#14814: Multivariate power series are missing integral and division method
-------------------------------------------------+-------------------------
       Reporter:  hivert                         |        Owner:
           Type:  enhancement                    |  AlexGhitza
       Priority:  major                          |       Status:
      Component:  algebra                        |  needs_review
       Keywords:  integral multivariate power    |    Milestone:  sage-5.13
  series                                         |   Resolution:
        Authors:  Florent Hivert, Nicolas        |    Merged in:
  Thiéry                                         |    Reviewers:  Frédéric
Report Upstream:  N/A                            |  Chapoton
         Branch:                                 |  Work issues:
   Dependencies:                                 |       Commit:
                                                 |     Stopgaps:
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Old description:

> {{{
> sage: R.<x>=PowerSeriesRing(QQ, 'x')
> sage: (x+x^2).integral()
> 1/2*x^2 + 1/3*x^3
> sage: R.<x,y>=PowerSeriesRing(QQ, 'x y')
> sage: (x+x^2).integral(x)
> ...
> AttributeError: 'MPowerSeries' object has no attribute 'integral'
> }}}
>
> I also implement division by a non unit series (thanks Nicolas for
> preliminary code) and fixes the latex method which was buggy

New description:

 {{{
 sage: R.<x>=PowerSeriesRing(QQ, 'x')
 sage: (x+x^2).integral()
 1/2*x^2 + 1/3*x^3
 sage: R.<x,y>=PowerSeriesRing(QQ, 'x y')
 sage: (x+x^2).integral(x)
 ...
 AttributeError: 'MPowerSeries' object has no attribute 'integral'
 }}}

 I also implement division by a non unit series (thanks Nicolas for
 preliminary code) and fixes the latex method which was buggy

 Apply:

 * [attachment:trac_14814-power_series_inverse_latex-fix-fh.patch]
 * [attachment:trac_14814_review.patch]
 * [attachment:trac_14814-review-2-dg.patch]

--

Comment (by darij):

 New review patch allows the denominator to lie in a different parent (as
 long as it coerces into that of the numerator), deals with an endless-loop
 bug, and adds doc and comments. If you are fine with it, Frederic and
 Florent, this is positive_review!

 for the '''patchbot'''

 apply trac_14814-power_series_inverse_latex-fix-fh.patch
 trac_14814_review.patch trac_14814-review-2-dg.patch

--
Ticket URL: <http://trac.sagemath.org/ticket/14814#comment:9>
Sage <http://www.sagemath.org>
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