The inverse of the inverse should be self in CoordChange

[egourgoulhon]

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

[egourgoulhon]

Commit: 923196a

[egourgoulhon]

New commits:

923196a

#31923: initialize the inverse of the inverse to self

[egourgoulhon]

Branch: public/manifolds/transition_map_inverse-31923

[mjungmath]

comment:2

LGTM.

Green bot => Green light

[mjungmath]

Reviewer: Michael Jung

[egourgoulhon]

comment:3

Thank you for this superfast review!

[egourgoulhon]

comment:4

Replying to @mjungmath:

Green bot => Green light

Well, no bot at all... I wonder why no patchbot has visited this ticket after two days. Maybe they are super busy at the moment...

[mjungmath]

comment:5

Mh, indeed. :-/

Maybe you can push the changes into another branch again to trigger the patchbot?

[egourgoulhon]

Changed branch from public/manifolds/transition_map_inverse-31923 to public/manifolds/transition_map_inverse_of_inverse-31923

[egourgoulhon]

comment:7

Replying to @mjungmath:

Mh, indeed. :-/

Maybe you can push the changes into another branch again to trigger the patchbot?

Done. Let's see...

[tscrim]

comment:8

IMO, that won't change anything.

[egourgoulhon]

comment:9

The ticket appears now at the top of the list at https://patchbot.sagemath.org/, but the order in this list is probably just the last modification time and not the priority for patchbots.

[egourgoulhon]

comment:10

Replying to @tscrim:

IMO, that won't change anything.

You were right, Travis, as always ;-)

[slel]

comment:11

Patchbots seem to be having a hard time with #31928,
see #31928 comment:1.

[egourgoulhon]

comment:12

The patchbot came eventually and is morally green: it reports only one doctest failure in src/sage/misc/package.py, which is the issue mentioned by Samuel in comment:11 and is not connected with the current ticket.

[egourgoulhon]

comment:13

On behalf of Michael, in view of comment:4 and comment:12.

[mjungmath]

comment:14

Replying to @egourgoulhon:

On behalf of Michael, in view of comment:4 and comment:12.

thumbs up!

[vbraun]

Changed branch from public/manifolds/transition_map_inverse_of_inverse-31923 to 923196a