#18640: Topological manifolds: scalar fields
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Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: geometry | Keywords: topological
Merged in: | manifolds
Reviewers: | Authors: Eric Gourgoulhon,
Work issues: | Michal Bejger
Commit: | Report Upstream: N/A
e06598ef9c9e90fcc7fb88061862f476143f9bab| Branch:
Stopgaps: | public/manifolds/top_manif_scalar_fields
| Dependencies: #18529
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This ticket implements scalar fields on topological manifolds. This is a
follow up of ticket #18529 within the [http://sagemanifolds.obspm.fr/
SageManifolds project]. See the meta-ticket #18528 for an overview.
By ''scalar field'', it is meant a continuous map f: M --> K, where K is a
topological field and M a topological manifold over K.
This ticket implements the following Python classes:
- `CoordFunction`: abstract base class for coordinate functions, i.e.
functions
V\subset K^n^ --> K, where V is some chart codomain and n=dim(M)
- `CoordFunctionSymb`: symbolic coordinate functions
- `MultiCoordFunction`: functions V\subset K^n^ --> K^m^, where V is some
chart codomain and m some
positive integer
- `ScalarFieldAlgebra`: set C^0^(M) of scalar fields M --> K as a
commutative algebra over K
(Parent class)
- `ScalarField`: scalar field M --> K (Element class)
Internally, `ScalarField`'s are described by their coordinate
representations in various charts, which are implemented as a dictionary
of `CoordFunction`'s, with the charts as keys.
At the moment, there is only one concrete class for coordinate functions:
`CoordFunctionSymb` (functions described by symbolic expressions of the
coordinates), but in the future there should be numerical coordinate
functions (hence the abstract base class `CoordFunction`).
--
Ticket URL: <http://trac.sagemath.org/ticket/18640>
Sage <http://www.sagemath.org>
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