On Wed, Feb 23, 2011 at 12:03 PM, kcrisman <[email protected]> wrote: > In all recent alphas and rc0:
And also in the *released* sage-4.6.1... This is definitely a serious bug. It should be reported to the sage trac and upstream to the PARI developers. ? znprimroot(15) %1 = Mod(2, 15) ? znprimroot(8) *** at top-level: znprimroot(8) *** ^------------- *** znprimroot: primitive root mod 8 does not exist. > > 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) > > Definition: b.znprimroot(self) > Docstring: > > Return a primitive root modulo self, whenever it exists. > > This is a generator of the group (ZZ/nZZ)^*, whenever this > group > is cyclic, i.e. if n=4 or n=p^k or n=2p^k, where p is an odd > prime > and k is a natural number. > > INPUT: > > * ``self`` - positive integer equal to 4, or a power of an odd > prime, or twice a power of an odd prime > > BUT > > ---------------------------------------------------------------------- > | 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 > > > Please tell me that I am just missing some obvious reason this is > correct behavior. Or has Pari changed its definition? But > http://pari.math.u-bordeaux.fr/dochtml/html.stable/Arithmetic_functions.html#znprimroot > says > > znprimroot(n) > > returns a primitive root (generator) of (Z/nZ)^*, whenever this latter > group is cyclic (n = 4 or n = 2p^k or n = p^k, where p is an odd prime > and k >= 0). > > The library syntax is gener(x). > > - kcrisman > > -- > To post to this group, send email to [email protected] > To unsubscribe from this group, send email to > [email protected] > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
