Re: Polynomial Reduction with Mod
- To: mathgroup at smc.vnet.net
- Subject: [mg30443] Re: [mg30436] Polynomial Reduction with Mod
- From: BobHanlon at aol.com
- Date: Sun, 19 Aug 2001 02:01:36 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 2001/8/18 4:17:05 AM, Flip at safebunch.com writes:
>Is Mathematica capable of calculating this type of problem?
>
>
>Mod[1 + x^3 + x^4 + x^5 + x^6 + x^8 + x^11 + x^13,
>1 + x + x^3 + x^4 + x^8]
>
>The second polynomial is irreducible?
>
>By the way, the soultion is: x^7 + x^6 + 1.
>
poly1 = 1 + x^3 + x^4 + x^5 + x^6 +
x^8 + x^11 + x^13;
poly2 = 1 + x + x^3 + x^4 + x^8;
pm = PolynomialMod[poly1, poly2]
-x^7 - x^6 + x^5 + x^4 + x^2 + x + 1
% == PolynomialRemainder[poly1, poly2, x]
True
pq = PolynomialQuotient[poly1, poly2, x]
x^5 + x^3 - x
poly2 * pq + pm == poly1 // Simplify
True
Bob Hanlon
Chantilly, VA USA