| Singular https://www.singular.uni-kl.de/forum/ |
|
| How to get a minpoly with specified degee in Fp[x] https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1994 |
Page 1 of 1 |
| Author: | magichowl [ Sat Oct 08, 2011 5:23 am ] |
| Post subject: | How to get a minpoly with specified degee in Fp[x] |
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. |
|
| Author: | gorzel [ Sat Oct 08, 2011 5:47 pm ] |
| Post subject: | Re: How to get a minpoly with specified degee in Fp[x] |
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) viewtopic.php?f=10&t=1912 |
|
| Page 1 of 1 | All times are UTC + 1 hour [ DST ] |
| Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group http://www.phpbb.com/ |
|