The inverse of the inverse should be self in CoordChange #31923
Description
When initializing the inverse of a transition map between two charts, either by the method CoordChange.inverse (computation of the inverse) or by CoordChange.set_inverse (inverse provided by the user), the attribute _inverse of self is set to the inverse object (for caching). Obviously, by symmetry, the attribute _inverse of the inverse should be set to self, but it is not. As a consequence, we have in Sage 9.3:
sage: E.<x,y> = EuclideanSpace()
sage: cart = E.cartesian_coordinates()
sage: polar = E.polar_coordinates()
sage: polar_to_cart = E.coord_change(polar, cart)
sage: polar_to_cart.display()
x = r*cos(ph)
y = r*sin(ph)
sage: cart_to_polar = E.coord_change(cart, polar)
sage: cart_to_polar.display()
r = sqrt(x^2 + y^2)
ph = arctan2(y, x)
sage: polar_to_cart.inverse() is cart_to_polar
True
So far so good, but
sage: cart_to_polar.inverse() is polar_to_cart
...
ValueError: no solution found; use set_inverse() to set the inverse manually
This is fixed in this ticket by the following one-line addition to the code of CoordChange.inverse and CoordChange.set_inverse:
self._inverse._inverse = self
Besides, this ticket improves a little bit the documentation of CoordChange.inverse.
CC: @tscrim @mjungmath @mkoeppe
Component: manifolds
Keywords: chart, transition_map
Author: Eric Gourgoulhon
Branch/Commit: 923196a
Reviewer: Michael Jung
Issue created by migration from https://trac.sagemath.org/ticket/31923