#18640: Topological manifolds: scalar fields
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Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-7.2
Component: geometry | Resolution:
Keywords: topological | Merged in:
manifolds | Reviewers:
Authors: Eric Gourgoulhon, | Work issues:
Michal Bejger | Commit:
Report Upstream: N/A | 3b92a85394e8fc6f7572c58d0a6ce8b1bebacce2
Branch: | Stopgaps:
public/manifolds/top_manif_scalar_fields|
Dependencies: #18529 |
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Comment (by tscrim):
Replying to [comment:29 egourgoulhon]:
> Replying to [comment:28 tscrim]:
> > - I am guessing there will eventually be another subclass of
`CoordFunction`? At present, there does not seem to be a reason to have an
ABC.
>
> Yes there will be other subclasses of `CoordFunction`: a major project
is to have a subclass for numerical functions, in order to deal with
numerical manifolds (for instance computer-generated spacetimes on a
grid). This was the very purpose for creating this ABC: it provides the
unique interface with the rest of tensor calculus on manifolds, factoring
out what has to be implemented by a concrete class (the abstract methods).
So I think it is important to maintain the ABC.
I guess what I am asking is how much of concrete class `CoordFunctionSym`
can be lifted to the ABC?
> > Moreover, you could probably make any numerical coordinate chart be
`._express` with the appropriate methods. However, I am wondering if there
should be a parent for `CoordFunction` (and have `CoordFunction` be a
subclass of `AlgebraElement`), which would allow you to not duplicate code
and use the coercion framework. Actually, perhaps `CoordFunction` should
be a subclass of `Morphism`.
>
> OK, I will give a try to this, introducing the proper algebra (no time
to do it right now, though...)
It should be a fairly small class; a parent that takes a chart as input. I
can work on this for my next commit.
> > - I understand why you want to put "the" in the string representations
(e.g., in `ScalarFieldAlgebra`) because it is how we would say it (in
English), but this breaks convention with other parts of Sage. Moreover,
it implies a certain amount of uniqueness to the manifold. However, there
could be 2 different manifolds with the same dimension, name, etc.
>
> Sorry, I am not sure I understand what you mean. Can you elaborate on
this?
When you say "the manifold," you are saying there is a unique manifold.
Context makes it clear exactly which manifold you're talking about (and
hence unique), but for something like documentation, "this manifold"
better defines what you are reference (although personally, I would just
replace it by {{{``self``}}}...).
> >The question becomes what to attach the global options to. I am
thinking `Manifold` (a function is a Python object too, so we can attach
data to it) and `TopologicalManifold`.
>
> `TopologicalManifold` sounds good, since this where the charts live in
the current approach.
I will do this on the next commit.
> > - There are failing doctests in `utilities.py` likely due to recent
changes in the symbolic function code (independent of my changes).
>
> Indeed this reflects some bug in the latest pynac (cf. #20456);
fortunately it is fixed by #20475; so if the latter is merged before the
current ticket, we can leave the doctests as they are.
So we will just watch what happens with #20475, which might means we need
to mark them as `# known bug` and revert them in #20475.
--
Ticket URL: <http://trac.sagemath.org/ticket/18640#comment:30>
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