#4000: Implement QQ['x'] via Flint ZZ['x'] + denominator
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   Reporter:  malb                                 |       Owner:  somebody    
       Type:  enhancement                          |      Status:  needs_review
   Priority:  major                                |   Milestone:  sage-4.3.2  
  Component:  basic arithmetic                     |    Keywords:              
     Author:  Sebastian Pancratz, Martin Albrecht  |    Upstream:  N/A         
   Reviewer:                                       |      Merged:              
Work_issues:                                       |  
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Comment(by spancratz):

 Here is a simpler instance of the problem:
 {{{
 sage: R.<x> = QQ[]
 sage: f = 3/2*x - 1/3
 sage: %time _ = f % f
 CPU times: user 5.67 s, sys: 0.17 s, total: 5.84 s
 Wall time: 5.86 s
 }}}

 I do *not* think that the problem is a coercion problem.  After inserting
 "print" statements into the Cython code at various points, I instead think
 the code in the block from line 881 in fmpq_poly_linkage.pxi actually
 takes this long, although I do not understand at all why this might be the
 case.

 The two lines at actually seem to take time (assuming that inserting
 "print" statements is a valid way to determine this) are
 {{{
     fmpz_pow_ui(t, lead, m)
     fmpz_mul(r.den, t, a.den)
 }}}
 but, once again, I've got not clue why this might be the case.

 Tomorrow or on Tuesday, I will try to reproduce the problem in plain C.
 If I manage to do this, I'll forward it to Bill Hart.  If not, I wouldn't
 really know what else to look into.

 Sebastian

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4000#comment:44>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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