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

CC: @tscrim

Component: geometry

Author: Eric Gourgoulhon

Branch/Commit: f5b9831

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/29953

[egourgoulhon]

Branch: public/manifolds/diff_functions_forms

[egourgoulhon]

New commits:

f5b9831

diff() acting on chart functions and differentiable forms

[egourgoulhon]

Commit: f5b9831

[egourgoulhon]

Description changed:

--- 
+++ 
@@ -39,4 +39,7 @@
 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`

[tscrim]

comment:3

LGTM.

[tscrim]

Reviewer: Travis Scrimshaw

[egourgoulhon]

comment:4

Thank you for the review!

[vbraun]

Changed branch from public/manifolds/diff_functions_forms to f5b9831