#1956: implement multivariate truncated power series arithmetic
-------------------------------------------+--------------------------------
   Reporter:  was                          |          Owner:  pernici           
       
       Type:  enhancement                  |         Status:  needs_review      
       
   Priority:  major                        |      Milestone:  sage-4.7          
       
  Component:  commutative algebra          |       Keywords:  multivariate 
power series
Work_issues:                               |       Upstream:  N/A               
       
   Reviewer:  Martin Albrecht, Simon King  |         Author:  Niles Johnson     
       
     Merged:                               |   Dependencies:                    
       
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Comment(by malb):

 This seems to be the current status:

 1. Sage passes all doctests with this patch

 waiting for patchbot :)

 2. All code is documented and doctested thoroughly; documentation builds
 without error or warning

 '''positive review'''

 3. The underlying concept of the implementation (a wrapper for certain
 univariate power series over multivariate polynomials) is sound

 '''positive review'''

 4. multi_power_series_ring.py: the code accurately does what it claims to
 do

 '''positive review'''

 5. multi_power_series_ring_element.py: the code accurately does what it
 claims to do

 '''needs review'''

 6. Integration with the rest of sage: construction and use of
 PowerSeriesRings works correctly, and parallels behavior of polynomial
 rings

 '''positive review'''

 7. Performance: the multivariate power series arithmetic is fast enough to
 be included in Sage

 '''positive review'''

 8. Coding: the code is free from obvious inefficiencies in error handling,
 memory management, etc.

 '''positive review'''

 9. The items on this list constitute a complete review

 '''positive review'''


 ----

 Thanks for explaining the default precision business to me! As I said, I
 rarely touch power series.

 ----
 > Excessive or not, each of the double underscore methods is necessary to
 replace the corresponding method of `PowerSeries` or
 `PowerSeriesRing_generic`, from which the `MPowerSeries*` classes inherit.
 Here's a complete list of the double underscore attributes:

 Sorry, I didn't mean stuff like {{{__init__}}} which of course has to be
 like it is. I meant stuff like {{{__poly_ring}}} which could easily be
 {{{_poly_ring}}}.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:110>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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