real nth root function

[burcin]

See sage-devel threads at:

http://groups.google.com/group/sage-devel/t/cea9b562ea49c9c1

and

https://groups.google.com/forum/#!topic/sage-devel/Q8VLKBypcJk

CC: @orlitzky @kcrisman karsten.naert@gmail.com @eviatarbach @slel

Component: symbolics

Author: Burcin Erocal, Kwankyu Lee

Branch: f8cb7a0

Reviewer: Karl-Dieter Crisman, Nils Bruin, Kwankyu Lee

Issue created by migration from https://trac.sagemath.org/ticket/12074

[burcin]

Work Issues: needs tests and documentation

[jdemeyer]

comment:2

Is there any chance this could be made into a function that we can do calculus with, like computing derivatives, integrals, solving equations... (I'm afraid the answer will be no though because we need maxima).

[burcin]

comment:3

Attachment: trac_12074-nth_root.patch.gz

Replying to @jdemeyer:

Is there any chance this could be made into a function that we can do calculus with, like computing derivatives, integrals, solving equations... (I'm afraid the answer will be no though because we need maxima).

This is already a symbolic function, so it plays well with symbolics generally (as opposed to piecewise functions for instance):

sage: v = nth_root(x,3)
sage: v*sin(x) + x^2
x^2 + real_nth_root(x, 3)*sin(x)

I updated the patch to add custom exponentiation and derivative methods as well:

sage: v^2
real_nth_root(x, 3/2)
sage: v*v
real_nth_root(x, 3/2)
sage: v.diff(x)
1/3*real_nth_root(x, -3/2)

This all needs a lot of work of course.

For integration and solving equations we call out to maxima. One way to get sensible results from these calls would be to convert this function to a regular (base)^(exp) representation when passing it to maxima. I don't think there is any way to read it back from the maxima result though.