#10836: primitive root is broken
-----------------------------+----------------------------------------------
Reporter: kcrisman | Owner: was
Type: defect | Status: new
Priority: critical | Milestone:
Component: number theory | Keywords:
Author: | Upstream: Not yet reported upstream; Will do
shortly.
Reviewer: | Merged:
Work_issues: |
-----------------------------+----------------------------------------------
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
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10836>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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