Let diff() act on chart functions and differentiable forms

[egourgoulhon]

In Sage 9.1, we have

sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = X.function(x^2*y)
sage: f.diff(x)
2*x*y
sage: diff(f, x)
...
NotImplementedError:

Similarly, if one tries to apply diff to get the exterior derivative of a differentiable form, one gets an error:

sage: a = M.one_form(-y, x)
sage: a.display()
-y dx + x dy
sage: diff(a)
...
TypeError: unable to convert 1-form on the 2-dimensional differentiable manifold M to a symbolic expression

With the code implemented in this ticket, we get

sage: diff(f, x)
2*x*y
sage: type(diff(f,x))
<class 'sage.manifolds.chart_func.ChartFunctionRing_with_category.element_class'>

and

sage: diff(a)
2-form on the 2-dimensional differentiable manifold M
sage: diff(a).display()
2 dx/\dy
sage: diff(a) is a.exterior_derivative()
True

To achieve this, the modification of the code reduces to

• rename ChartFunction.diff to ChartFunction.derivative, making diff an alias for the method derivative
• add the alias derivative for the method DiffForm.exterior_derivative
• add the alias derivative for the method DiffScalarField.differential

[egourgoulhon]

New commits:

​f5b9831

diff() acting on chart functions and differentiable forms

[tscrim]

LGTM.

[egourgoulhon]

Thank you for the review!