fix bugs in is_prime

[williamstein]

This is not good:

sage: is_prime(GF(5)(3))
True
sage: is_prime(GF(5)(4))
False

The fix is to totally 100% rewrite is_prime in arith.py so that it first calls x.is_prime() and if that isn't defined, then in some special cases (e.g., python ints) converts to Integer and calls is_prime. Otherwise, it raises a NotImplementedError.

Component: number theory

Author: Kevin Stueve

Reviewer: Sebastian Pancratz

Merged: sage-4.3.1.rc1

Issue created by migration from https://trac.sagemath.org/ticket/5496

[sagetrac-kevin-stueve]

comment:1

Right now finite fields don't seem to have an is_prime function, so I believe that currently, is_prime(GF(5)(3)) should raise NotImplementedError. I'm going to try to fix is_prime so that it raises NotImplementedError for is_prime(GF(5)(3)).

Kevin Stueve

[sagetrac-kevin-stueve]

Attachment: 5496.patch.gz

changed delegation of is_prime calculation to n.is_prime()

[sagetrac-kevin-stueve]

Attachment: 5496.2.patch.gz

[sagetrac-kevin-stueve]

comment:4

Apply only 5496.2.patch.

[sagetrac-spancratz]

Three small changes throughout the Sage library

[sagetrac-spancratz]

Attachment: trac5496_rationals_to_int.patch.gz

Attachment: trac5496_symbolic_expressions.patch.gz

Second addendum, for symbolic expressions

[sagetrac-spancratz]

Reviewer: spancratz

[sagetrac-spancratz]

comment:5

Applying Kevin's second patch 5496.2.patch and the two small changes I added, this now passes all doctests done with sage -t devel/sage/sage, and can get a positive review.