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MathGroup Archive 2001

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Re: Polynomial Reduction with Mod

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30439] Re: [mg30436] Polynomial Reduction with Mod
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Sun, 19 Aug 2001 02:01:34 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Mathematica is not capable of that because it certainly is not true!

In[1]:=
PolynomialRemainder[1+x^3+x^4+x^5+x^6+x^8+x^11+x^13,1+x+x^3+x^4+x^8,x]

Out[1]=
1 + x + x^2 + x^4 + x^5 - x^6 - x^7

In[2]:=
PolynomialMod[1+x^3+x^4+x^5+x^6+x^8+x^11+x^13,1+x+x^3+x^4+x^8]

Out[2]=
1 + x + x^2 + x^4 + x^5 - x^6 - x^7

In[3]:=
Last[PolynomialReduce[1+x^3+x^4+x^5+x^6+x^8+x^11+x^13,{1+x+x^3+x^4+x^8},
{x}]]


Out[3]=
1 + x + x^2 + x^4 + x^5 - x^6 - x^7

Maybe you mean something else but I can't think of any sense in which 
yours could be the right answer (???)

On Saturday, August 18, 2001, at 05:04  PM, Flip at safebunch.com wrote:

> Hello,
>
> 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.
>
> Thank you for any inputs ...
>
>
>

Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/


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