Opened 12 years ago

Closed 12 years ago

#9500 closed enhancement (fixed)

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

Reported by: William Stein Owned by: Alex Ghitza
Priority: major Milestone: sage-4.5.2
Component: algebra Keywords:
Cc: Merged in: sage-4.5.2.alpha0
Authors: William Stein Reviewers: Martin Albrecht
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Status badges

Description (last modified by William Stein)

* 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

Attachments (1)

trac_9500.patch (5.3 KB) - added by William Stein 12 years ago.

Download all attachments as: .zip

Change History (7)

comment:2 Changed 12 years ago by William Stein

Description: modified (diff)

Changed 12 years ago by William Stein

Attachment: trac_9500.patch added

comment:3 Changed 12 years ago by William Stein

Status: newneeds_review

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

comment:4 Changed 12 years ago by Martin Albrecht

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

comment:5 Changed 12 years ago by Martin Albrecht

Status: needs_reviewpositive_review

Doctests pass.

comment:6 Changed 12 years ago by Mitesh Patel

Authors: William Stein
Merged in: sage-4.5.2.alpha0
Resolution: fixed
Reviewers: Martin Albrecht
Status: positive_reviewclosed
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