#19957: Asymptotic ring: list plot comparing values
-------------------------------------+-------------------------------------
       Reporter:  cheuberg           |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-7.1
      Component:  asymptotic         |   Resolution:
  expansions                         |    Merged in:
       Keywords:                     |    Reviewers:
        Authors:  Benjamin Hackl,    |  Work issues:
  Clemens Heuberger                  |       Commit:
Report Upstream:  N/A                |  5b20379b8dafbf0467eb040d55bc0d857f2a1ea3
         Branch:  u/behackl/asy      |     Stopgaps:
  /compare-with-values               |
   Dependencies:  #19931             |
-------------------------------------+-------------------------------------
Changes (by {'newvalue': u'Benjamin Hackl, Clemens Heuberger', 'oldvalue': 
u'Clemens Heuberger'}):

 * status:  needs_info => needs_review
 * commit:  fd6b4ec75f7917d326c3c1e4ab5b1f2b715a6c95 =>
     5b20379b8dafbf0467eb040d55bc0d857f2a1ea3
 * branch:  u/cheuberg/asy/commpare-with-values => u/behackl/asy/compare-
     with-values
 * author:  Clemens Heuberger => Benjamin Hackl, Clemens Heuberger


Comment:

 Replying to [comment:7 cheuberg]:
 > > - should there be a keyword `scaled=True` with which the division by
 the error term can be controlled?
 >
 > what would `scaled=True` and `scaled=False` do?

 Plot the relative and the absolute error, respectively. Sometimes I like
 to look at both.

 >
 > > - what do you think of a `PLOTS::`-section for the documentation?
 >
 > Within a finite amount of time, I could not get it to work. In any case,
 this is distinct from doctesting; thus one would have to repeat all
 commands to generate the plot. Sage preparsing apparently does not work
 here. Then I got a strange error message.
 >

 I couldn't get it to work either: some strange error regarding coercion of
 a function to `SR` occurrs...

 > For doctests, I rather think that we might want to output the list
 itself instead of the list plot, perhaps already piped through `RIF` or
 something like that. That would make useful doctests (and could be used
 throughout the modules during review phases). Thus there could be a flag
 `return_list=True` or something like that (or a separate method computing
 the list which could be used in this method here ...).

 I've implemented parts of this: there are now two methods; one for
 computing the list of differences and one for actually plotting. Also, for
 the sake of convenience, I've added the option to input a symbolic
 expression containing at most one variable.

 Regarding the output: while I'd really like to have RIFs in the output of
 the difference method, unfortunately this causes problems for `list_plot`,
 e.g. try
 {{{
 sage: list_plot([(k, RIF(sqrt(k))) for k in srange(10)])
 }}}
 If the difference should lie in a RIF, the list would have to be processed
 again before plotting.

 Opinions?
 ----
 New commits:
 
||[http://git.sagemath.org/sage.git/commit/?id=83125aa065b7dc7c5f0e2bd5d18f684b3e81c6c9
 83125aa]||{{{let compare_with_values return a list of tuples}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=85bf9a04e78124afb27bac5733dc50354f816eed
 85bf9a0]||{{{add rescaled-parameter}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=d1105800bb03becdac4d6dbbe97a2640000d18fe
 d110580]||{{{allow symbolic arguments for values}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=b09ae927e5fc9da867b8239f1a96ff09e2a09fad
 b09ae92]||{{{improve doctests with shorter workaround}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=5b20379b8dafbf0467eb040d55bc0d857f2a1ea3
 5b20379]||{{{add plot_comparison method}}}||

--
Ticket URL: <http://trac.sagemath.org/ticket/19957#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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