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MathGroup Archive 2001

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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


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