#8495: Regression: Many mathematica doctests now fail
------------------------------------------+---------------------------------
   Reporter:  flawrence                   |       Owner:  flawrence 
       Type:  defect                      |      Status:  needs_work
   Priority:  major                       |   Milestone:  sage-4.7  
  Component:  interfaces                  |    Keywords:            
     Author:  Felix Lawrence              |    Upstream:  N/A       
   Reviewer:  Mike Hansen, Burcin Erocal  |      Merged:            
Work_issues:                              |  
------------------------------------------+---------------------------------
Changes (by drkirkby):

  * status:  needs_review => needs_work


Comment:

 For me at least, on !OpenSolaris with Mathematica 7.0.1, this is a
 definite improvement, as it reduced the number of failures in
 {{{devel/sage/sage/interfaces/mathematica.py}}} from 17 to 2.

  == Prior to adding the patch ==
 {{{

 <snip out lots of failures>

 4 items had failures:
    5 of  84 in __main__.example_0
    4 of   6 in __main__.example_1
    4 of  19 in __main__.example_12
    4 of   6 in __main__.example_2
 ***Test Failed*** 17 failures.
 For whitespace errors, see the file
 /export/home/drkirkby/.sage//tmp/.doctest_mathematica.py
          [5.4 s]

 ----------------------------------------------------------------------
 The following tests failed:


         sage -t -optional "devel/sage/sage/interfaces/mathematica.py"
 Total time for all tests: 5.4 seconds
 }}}

 == After adding the patch ==
 After applying the patch, the number of failures is reduced to 2.

 {{{
 sage-4.6.2.rc1$ ./sage -t -optional devel/sage/sage/interfaces/
 sage -t -optional "devel/sage/sage/interfaces/mathematica.py"
 **********************************************************************
 File
 
"/export/home/drkirkby/3/sage-4.6.2.rc1/devel/sage/sage/interfaces/mathematica.py",
 line 270:
     sage: print n                   # optional - mathematica
 Expected:
                   1.5707963267948966192313216916397514420985846996876
 Got:
     1.5707963267949
 **********************************************************************
 File
 
"/export/home/drkirkby/3/sage-4.6.2.rc1/devel/sage/sage/interfaces/mathematica.py",
 line 311:
     sage: math_bessel_K(2,I)                      # optional - mathematica
 Exception raised:
     Traceback (most recent call last):
       File
 "/export/home/drkirkby/3/sage-4.6.2.rc1/local/bin/ncadoctest.py", line
 1231, in run_one_test
         self.run_one_example(test, example, filename, compileflags)
       File
 "/export/home/drkirkby/3/sage-4.6.2.rc1/local/bin/sagedoctest.py", line
 38, in run_one_example
         OrigDocTestRunner.run_one_example(self, test, example, filename,
 compileflags)
       File
 "/export/home/drkirkby/3/sage-4.6.2.rc1/local/bin/ncadoctest.py", line
 1172, in run_one_example
         compileflags, 1) in test.globs
       File "<doctest __main__.example_0[75]>", line 1, in <module>
         math_bessel_K(Integer(2),I)                      # optional -
 mathematica###line 311:
     sage: math_bessel_K(2,I)                      # optional - mathematica
       File "<doctest __main__.example_0[74]>", line 2, in math_bessel_K
         return mathematica(nu).BesselK(x).N(Integer(20))
       File "element.pyx", line 617, in
 sage.structure.element.Element.numerical_approx
 (sage/structure/element.c:4658)
       File "/export/home/drkirkby/3/sage-4.6.2.rc1/local/lib/python/site-
 packages/sage/misc/functional.py", line 1265, in numerical_approx
         return sage.rings.complex_field.ComplexField(prec)(x)
       File "/export/home/drkirkby/3/sage-4.6.2.rc1/local/lib/python/site-
 packages/sage/rings/complex_field.py", line 279, in __call__
         return Parent.__call__(self, x)
       File "parent.pyx", line 915, in
 sage.structure.parent.Parent.__call__ (sage/structure/parent.c:6668)
       File "coerce_maps.pyx", line 82, in
 sage.structure.coerce_maps.DefaultConvertMap_unique._call_
 (sage/structure/coerce_maps.c:3119)
       File "coerce_maps.pyx", line 77, in
 sage.structure.coerce_maps.DefaultConvertMap_unique._call_
 (sage/structure/coerce_maps.c:3022)
       File "/export/home/drkirkby/3/sage-4.6.2.rc1/local/lib/python/site-
 packages/sage/rings/complex_field.py", line 310, in _element_constructor_
         return complex_number.ComplexNumber(self, x)
       File "complex_number.pyx", line 162, in
 sage.rings.complex_number.ComplexNumber.__init__
 (sage/rings/complex_number.c:3995)
     TypeError: unable to coerce to a ComplexNumber: <class
 'sage.interfaces.mathematica.MathematicaElement'>
 **********************************************************************
 1 items had failures:
    2 of  84 in __main__.example_0
 ***Test Failed*** 2 failures.
 For whitespace errors, see the file
 /export/home/drkirkby/.sage//tmp/.doctest_mathematica.py
          [5.2 s]

 ----------------------------------------------------------------------
 The following tests failed:


         sage -t -optional "devel/sage/sage/interfaces/mathematica.py"
 Total time for all tests: 5.2 seconds
 }}}


 == Mathematica session on the sage machine computing Pi/2 ==

 {{{
 drkirkby@hawk:~$ math
 Mathematica 7.0 for Sun Solaris x86 (64-bit)
 Copyright 1988-2009 Wolfram Research, Inc.

 In[1]:= n=Pi/2

         Pi
 Out[1]= --
         2

 In[2]:= N[n,50]

 Out[2]= 1.5707963267948966192313216916397514420985846996876
 }}}

 == Sage session on the same machine computing pi/2 with the Mathematica
 interface ==

 {{{
 sage: x = mathematica(pi/2)
 sage: print x
         Pi
         --
         2
 sage: loads(dumps(x)) == x
 True
 sage: n = x.N(50)
 sage: print n
 1.5707963267949
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8495#comment:14>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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