Allow for coordinate changes in curve plots

[egourgoulhon]

In Sage 9.5.beta2, the following attempt to plot a cardioid fails:

sage: E.<r,ph> = EuclideanSpace(coordinates='polar')
sage: c = E.curve((1 + cos(ph), ph), (ph, 0, 2*pi))
sage: c.plot(chart=E.cartesian_coordinates())
...
ValueError: No expression has been found for Curve in the Euclidean plane E^2
 in terms of Chart (E^2, (x, y))

This is because the curve c is known only in polar coordinates and no attempt is made to compute its expression in terms of Cartesian coordinates. Forcing the latter computation by e.g.

sage: c.display(chart2=E.cartesian_coordinates())

before invoking c.plot(chart=E.cartesian_coordinates()) makes things work.

In the current ticket, the method plot is modified, so that the expression in the coordinates specified by the argument chart is computed by means of ContinuousMap.coord_functions. Moreover, this simplifies significantly the code of DifferentiableCurve.plot.

CC: @tscrim @mjungmath @mkoeppe

Component: manifolds

Keywords: curve, plot

Author: Eric Gourgoulhon

Branch/Commit: 5ac0f28

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/32578

[egourgoulhon]

Branch: public/manifolds/curve_plot-32578

[egourgoulhon]

New commits:

5ac0f28

Allow for coordinate changes in curve plots (Trac #32578)

[egourgoulhon]

Commit: 5ac0f28

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:2

LGTM.

[egourgoulhon]

comment:3

Thank you for the review!

[vbraun]

Changed branch from public/manifolds/curve_plot-32578 to 5ac0f28