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implement inversion of elements in a (more) general quotient ring #9500

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williamstein opened this issue Jul 14, 2010 · 9 comments
Closed

implement inversion of elements in a (more) general quotient ring #9500

williamstein opened this issue Jul 14, 2010 · 9 comments
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@aghitza
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c: algebra p: major / 3 t: enhancement
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sage-4.5.2

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@williamstein
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*** 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

Component: algebra

Author: William Stein

Reviewer: Martin Albrecht

Merged: sage-4.5.2.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/9500
@williamstein williamstein added this to the sage-4.5.2 milestone Jul 14, 2010
@williamstein
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comment:1

Relevant benchmarks: http://wiki.sagemath.org/days23.5/projects/relative_number_fields

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Attachment: trac_9500.patch.gz

@williamstein
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comment:3

#9499 needs to be finished before this can be reviewed.

@malb
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malb commented Jul 14, 2010

comment:4

Patch look good and applies cleanly to 4.4.4 +#9499 (which is required).

@malb
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malb commented Jul 14, 2010

comment:5

Doctests pass.

@qed777
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qed777 mannequin commented Jul 20, 2010

Merged: sage-4.5.2.alpha0

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qed777 mannequin commented Jul 20, 2010

Author: William Stein

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qed777 mannequin commented Jul 20, 2010

Reviewer: Martin Albrecht

@qed777 qed777 mannequin removed the s: positive review label Jul 20, 2010
@qed777 qed777 mannequin closed this as completed Jul 20, 2010
@sagetrac-Bouillaguet sagetrac-Bouillaguet mannequin mentioned this issue Nov 6, 2012
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@aghitza aghitza

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