#18640: Topological manifolds: scalar fields
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: geometry | Resolution:
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 |
-------------------------------------+-------------------------------------
Description changed by egourgoulhon:
Old description:
> 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`).
New description:
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)
- `ExpressionNice`: a subclass of `sage.symbolic.expression.Expression`
with enhanced display of callable symbolic expressions
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`).
--
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Ticket URL: <http://trac.sagemath.org/ticket/18640#comment:1>
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