This ticket implements some improvements regarding integrated curves on manifolds, first appearing in #22951.

It adds scipy.integrate.ode as an integration solver. The main advantage is that it supports basic event handling, making it possible to detect frontiers of charts. This allows for integration on multiple charts, as shown in this notebook, which can be particularly useful to avoid singularities, or in manifold which cannot be represented by a single chart, like in this one (not commented).

A side effect of this new method is that the time needed for the integration can be reduced (a lot!) by using objects created with fast_callable instead of symbolic expressions. This is used in this notebook to compute the shape of a geodesic in a Kerr spacetime. Speed test shows a x700 speedup compared to the default integration method "rk4_maxima".

CC: @egourgoulhon @sagetrac-karimvanaelst

Component: geometry

Keywords: geodesic, integrated curve, integration, chart

Author: Florentin Jaffredo

Branch/Commit: 61061c1

Reviewer: Travis Scrimshaw, Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/25936