#6648: adds riemann mapping and complex interpolation
---------------------------+------------------------------------------------
   Reporter:  evanandel    |       Owner:  evanandel                            
         
       Type:  enhancement  |      Status:  needs_work                           
         
   Priority:  major        |   Milestone:  sage-4.3                             
         
  Component:  calculus     |    Keywords:  complex                              
         
Work_issues:               |      Author:  Ethan Van Andel                      
         
   Upstream:  N/A          |    Reviewer:  David Joyner, Martin Albrecht, Minh 
Van Nguyen
     Merged:               |  
---------------------------+------------------------------------------------
Changes (by mvngu):

  * reviewer:  => David Joyner, Martin Albrecht, Minh Van Nguyen
  * upstream:  => N/A


Comment:

 '''Referee Report'''
 [[BR]]

 I have attached the reviewer patch `trac_6648-reviewer.patch`. My changes
 include:

  1. Proper ReST formatting to resolve dozens of warnings when building the
 HTML version of the reference manual.
  1. Fix various typos.
  1. Some formatting of the docstrings to keep them less than 80 characters
 wide. Beyond 80 characters, the docstring can be difficult to read from
 the command line interface.
  1. Proper formatting of code so it conforms to Python coding conventions
 as covered in the [http://www.sagemath.org/doc/developer/conventions.html
 #python-coding-conventions Developers' Guide].
  1. In the file `sage/calculus/riemann.pyx`, don't redefine `xrange`,
 which is a built-in command of Python. Instead, define `x_range` and
 similarly define `y_range`. Also, don't use the name `list` as a parameter
 to the function `comp_pt()` because `list` is the name of the Python
 function for creating a list data structure. I have changed it to `clist`
 instead.
  1. For the file `sage/calculus/riemann.pyx`, in the `__init__()` method
 of the class `Riemann_Map`, I changed the test
  {{{
 if <= 2:
     ...
  }}}
  to raise an exception instead. That is, if the number of collocations
 points is less than 3, then you don't want to proceed any further with
 initializing the `Riemann_Map` object.


 You should apply patches in this order:

  1. `12659.5.patch`
  1. `12660.patch`
  1. `trac_6648-reviewer.patch`

 The reviewer patch should resolve doctest failures and reference manual
 build warnings that I reported above. So my patch needs some reviewing.
 Also, here are some required changes once patches are applied in the above
 order:

  1. In the file `sage/calculus/riemann.pyx`, you need to explain what the
 function `_render_on_subplot` does.
  1. Also, you need to explain the purpose of the class `ColorPlot` and
 provide examples in the docstring of that class.
  1. In the file `sage/calculus/interpolators.pyx`, explain the purpose of
 the class `PSpline` and provide examples in the docstring of that class.
  1. Explain the purpose of the class `CCSpline` and provide examples in
 its docstring.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6648#comment:24>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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