Mc Laughlin, James on Tue, 15 Jun 2004 23:28:49 +0200

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RE: question about primitive roots

Thanks to all who responded with the solution to my problem - the "lift"
command does exactly what I want.

Jimmy Mc Laughlin.

-----Original Message-----
From: Mc Laughlin, James 
Sent: Tuesday, June 15, 2004 3:45 PM
Cc: Mc Laughlin, James
Subject: question about primitive roots

Hello everyone,

I have a question about primitive roots. 
I have a prime p and I want a primitive root g.

I know that znprimroot(79) will return a primitive root for the prime p
= 79 in the form Mod(3,79), meaning that if p=79, g=3 is a primitive

Is there anyway I can extract this "3" from the "Mod(3,79)" and set
(I want to be able to do this automatically via a line of code, since I
want to work through a large list of primes)? 

There are two reasons I want to do this. 

First of all, I might only want to proceed if g has a certain value (say
3, for example, in which case I can do something like 
" if( abs(g-3)<1, .........etc  ", provided I have somehow been able to
extract the "3" and set "g=3;". 

The second reason is that I have various polynomials $f(x) \in
\mathbb{Z}{x]$ and I want to be able to evaluate 
f(g^i)(mod p), i=1, ..., p-1 and I would like to have the output each
time as an integer a, say, rather than an expression of the form Mod(a,

Any help appreciated, as this has been holding up somewhat for the past
couple of days.


Jimmy Mc Laughlin.