#10836: primitive root is broken
--------------------------------------------------+-------------------------
Reporter: kcrisman | Owner: was
Type: defect | Status:
positive_review
Priority: critical | Milestone: sage-4.7
Component: number theory | Keywords:
Author: Karl-Dieter Crisman, William Stein | Upstream: Reported
upstream. Developers deny it's a bug.
Reviewer: William Stein, Karl-Dieter Crisman | Merged:
Work_issues: |
--------------------------------------------------+-------------------------
Changes (by kcrisman):
* status: needs_review => positive_review
Old description:
> Pari has a major bug in its primitive root:
> {{{
> sage: primitive_root(15)
> 2
> sage: mod(2,15).multiplicative_order()
> 4
> sage: euler_phi(15)
> 8
> sage: [mod(2,15)^i for i in [1..8]]
> [2, 4, 8, 1, 2, 4, 8, 1]
> sage: b = pari(15)
> sage: b.znprimroot()
> Mod(2, 15)
> }}}
> Note that this DOES work correctly with whatever Pari is in Sage 4.4.4.
> {{{
> ---------------------------------------------------------------------
> | Sage Version 4.4.4, Release Date: 2010-06-23 |
> | Type notebook() for the GUI, and license() for information. |
> ----------------------------------------------------------------------
> Loading Sage library. Current Mercurial branch is: hackbranch
> sage: primitive_root(15)
> <snip>
> ArithmeticError: There is no primitive root modulo n
> }}}
New description:
Pari has a major bug in its primitive root:
{{{
sage: primitive_root(15)
2
sage: mod(2,15).multiplicative_order()
4
sage: euler_phi(15)
8
sage: [mod(2,15)^i for i in [1..8]]
[2, 4, 8, 1, 2, 4, 8, 1]
sage: b = pari(15)
sage: b.znprimroot()
Mod(2, 15)
}}}
Note that this DOES work correctly with whatever Pari is in Sage 4.4.4.
{{{
---------------------------------------------------------------------
| Sage Version 4.4.4, Release Date: 2010-06-23 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
Loading Sage library. Current Mercurial branch is: hackbranch
sage: primitive_root(15)
<snip>
ArithmeticError: There is no primitive root modulo n
}}}
----
Apply only [attachment:trac_10836.2.patch].
--
Comment:
Had to fix one tiny thing for the note to look right. Positive review.
Apply only [attachment:trac_10836.2.patch].
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10836#comment:18>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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