#10910: Avoid nfinit while factoring polynomials
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   Reporter:  lftabera       |       Owner:  tbd                                
      
       Type:  enhancement    |      Status:  new                                
      
   Priority:  major          |   Milestone:  sage-4.7                           
      
  Component:  factorization  |    Keywords:  factorization, pari, nfinit, 
number field
     Author:                 |    Upstream:  N/A                                
      
   Reviewer:                 |      Merged:                                     
      
Work_issues:                 |  
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 In previous versions of pari the options to factor a univariate polynomial
 over a number field where Trager's or Van Hoeij modular algorithm. The
 second method is the preferred one, but it used to need a nf structure.

 Hence Sage computed nfinit on the number field before factoring the
 polynomial via Pari.

 With current pari version the whole nf structure is not needed. So, the
 factor routines should not call nfinit that can be a very expensive
 operation for large fields.

 The patch modifies the factor method. If the nf structure is already
 computed we use it, as it will be faster. If the nf structure is not
 already computed then do not compute it to factor the polynomial.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10910>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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