polar coordinates

Stream: maths

[Patrick Massot]

@Sebastien Gouezel how hard do you think it would be to go from docs#measure_theory.integral_image_eq_integral_abs_det_fderiv_smul to the special case of polar (or spherical) coordinates? It would be nice to remove these items from the undergrad todo list.

[Sebastien Gouezel]

At least in the complex plane, I think it shouldn't be hard, but it would probably reveal some API holes. Unfortunately, I don't have time for it currently -- it would be a nice student project! In higher dimension, it looks more complicated to formulate because we don't have Lebesgue measure on the sphere, as far as I can tell.

[Heather Macbeth]

We could give it Hausdorff measure.

[Sebastien Gouezel]

Yes, but the change of variables formula is currently formulated for functions from one vector space to the same vector space (because otherwise you don't have a determinant), so this looks like a can of worms :-)

[Heather Macbeth]

Ah! I should look closely at the change of variables formula!

[Patrick Massot]

Sébastien, yes I'm hoping some student could do it. I wasn't suggesting you should do it.

[Patrick Massot]

About spheres, I meant spherical coordinates on ℝ³ not on the sphere.