#4533: [with patch; needs work] divisors function slow for integers
----------------------+-----------------------------------------------------
 Reporter:  robertwb  |        Owner:  tbd       
     Type:  defect    |       Status:  new       
 Priority:  major     |    Milestone:  sage-3.2.1
Component:  algebra   |   Resolution:            
 Keywords:            |  
----------------------+-----------------------------------------------------
Changes (by mabshoff):

  * summary:  [with patch; with positive review] divisors function slow for
              integers => [with patch; needs work] divisors
              function slow for integers

Comment:

 Another oops:
 {{{
 sage -t -long devel/sage/sage/combinat/species/species.py
 **********************************************************************
 File "/scratch/mabshoff/release-cycle/sage-3.2.1.alpha0/devel/sage-
 main/sage/combinat/species/species.py", line 292:
     sage: G.isotype_generating_series().coefficients(5)
 Exception raised:
     Traceback (most recent call last):
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/bin/ncadoctest.py", line 1231, in
 run_one_test
         self.run_one_example(test, example, filename, compileflags)
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/bin/sagedoctest.py", line 38, in
 run_one_example
         OrigDocTestRunner.run_one_example(self, test, example, filename,
 compileflags)
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/bin/ncadoctest.py", line 1172, in
 run_one_example
         compileflags, 1) in test.globs
       File "<doctest __main__.example_12[7]>", line 1, in <module>
         G.isotype_generating_series().coefficients(Integer(5))###line 292:
     sage: G.isotype_generating_series().coefficients(5)
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/lib/python2.5/site-
 packages/sage/combinat/species/series.py", line 668, in coefficients
         return [self.coefficient(i) for i in range(n)]
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/lib/python2.5/site-
 packages/sage/combinat/species/series.py", line 830, in coefficient
         return self._stream[n]
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/lib/python2.5/site-
 packages/sage/combinat/species/stream.py", line 311, in __getitem__
         self._list.append(self._gen.next())
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/lib/python2.5/site-
 packages/sage/combinat/species/generating_series.py", line 428, in
 _ogs_gen
         yield sum( self.coefficient(i).coefficients() )
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/lib/python2.5/site-
 packages/sage/combinat/species/series.py", line 830, in coefficient
         return self._stream[n]
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/lib/python2.5/site-
 packages/sage/combinat/species/stream.py", line 311, in __getitem__
         self._list.append(self._gen.next())
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/lib/python2.5/site-
 packages/sage/combinat/species/generating_series.py", line 506, in
 _functorial_compose_gen
         t = g._cycle_type(s)
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/lib/python2.5/site-
 packages/sage/combinat/species/generating_series.py", line 530, in
 _cycle_type
         for d in divisors(k):
       File "/scratch/mabshoff/release-
 cycle/sage-3.2.1.alpha0/local/lib/python2.5/site-
 packages/sage/rings/arith.py", line 924, in divisors
         n = integer_ring.ZZ(n) # we have specalized code for this case,
 make sure it gets used
     NameError: global name 'integer_ring' is not defined
 **********************************************************************
 }}}
 The problem pops up in a lot of places.

 Cheers,

 Michael

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4533#comment:17>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of 
Reinventing the Wheel
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