#11273: Riemann Enhancements: Docs, Exterior, Multiple Spiderweb, Error Testing
-------------------------+-------------------------------------------------
Reporter: | Owner: burcin
evanandel | Status: needs_review
Type: | Milestone: sage-5.13
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers: Burcin Erocal, Karl-Dieter
calculus | Crisman
Keywords: | Work issues:
riemann map | Commit:
Authors: Ethan | Stopgaps:
Van Andel |
Report Upstream: N/A |
Branch: |
Dependencies: |
-------------------------+-------------------------------------------------
Changes (by evanandel):
* status: needs_info => needs_review
Old description:
> This is a major upgrade of the riemann module. Features are:
>
> Fixes and expansions to the docs, covering the issues in #10945.
>
> I've added some test methods that compute the explicit map of an ellipse
> to a high degree of accuracy. The doctests for these methods contain
> tests that show that the numerical Riemann_Map values remain accurate.
> The precision of the normal doctests has been reduced accordingly, so
> hopefully they will no longer fail for different architectures/numpy
> versions. This covers #10957
>
> The exterior Riemann map can now be computed, that is a conformal mapping
> of the exterior of a region to the exterior of the unit circle. The docs
> specify how this may be done.
>
> I've added support for computing the spiderweb plot for multiply
> connected domains. This uses a different method than the simply connected
> spiderweb and is takes about the same time as a color plot of the same
> resolution. (It's worth noting that I don't think this has ever been done
> before.)
>
> I've also fiddled around under the hood, cleaning up some code, moving
> things around for more efficiency and trying to add a few more helpful
> inline comments.
>
> ----
>
> Apply [attachment:trac_11273-rebase-part1.patch], [attachment:trac_11273
> -rebase-part2.patch], [attachment:trac_11273-rebase-part3.patch],
> [attachment:trac_11273-reviewer.patch], and
> [attachment:trac_11273-fix.patch].
New description:
This is a major upgrade of the riemann module. Features are:
Fixes and expansions to the docs, covering the issues in #10945.
I've added some test methods that compute the explicit map of an ellipse
to a high degree of accuracy. The doctests for these methods contain tests
that show that the numerical Riemann_Map values remain accurate. The
precision of the normal doctests has been reduced accordingly, so
hopefully they will no longer fail for different architectures/numpy
versions. This covers #10957
The exterior Riemann map can now be computed, that is a conformal mapping
of the exterior of a region to the exterior of the unit circle. The docs
specify how this may be done.
I've added support for computing the spiderweb plot for multiply connected
domains. This uses a different method than the simply connected spiderweb
and is takes about the same time as a color plot of the same resolution.
(It's worth noting that I don't think this has ever been done before.)
I've also fiddled around under the hood, cleaning up some code, moving
things around for more efficiency and trying to add a few more helpful
inline comments.
----
Apply [attachment:trac_11273-rebase-part1.patch], [attachment:trac_11273
-rebase-part2.patch], [attachment:trac_11273-rebase-part3.patch],
[attachment:trac_11273-reviewer.patch], [attachment:trac_11273-fix.patch],
and [attachment:trac_11273_multi_web_fix.patch].
--
Comment:
It seems that for some domains, particularly those with corners, the
numerical integration outside the corners is bad enough to cause "bleed"
so that the value outside the domain is farther from zero than desirable.
This meant that those portions were escaping the normal check to not draw
external lines.
I've made the cutoff a parameter (min_mag) so that the user can make it
higher if they're observing lines outside the domain. The only trade-off
is that the lines will stop slightly farther from the "centers" of the
domain. There is a doctest illustrating the increased cutoff.
At the request of the reviewer in correspondence, I've also added a fun
example to the top level doctests.
--
Ticket URL: <http://trac.sagemath.org/ticket/11273#comment:31>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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