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In Sage 8.9, we have:
sage: E.<r,phi> = EuclideanSpace(coordinates='polar')
sage: p = E((1, 0)) # the initial point
sage: v = E.tangent_space(p)((2, 1)) # the initial vector
sage: t = var('t')
sage: c = E.integrated_geodesic(E.metric(), (t, 0, 10), v)
...
ValueError: initial point should be in the domain of the chart
Now, the initial point p does lie in the domain of the chart:
sage: E.default_chart()(p)
(1, 0)
Indeed, 0 is a perfectly valid value for the polar coordinate phi:
sage: E.default_chart().coord_range()
r: (0, +oo); phi: [0, 2*pi] (periodic)
The above error turns out to result from a too strict and unnecessary coordinate check performed in IntegratedCurve.__init__(). This check is removed here.
CC: @sagetrac-karimvanaelst
Component: geometry
Keywords: integrated_curve, geodesic
Author: Eric Gourgoulhon
Branch/Commit: c0efb2e
Reviewer: Karim Van Aelst
Issue created by migration from https://trac.sagemath.org/ticket/28669