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

[mjungmath]

comment:2

Possibly related: #30824