#7763: make nintegrate/nintegral top-level functions
-----------------------------------+----------------------------------------
   Reporter:  jason                |       Owner:  burcin    
       Type:  enhancement          |      Status:  needs_work
   Priority:  major                |   Milestone:  sage-4.6.2
  Component:  calculus             |    Keywords:            
     Author:  Gagan Sekhon         |    Upstream:  N/A       
   Reviewer:  Karl-Dieter Crisman  |      Merged:            
Work_issues:                       |  
-----------------------------------+----------------------------------------
Changes (by kcrisman):

  * keywords:  beginner =>
  * status:  needs_review => needs_work


Comment:

 Again, a good start at this!

 Unfortunately, there are now MANY small issues that need to be cleared up
 before testing and positive review can occur.  I don't see any of these as
 insurmountable.  However, I'm definitely removing the 'beginner' tag,
 given that this has become a more subtle ticket.

 First, there are still a fair number of typos, English issues like `every
 floating point evaluation of return` (which was in the original, not
 introduced by the author of the patch, but should be fixed), etc.   There
 should be better formatting (`Examples::` should be capitalized, for
 example), and hopefully links to the functions put in - see the plotting
 functions, especially plot.py, for examples of how to do that in Sphinx.

 > I would caution that for annoying reasons we like to have the lines in
 the documentation be fairly short; see some of the other calculus or
 plotting files for examples of about how many characters (80? 84?) are
 appropriate.  (Otherwise it looks really bad in command line.)  So any
 updates should fix that.

 This comment still applies.

 Another interesting thing is the use of `*args` and `**kwds`.  Really, we
 expect only a few cases of args, and only one keyword.  I think the syntax
 for this should be like for symbolic integrals, e.g.
 `f.integrate(algorithm="mathematica_free")` - that is to say, maybe it
 should be `algorithm` instead of `alg`.  Maybe even specifically check the
 args?  I don't know.

 The private function `_numerical_integral` needs documentation.

 {{{
 #This is so the old numerical_integral will still work
 }}}
 is not quite accurate, as it's doing more than that :)

 I'm not sure whether the Mma or sympy ones actually will return numerical
 values.  Also, one should doctest all those options.

 What is the idea with calling the other numerical integral (from Maxima)
 `_nintegral_sym`, since it's not symbolic?  Maybe I'm missing something.

 I think you now have `Note that in exotic cases` twice in the same
 docstring - is that correct?

 Anyway, all doable things, and the final produce will be quite valuable.

 (As a final comment, it would be worth seeing whether the issues at
 [http://ask.sagemath.org/question/95/numerical-integration-in-a-function
 this discussion] are solved with this ticket.  I don't believe so - since
 these integrals aren't made symbolic - but it's worth checking.)

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7763#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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