#12417: extend partial_fraction_decomposition() to work on ratios of 
multivariate
polynomials
---------------------------+------------------------------------------------
   Reporter:  araichev     |          Owner:  nthiery                           
                         
       Type:  enhancement  |         Status:  new                               
                         
   Priority:  major        |      Milestone:  sage-5.0                          
                         
  Component:  categories   |       Keywords:  partial fraction decomposition 
multivariate polynomial ring
Work_issues:               |       Upstream:  N/A                               
                         
   Reviewer:               |         Author:  Alex Raichev                      
                         
     Merged:               |   Dependencies:                                    
                         
---------------------------+------------------------------------------------

Comment(by malb):

 {{{
 diff --git a/sage/categories/quotient_fields.py
 b/sage/categories/quotient_fields.py
 --- a/sage/categories/quotient_fields.py
 +++ b/sage/categories/quotient_fields.py
 @@ -1052,8 +1052,8 @@

          - Alex Raichev (2011-01-10)
          """
 -        from sage.structure.sequence import *
 -        from sage.rings.polynomial.polynomial_ring_constructor import *
 +        from sage.structure.sequence import Sequence
 +        from sage.rings.polynomial.polynomial_ring_constructor import
 PolynomialRing

          parts = REFDSum([])
          R = self.base_ring()
 @@ -1195,4 +1195,4 @@
          if done_decomposing:
              return parts
          else:
 -            return parts.decompose_via_nullstellensatz()
 \ No newline at end of file
 +            return parts.decompose_via_nullstellensatz()
 diff --git a/sage/rings/polynomial/multi_polynomial_sequence.py
 b/sage/rings/polynomial/multi_polynomial_sequence.py
 --- a/sage/rings/polynomial/multi_polynomial_sequence.py
 +++ b/sage/rings/polynomial/multi_polynomial_sequence.py
 @@ -159,6 +159,7 @@
  from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
  from sage.rings.polynomial.multi_polynomial import is_MPolynomial
  from sage.structure.sequence import Sequence_generic
 +from sage.rings.polynomial.polynomial_ring_constructor import
 PolynomialRing

  from sage.interfaces.singular import singular
 }}}

 gets you further. There was indeed an import missing, I wonder why we
 didn't catch this before?

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12417#comment:2>
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