How to get a minpoly with specified degee in Fp[x]

magichowl · Sat Oct 08, 2011 5:23 am

How to get a minpoly in Fp[x], p is prime
For example,
ring r= 3,x,dp;

How to get a minpoly with degree 2 ??

Though I can get a similar result
ring s = (9,a) ,y. dp;
minpoly;
//1*a^2+2*a^1+2*a^0
but I want substitute this poly in variable x to become a poly in ring r.
i thought of building a map
map m = r, a;
However, the preimage of the minpoly is not that I want.

Re: How to get a minpoly with specified degee in Fp[x]

gorzel · Sat Oct 08, 2011 5:47 pm

To get an irreducible polynomial of degree 2 in char 3,
generate a random poly of degree 2 and check with factorize
whether it is irreducible.

In fact it is irreducible if and only if none of 0,1,2 is a zero
of your chosen polynomial.

---
Your method with map does not work since displayed minpoly
is 0 in the given ring. You have convert it to string which you
execute then.

Code:

> ring s = (9,a) ,y, dp;
> minpoly ;
1*a^2+2*a^1+2*a^0
> poly f = _;                   // this algebriac relation is evalueted to 0
> f;
0
> string(minpoly);
1*a^2+2*a^1+2*a^0
> string S = " poly mipo = " +  string(minpoly) + ";";
> ring r3a = 3,(a,x),dp;
> execute(S);
> mipo;
a2-a-1
> subst(_,a,x);
x2-x-1

---

The minpolys are listed in the file gftables in the LIB directory

See the similar question:
Method to list all possible minimal polynomials for GF(2^n)
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