#4539: plural wrapper
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Reporter: burcin | Owner: OleksandrMotsak, AlexanderDreyer
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.6
Component: algebra | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by SimonKing):
Replying to [comment:32 nthiery]:
> I started playing with ideals. Currently, one creates an ideal I, and
> then when one calls I.std() or I.twostd() to create a new left or
> twosided ideal, and actually compute the Groebner basis. What about
> the following variants:
Currently, if R is a commutative ring and L is a list of elements of R,
one may use the shorthand notation {{{I = R*L}}} or {{{I = L*R}}} to
create an ideal. It seems natural to me to extend this to the non-
commutative case: {{{R*L}}} for left ideal, {{{L*R}}} for right ideal,
and {{{R*L*R}}} for two-sided ideal.
How to implement it? Well, on could have a base class for ideals over non-
commutative rings (let's call it {{{NCIdeal}}}), and derive from it
{{{NCIdeal_left}}}, {{{NCIdeal_right}}}, {{{NCIdeal_twodsided}}}.
Then, one has to modify the multiplication method for rings so that
sidedness is taken care of (there is a method ideal_class(), that probably
needs to accept an optional argument "side"). And of course, the one-sided
ideal classes need a multiplication method as well.
And then, {{{NCIdeal_twodsided.groebner_basis()}}} would yield a two-sided
Gröbner basis, while {{{NCIdeal_left/right.groebner_basis()}}} would only
yield a one-sided Gröbner basis, of course unless a two-sided Gröbner
basis is requested by using an optional argument.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4539#comment:33>
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