#9944: categories for polynomial rings
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    Reporter:  robertwb                     |         Owner:  nthiery           
                         
        Type:  defect                       |        Status:  needs_work        
                         
    Priority:  major                        |     Milestone:  sage-4.7.1        
                         
   Component:  categories                   |    Resolution:                    
                         
    Keywords:                               |   Work_issues:                    
                         
    Upstream:  N/A                          |      Reviewer:  Nicolas M. 
ThiƩry, Mike Hansen, Martin Raum
      Author:  Robert Bradshaw, Simon King  |        Merged:                    
                         
Dependencies:                               |  
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Comment(by SimonKing):

 Using prun, I found for one case:
 {{{
    Ordered by: internal time

    ncalls  tottime  percall  cumtime  percall filename:lineno(function)
         1    0.141    0.141    0.238    0.238
 polynomial_ring.py:178(__init__)
      1414    0.055    0.000    0.071    0.000
 polynomial_ring.py:234(_element_constructor_)
     11104    0.020    0.000    0.020    0.000
 polynomial_ring.py:1821(modulus)
      1420    0.005    0.000    0.005    0.000
 finite_field_givaro.py:153(degree)
 ...
 }}}

 In other words: In order to construct just ''one'' polynomial ring over an
 iterated polynomial ring, the element constructor is called 1414 times and
 the modulus method 11104 times. At a different ticket, I suggested to turn
 the modulus method into a cached method. Perhaps that should already be
 done here. However, there should be no need to construct 1414 elements,
 just to initialise one ring!

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9944#comment:51>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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