Euclidean 3-space: offer several flavours of spherical coordinates

[slel]

Spherical coordinates (r, theta, phi) involve one length coordinate r and two angle coordinates theta and phi, one representing longitude and varying in a length 2*pi interval, typically [0, 2*pi], the other representing latitude and varying in a length pi interval: either [0, pi] if the latitude is measured from one of the poles, or [-pi/2, pi/2] if the latitude is measured from the equator.

Sage's euclidean space has a spherical_coordinates method using pole-based latitude. Providing equator-based latitude would be a nice option.

Besides, the order of the angular coordinates could be customized.

Requested at

• Ask Sage question 56843: Differential forms on non-standard spherical coordinates

CC: @egourgoulhon @slel

Component: manifolds

Issue created by migration from https://trac.sagemath.org/ticket/31747

[egourgoulhon]

Description changed:

--- 
+++ 
@@ -12,6 +12,8 @@
 method using pole-based latitude. Providing
 equator-based latitude would be a nice option.

+Besides, the order of the angular coordinates could be customized.
+
 Requested at

 - [Ask Sage question 56843: Differential forms on non-standard spherical coordinates](https://ask.sagemath.org/question/56843)

[mjungmath]

comment:2

Possibly related: #30824