is_prime_power fails on powers of 30011

[jpflori]

Playing with finite fields on Sage 6.10 or 7.0:

GF(30011**(19*3), name='z')
...
ValueError: the order of a finite field must be a prime power

Apparently is_prime_power returns False for that cardinality.

PARI bug report:
http://pari.math.u-bordeaux.fr/cgi-bin/bugreport.cgi?bug=1782

Tarball: http://sage.ugent.be/www/jdemeyer/sage/pari-2.8-2341-g61b65cc.tar.gz

Upstream: Fixed upstream, but not in a stable release.

CC: @videlec

Component: basic arithmetic

Author: Jeroen Demeyer

Branch/Commit: 9c5d20c

Reviewer: Jean-Pierre Flori

Issue created by migration from https://trac.sagemath.org/ticket/20025

[nathanncohen]

comment:1

:-P

sage: print [i for i in range(1,100) if not is_prime_power(30011**i)]
[22, 26, 33, 34, 38, 39, 44, 46, 51, 52, 55, 57, 58, 62, 65, 66, 68, 69, 74, 76, 77, 78, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 99]

[jpflori]

comment:2

Thanks, I was building the latest beta to see if the PARI update changed anything (though I could not say at this point if PARI is involved).
It seems its not the case.

[nathanncohen]

comment:3

Funny

sage: set([p for i in range(1,100) for p in primes(200000) if not is_prime_power(p**i)])
{30011}

[jpflori]

comment:4

So it is an issue in the PARI versions we ship (at least the one in 7.0):

? isprimepower(30011^(17*3))
OddPwrs: examining 758-bit integer
OddPwrs: examining 252-bit integer

OddPwrs: not a power
Z_isanypower: now k=3, x=252-bit

OddPwrs: [17] passed modular checks
%1 = 0

[jpflori]

comment:5

I attempted to send a bug report upstream.
If it appears on their bugtracker, I'll report here.

[jpflori]

Upstream: Reported upstream. No feedback yet.

[jpflori]

comment:6

http://pari.math.u-bordeaux.fr/cgi-bin/bugreport.cgi?bug=1782

[jdemeyer]

comment:8

I tried all primes up to 10⁶ and still only 30011 fails.

[jpflori]

Changed upstream from Reported upstream. No feedback yet. to Fixed upstream, but not in a stable release.

[jpflori]

comment:9

Fixed in master according to Karim, though he did not push the commit yet :)

[jdemeyer]

comment:10

Let's me know when it's fixed in PARI master, then I can make a package.

[jpflori]

comment:11

Done:

• http://pari.math.u-bordeaux.fr/cgi-bin/gitweb.cgi?p=pari.git;a=commit;h=61b65cc7e4fc3ce51a2daed4d48e3c675e8417e8

[jdemeyer]

Author: Jeroen Demeyer

[jdemeyer]

Branch: u/jdemeyer/is_prime_power_fails_on_some_inputs

[jdemeyer]

Commit: ddf018b

[jdemeyer]

comment:15

I did not yet run full doctests, but otherwise this seems to work.

---

New commits:

ddf018b

Upgrade PARI to latest master

[sagetrac-git]

Changed commit from ddf018b to 9c5d20c

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

9c5d20c

Fix gamma_inc doctest

[jdemeyer]

comment:17

Doctests pass now.

[jpflori]

comment:18

Thanks, looks ok.

[jpflori]

Reviewer: Jean-Pierre Flori

[vbraun]

Changed branch from u/jdemeyer/is_prime_power_fails_on_some_inputs to 9c5d20c