Open mkoeppe opened 3 years ago
Should ManifoldPoint.add_coordinates
canonicalize the coordinates?
Or should ManifoldPoint.coordinates
do this?
Replying to @egourgoulhon:
Just a word of context about periodic charts: they have been introduced because they are useful when computing a geodesic with some numerical integrator. Typically, when the geodesic is an orbit around some center, the azimuthal coordinate returned by the integrator increases without any bound, instead of being confined to [0, 2\pi). Here are some examples in Kerr spacetime.
I'm sorry. What is the punchline here?
Just forget what I just said. It didn't make sense. Sorry.
Replying to @egourgoulhon:
W.l.o.g. we can always choose the minimum/maximum the chart maps to?
What do you mean?
What we can do is that the user has to state the fundamental domain (which currently happens up to boundary only). Or we provide which boundary component belongs to the fundamental domain (I opt for the lower bound). Then it is clear which points the section map has to map to.
For the 1-sphere this could be for example the clopen interval [-pi,pi)
. Then it becomes clear that the point on the 1-sphere determined by pi
is mapped to -pi
via the (section) chart. Similarly then for any other point.
The only obstruction I see right now is that the symbolic ring doesn't provide any modulo operation in the spirit of x - y*floor(x/y)
. Or does it?
Replying to @mjungmath:
the symbolic ring doesn't provide any modulo operation in the spirit of
x - y*floor(x/y)
.
That's right - this is #25644
Setting a new milestone for this ticket based on a cursory review.
Replying to @mjungmath:
Replying to @egourgoulhon:
Just a word of context about periodic charts: they have been introduced because they are useful when computing a geodesic with some numerical integrator. Typically, when the geodesic is an orbit around some center, the azimuthal coordinate returned by the integrator increases without any bound, instead of being confined to [0, 2\pi). Here are some examples in Kerr spacetime.
I'm sorry. What is the punchline here?
Periodic charts are useful in practice. Otherwise, we could have lived without them, sticking to the standard definition of a chart on a manifold.
I guess then, this ticket depends on #25644...
Changed dependencies from #32009, #32116, #32089, #32102 to #32009, #32116, #32089, #32102, #25644
Replying to @egourgoulhon:
I'm sorry. What is the punchline here?
Periodic charts are useful in practice. Otherwise, we could have lived without them, sticking to the standard definition of a chart on a manifold.
Thank you. It's clear now. It was my fault yesterday...
Currently:
A
Chart
instance (with non-periodic coordinates) is a continuous map from its domain toR^n
. This should be reflected in the category.With this ticket:
Also:
To put the map in a better category than
Sets
will need some follow-up tickets.Depends on #32009 Depends on #32116 Depends on #32089 Depends on #32102 Depends on #25644
CC: @egourgoulhon @tscrim @mjungmath
Component: manifolds
Author: Matthias Koeppe
Branch/Commit: u/mkoeppe/refine_categories_of_chart_objects__add_method_codomain @
89039b2
Issue created by migration from https://trac.sagemath.org/ticket/31894