Opened 9 years ago

Last modified 8 years ago

#10945 closed defect

Fix lots of minor docs and redundancy for riemann.pyx — at Version 3

Reported by: kcrisman Owned by: burcin
Priority: minor Milestone: sage-duplicate/invalid/wontfix
Component: calculus Keywords: riemann map complex plot
Cc: evanandel, jason, wdj, mvngu Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description (last modified by kcrisman)

The Riemann mapping stuff is a great addition - excellent work!

But there are lots of minor problems that should be fixed. Here are some. Closing this ticket wouldn't require fixing them all, but if not, then explanations should be provided here and followup tickets (if needed) opened.

  • Awkward phrasing:
        Note that all the methods are numeric rather than analytic, for unusual
        regions or insufficient collocation points may give very inaccurate
        results.
    
    This is hard to follow, though I see what it says.
  • There is also a 'reimann' several times, and a 'correspondance'.
  • A lot of the code is redundant with plot/complex_plot.pyx. This should be factored out somehow, or imported, or whatever, unless it would lead to gross slowdowns.
    • Is there anything different about complex_to_rgb except that it's cdef'd (and the changes needed for that, including some efficiencies like the phase command)?
    • Similarly, the ColorPlot class is apparently identical to the ComplexPlot class, except that it's better documented, uses only the default interpolation, and won't take options.
    • Note that the documentation for ColorPlot only uses complex_plot!!! I view this as an error by mvngu and wdj in reviewing #6648, though that was a long review process so it's easy to see how it slipped through.
  • This also seems to have a transposition in how it's put in. Presumably the redefinition of I is supposed to demonstrate it works with lots of different complex types. I suggest the following.
            Can work for different types of complex numbers::
    
                sage: m = Riemann_Map([lambda t: e^(I*t) - 0.5*e^(-I*t)], [lambda t: I*e^(I*t) + 0.5*I*e^(-I*t)], 0)  # long time (4 sec)
                sage: m.riemann_map(0.25 + sqrt(-0.5))  # long time
                (0.137514137885...+0.876696023004...j)
    +            sage: I = CDF.gen()  # long time
                sage: m.riemann_map(1.3*I)  # long time
                (-1.561029396...+0.989694535737...j)
    -            sage: I = CDF.gen()  # long time
                sage: m.riemann_map(0.4)  # long time
    
  • Add a few analytic examples as mentioned at #10792.
  • Add any information at all about theoretical error bounds, if known. Since not everyone will be able to just look up that paper referenced, it would be helpful to have at least order of magnitude ideas (e.g., if N=2000 on a map from the unit circle to itself, we expect errors no greater than epsilon=blah).

Change History (3)

comment:1 Changed 9 years ago by kcrisman

  • Description modified (diff)

comment:2 Changed 9 years ago by kcrisman

  • Description modified (diff)

comment:3 Changed 9 years ago by kcrisman

  • Description modified (diff)
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