Integer and Rational classes need nth_root and exact_power functions

[sagetrac-dmharvey]

It would be useful for Integer and Rational classes to have:

(1) nth_root: this would wrap GMP's mpz_root.
(2) exact_power: would accept a rational number as an index, and work out which root to take. For example

(-8/27).exact_power(2/3) == 4/9

I had to take an exact 6th root of a rational in some code the other day and it was painful going via real numbers, worrying about bits of precision and all that.

Component: basic arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/8

[sagetrac-dmharvey]

comment:1

Fixed.

Fri Sep 15 17:19:10 PDT 2006 dmharvey@math.harvard.edu

• Rational.nth_root() -- adds Rational nth root method

Fri Sep 15 17:18:20 PDT 2006 dmharvey@math.harvard.edu

• Integer.nth_root() -- adds nth root method to Integer (wraps GMP mpz_root)