#9500: implement inversion of elements in a (more) general quotient ring
---------------------------+------------------------------------------------
Reporter: was | Owner: AlexGhitza
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.5.1
Component: algebra | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Description changed by was:
Old description:
> Make this work:
>
> {{{
>
> sage: R.<x,y> = QQ[]
> sage: I = R.ideal([x^2 + 1, y^3 - 2])
> sage: S.<i,cuberoot> = R.quotient(I)
> sage: 1/(1+i)
> -1/2*i + 1/2
>
> Confirm via symbolic computation::
>
> sage: 1/(1+sqrt(-1))
> -1/2*I + 1/2
>
> Another more complicated quotient::
>
> sage: b = 1/(i+cuberoot); b
> 1/5*i*cuberoot^2 - 2/5*i*cuberoot + 2/5*cuberoot^2 - 1/5*i +
> 1/5*cuberoot - 2/5
> sage: b*(i+cuberoot)
> 1
> }}}
New description:
*** This ticket depends on #9499 ***
Make this work:
{{{
sage: R.<x,y> = QQ[]
sage: I = R.ideal([x^2 + 1, y^3 - 2])
sage: S.<i,cuberoot> = R.quotient(I)
sage: 1/(1+i)
-1/2*i + 1/2
Confirm via symbolic computation::
sage: 1/(1+sqrt(-1))
-1/2*I + 1/2
Another more complicated quotient::
sage: b = 1/(i+cuberoot); b
1/5*i*cuberoot^2 - 2/5*i*cuberoot + 2/5*cuberoot^2 - 1/5*i +
1/5*cuberoot - 2/5
sage: b*(i+cuberoot)
1
}}}
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9500#comment:2>
Sage <http://www.sagemath.org>
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