#1956: implement multivariate power series arithmetic
-------------------------------------------+--------------------------------
   Reporter:  was                          |       Owner:  pernici              
    
       Type:  enhancement                  |      Status:  needs_review         
    
   Priority:  major                        |   Milestone:  sage-4.6.1           
    
  Component:  commutative algebra          |    Keywords:  multivariate power 
series
     Author:  Niles Johnson                |    Upstream:  N/A                  
    
   Reviewer:  Martin Albrecht, Simon King  |      Merged:                       
    
Work_issues:                               |  
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Comment(by pernici):

 Multivariate series in one variable differ from univariate series;
 is it the intended behaviour?

 {{{
 sage: R = PowerSeriesRing(GF(127),'t');R
 Power Series Ring in t over Finite Field of size 127
 sage: %timeit R.random_element(100)
 625 loops, best of 3: 856 µs per loop
 sage: K = PowerSeriesRing(GF(127),1,'a'); K
 Multivariate Power Series Ring in a over Finite Field of size 127
 sage: %timeit K.random_element(100)
 5 loops, best of 3: 146 ms per loop
 }}}

 I noticed this since
 the patch trac_1956_faster_MPowerSeries_mul.patch does not work in this
 case, because _send_to_bg calls the degrees method

 {{{
 sage: %timeit K.random_element(100)
 AttributeError:
 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object
 has no attribute 'degrees'
 }}}

 If multivariate series in one variable are meant to differ from
 univariate series I will modify _send_to_bg to deal with this case.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:64>
Sage <http://www.sagemath.org>
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