[with patch, positive review] Vectors of callable things should be callable

[jwmerrill]

The motivation here is being able to evaluate the gradient of a function at a point.

The desired behavior is
    sage: x, y = var('x, y')
    sage: f = x^2 + y^2
    sage: g = f.gradient()
    sage: g(x=3,y=2)
    (6,4)

Currently, however
    sage: g(x=3,y=2)
    Traceback (most recent call last):
    ...
    TypeError:
    'sage.modules.free_module_element.FreeModuleElement_generic_dense'
    object is not callable

Calls should also work for a vector of callable symbolic expressions.
Note that the gradient part will only work once #2547 is applied.
    sage: f(x,y) = x^2 + y^2
    sage: g = f.gradient()
    sage: g(3,2)
    (6,4)
    sage: g(y=2,x=3)
    (6,4)
}}

[jwmerrill]

The attached patch solves all the cases above except the last, which returns

sage: g(y=2,x=3)
Traceback (most recent call last):
...
TypeError: __call__() got an unexpected keyword argument 'y'

Not sure what the deal is with that.

This patch should only be applied after #2547.

[jwmerrill]

After applying #4031, the patch here gives the desired behavior.

[mabshoff]

Jason,

please assign a milestone to new tickets. The next release is usually the right choice.

Cheers,

Michael

[mhansen]

Looks good to me. Apply only after #4031.

[jwmerrill]

Just to be clear, both #2547 and #4031 should be applied before this patch. The functionality doesn't depend on #2547, but the doctests do.

[mabshoff]

Merged in Sage 3.1.2.alpha4