#9138: Categories for polynomial rings
-----------------------------------------+----------------------------------
   Reporter:  jbandlow                   |       Owner:  nthiery                
            
       Type:  defect                     |      Status:  needs_work             
            
   Priority:  major                      |   Milestone:  sage-4.7               
            
  Component:  categories                 |    Keywords:  introspection, 
categories for rings
     Author:  Simon King                 |    Upstream:  N/A                    
            
   Reviewer:                             |      Merged:                         
            
Work_issues:  Improve Monsky-Washnitzer  |  
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Changes (by SimonKing):

  * status:  needs_review => needs_work
  * work_issues:  Doctest errors => Improve Monsky-Washnitzer


Comment:

 I see that there is a lot of slow-down in the Monsky-Washnitzer code,
 namely arithmetic in `SpecialCubicQuotientRing`:
 {{{
 sage: B.<t> = PolynomialRing(Integers(125))
 sage: R = monsky_washnitzer.SpecialCubicQuotientRing(t^3 - t + B(1/4))
 sage: x, T = R.gens()
 sage: x
 (0) + (1)*x + (0)*x^2
 sage: T
 (T) + (0)*x + (0)*x^2
 }}}
 In vanilla sage-4.6.2, I get
 sage: timeit('x*T')
 625 loops, best of 3: 491 µs per loop
 }}}
 With the patches, I get
 {{{
 sage: timeit('x*T')
 625 loops, best of 3: 612 µs per loop
 }}}

 So, there is your problem!

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9138#comment:28>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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