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18640 Topological manifolds: scalar fields egourgoulhon egourgoulhon "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 metaticket #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`).
'''Documentation''':
The reference manual is produced by
`sage -docbuild reference/manifolds html`
It can also be accessed online at http://sagemanifolds.obspm.fr/doc/18640/reference/manifolds/
More documentation (e.g. example worksheets) can be found [http://sagemanifolds.obspm.fr/documentation.html here]." enhancement closed major sage-7.2 geometry fixed topological manifolds mbejger Eric Gourgoulhon, Michal Bejger, Travis Scrimshaw Travis Scrimshaw, Eric Gourgoulhon N/A 9ec7d3e4d636676e7091f6e7032f274853677418 9ec7d3e4d636676e7091f6e7032f274853677418 #18529