This is not what you are proposing but somehow related to it: provided you
consider (x,y) as coordinates on a manifold, you may define g as a named
function as follows:
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart() # declares the chart X on M, with coordinates
(x,y)
sage: g = M.scalar_field(x+sin(y), name='g')
sage: g.display()
g: M --> R
(x, y) |--> x + sin(y)
Then you may use the function set_name to change the name of g:
sage: g.set_name('G')
sage: g.display()
G: M --> R
(x, y) |--> x + sin(y)
You can also set the LaTeX display of g:
sage: g.set_name('G', latex_name=r'\mathcal{G}')
A difference with callable symbolic expressions is that you cannot call
directly g on a pair of coordinates, i.e. write g(1,2), but have to go
through the manifold point corresponding to these coordinates, i.e.
M((1,2)) (in the present case, there is no need to specify the chart to
which the coordinates belong, since only one chart has been declared;
otherwise, one should declare the point as M((1,2), chart=X)). Hence
sage: g(M((1,2)))
sin(2) + 1
Another difference regards derivatives: the scalar function g has no diff()
method, but it has a differential:
sage: g.differential().display()
dG = dx + cos(y) dy
and you can get the two partial derivatives via
sage: g.differential()[:]
[1, cos(y)]
Best wishes,
Eric.
PS: a big +1 to Paul's suggestion of turning the very nice answer of Nils
into a proper documentation.
Le dimanche 19 mars 2017 08:54:34 UTC+1, Aidan a écrit :
>
>
> I wrote some code
> <https://gist.github.com/aijony/8675b9b348a7c510d634f768d5ad7e8e> I would
> like to contribute, but I don't know the most appropriate place to put it.
>
>
>
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