#5074: singular factorization over GF(p) need not be a complete factorization
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   Reporter:  was                  |       Owner:  malb                         
              
       Type:  defect               |      Status:  needs_work                   
              
   Priority:  major                |   Milestone:  sage-4.5                     
              
  Component:  commutative algebra  |    Keywords:                               
              
     Author:                       |    Upstream:  Not yet reported upstream; 
Will do shortly.
   Reviewer:                       |      Merged:                               
              
Work_issues:                       |  
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Changes (by malb):

  * status:  new => needs_work
  * upstream:  => Not yet reported upstream; Will do shortly.


Comment:

 The original problem seems to be fixed by now. I ran the above snipped and
 everything was fine. However, for GF(9) I do get an error:
 {{{
 sage: k.<a> = GF(9)
 sage: R.<x,y> = PolynomialRing(k)
 sage: h = - (-x^2 - x*y + y^2 - 1)^2 * (x^2*y^2 + y^4 + x^2*y + x*y^2 +
 y^3 - x^2 + x*y + y^2 - 1) * (-x^4 - x^3*y - x*y^3 + y^4 - x^3 + x^2*y +
 x*y^2 - x^2 - x*y - y^2 + x + 1)
 sage: factor(h)
 ---------------------------------------------------------------------------
 AssertionError                            Traceback (most recent call
 last)

 
sage.rings.polynomial.multi_polynomial.MPolynomial._factor_over_nonprime_finite_field()
 AssertionError: bug in Singular factoring an auxiliary polynomial over
 GF(p): bad multiplicity (1, 2)
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5074#comment:2>
Sage <http://www.sagemath.org>
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