FractionFieldElement lacks derivative method

[burcin]

Attached patch adds a derivative method to FractionFieldElements, and fixes a bug in the _derivative method of Polynomial_rational_dense.

So these now work:

sage: R = ZZ['x']
sage: S = R.fraction_field(); x = S.gen()
sage: R(1).derivative(R(x))
0

sage: F = FractionField(PolynomialRing(RationalField(),'x,y'))
sage: x,y = F.gens()
sage: (1/(x+y)).derivative(x,y)
2/(x^3 + 3*x^2*y + 3*x*y^2 + y^3)

Component: basic arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/2545

[burcin]

derivative method for FractionFieldElement

[aghitza]

comment:1

Attachment: sage_fraction_field_derivative.patch.gz

This appears to work as advertised. I have one request: the docstrings for derivative() and _derivative() refer to "the derivative of this polynomial", which is bad since these elements are (most of the time) not polynomials. This should be replaced with "rational function" or something similar.

[burcin]

new patch with requested doc changes

[burcin]

comment:2

Attachment: 2545-sage_fraction_field_derivative-1.patch.gz

You're right, I copied the text from the docstring for polynomials, and forgot to change it. :)

attachment: 2545-sage_fraction_field_derivative-1.patch replaces "polynomial" with "rational function" as suggested.

[aghitza]

comment:3

Cool. I'm satisfied.

[sagetrac-mabshoff]

comment:4

Merged in Sage 2.11.alpha0