Customizing simplifications in symbolic calculus on manifolds

[egourgoulhon]

Currently the end user has no direct control of the simplification algorithm used in coordinate calculus on manifolds. For instance, if the manifold is real and the coordinate calculus method is Sage's default symbolic engine (SR), the simplifying function is ​simplify_chain_real. This function is quite exhaustive (similar to simplify_full()) but since it is invoked at each elementary step of a calculation, the computation can be quite slow. In some cases, it would be desirable to use a lighter simplifying function. See for instance ​this ask.sagemath question.

This ticket proposes some interface for passing any user-defined simplifying function. As an example, let us perform the addition of two scalar fields on a 2-dimensional real smooth manifold:

sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.scalar_field(cos(x)^2)
sage: g = M.scalar_field(sin(x)^2)
sage: s = f + g

Thanks to the use of simplify_chain_real in the _add_ operator, the result is automatically simplified:

sage: s.display()
M --> R
(x, y) |--> 1

With the code indroduce in this ticket, one can replace simplify_chain_real by any function, for instance Sage's simplify:

sage: M.set_simplify_function(simplify)
sage: s = f + g
sage: s.display()
M --> R
(x, y) |--> cos(x)^2 + sin(x)^2

As we can see, the capabilities of simplify are quite limited! Let us replace it by a user-defined function:

sage: def simpl(expr):
....:     return expr.simplify_trig()
....: 
sage: M.set_simplify_function(simpl)
sage: s = f + g
sage: s.display()
M --> R
(x, y) |--> 1

For more flexibility, it is possible to provide a different simplifying function for each chart on the manifold, via

sage: X.calculcus_method().set_simplify_function(simpl)

Besides, this ticket improves the documentation and functionalities of the class ​CalculusMethod, which governs the various symbolic backends available on manifolds (SR and SymPy at the moment).

[egourgoulhon]

New commits:

​9b16e40	Add possibility to custom the simplification algorithm in coordinate calculus on manifolds
​80b87d8	Minor cleaning (flake8) in the code for customized simplifications on manifolds

[tscrim]

LGTM.

[egourgoulhon]

Thank you for the review!