Right Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
sage: A*[A.0,A.1^2]*A
Twosided Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
}}}
It was suggested to also add quotients by twosided ideals, although it
will be difficult to provide examples before having letterplace ideals.
Depends on #10961
--
Comment:
Depends on #10961
The patch is incomplete, since proper examples are missing. Proper
examples will be provided by #7797, but Nicolas promised to try and find
some "small" example.
Really, all what we need is a non-commutative ring and something that
inherits from `Ideal_nc` and provides a `reduce()` method yielding normal
forms.
Also, that patch is preliminary, since it copies some code from
sage/rings/ring.pyx to sage/categories/rings.py, rather than ''moving''
it.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11068#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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