Improve accuracy of polytopes.regular_polygon()

[jdemeyer]

The function polytopes.regular_polygon() uses a hard-coded approximation of pi (3.14159265359) which has an error of 466 ulp. Moreover, it uses Python floats instead of RR.

Note: there are actually a lot of these fishy approximations (like QQ(1618033)/1000000 for the golden ratio). Since this ticket is intended to avoid a doctest failure in #17130, I only fixed regular_polygon().

Component: geometry

Author: Jeroen Demeyer

Branch/Commit: 0001941

Reviewer: Volker Braun

Issue created by migration from https://trac.sagemath.org/ticket/17131

[jdemeyer]

Branch: u/jdemeyer/ticket/17131

[jdemeyer]

Author: Jeroen Demeyer

[jdemeyer]

New commits:

0001941

Improve accuracy of polytopes.regular_polygon()

[jdemeyer]

Commit: 0001941

[jdemeyer]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
-The function `polytopes.regular_polygon()` uses a hard-coded approximation of `pi` (3.14159265359) which has an error of 466 ulp. Moreover, it uses Python `float`s instead of `RR`, which breaks a doctest in #17130.
+The function `polytopes.regular_polygon()` uses a hard-coded approximation of `pi` (3.14159265359) which has an error of 466 ulp. Moreover, it uses Python `float`s instead of `RR`.
+
+Note: there are actually a lot of these fishy approximations (like `QQ(1618033)/1000000` for the golden ratio). Since this ticket is intended to avoid a doctest failure in #17130, I only fixed `regular_polygon()`.

[vbraun]

Reviewer: Volker Braun

[vbraun]

comment:4

Yes, this is all ancient cruft...

[vbraun]

Changed branch from u/jdemeyer/ticket/17131 to 0001941