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Re: PolynomialMod

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121350] Re: PolynomialMod
  • From: Artur <grafix at csl.pl>
  • Date: Mon, 12 Sep 2011 04:19:45 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <1427062901.24745.1315763991756.JavaMail.root@wrimail02.wolfram.com>
  • Reply-to: grafix at csl.pl

Dear Daniel,
I'm apologize for confusions but I was used wrong function PolynomialMod 
inspite PolynomialRemainder

Now work perfect:

f = 1 + 3 x + 5 x^2 + 5 x^3 + 5 x^4 + 3 x^5 + x^6;
p = -c - b x +  x^3;
q = PolynomialRemainder[f, p, x]

result is OK and work symbolically

1 + 5 c + 3 b c + c^2 + (3 + 5 b + 3 b^2 + 5 c + 2 b c) x + (5 + 5 b + 
b^2 +  3 c) x^2

Best wishes
Artur

W dniu 2011-09-11 19:59, Daniel Lichtblau pisze:
>
> ----- Original Message -----
>> From: "Artur"<grafix at csl.pl>
>> To: mathgroup at smc.vnet.net
>> Sent: Sunday, September 11, 2011 6:28:34 AM
>> Subject: PolynomialMod
>> Dear Mathematica Gurus,
>>
>> Who is able help me to write Mathematica procedure which will be
>> improovment of recent PolynomialMod.
>>
>> If we do
>> PolynomialMod[ 1 + 3 #1 + 5 #1^2 + 5 #1^3 + 5 #1^4 + 3 #1^5 + #1^6, -1
>> +
>> 2 #1^2 + #1^3]
>> result is OK
>> 1 + 6 #1 + 6 #1^2
>>
>> But if we do
>> PolynomialMod[1 + 3 #1 + 5 #1^2 + 5 #1^3 + 5 #1^4 + 3 #1^5 + #1^6, -1
>> +
>> (-(3/2) - (I Sqrt[23])/2) #1 + (3/2 - (I Sqrt[23])/2) #1^2 + #1^3]
>> Result is wrong
>> good should be
>> -2 + (-(1/2) - (I Sqrt[23])/2) x + x^2
>>
>> Who is able to write good one procedure e.g. PolMod to automatic
>> reduction of any degree polynomials by polynomial smaller degree?
>>
>> Best wishes
>> Artur Jasinskii
> Actually a correct result should be zero. PolynomialRemainder, among other functions, can be used for this.
>
> In[256]:= p1 = (1 + 3 #1 + 5 #1^2 + 5 #1^3 + 5 #1^4 +
>       3 #1^5 + #1^6)&[x]
>
> Out[256]= 1 + 3*x + 5*x^2 + 5*x^3 + 5*x^4 + 3*x^5 + x^6
>
> In[257]:= m1 = (-1 + (-(3/2) - (I*Sqrt[23])/2)*#1 + (3/
>           2 - (I*Sqrt[23])/2)*#1^2 + #1^3&  )[x]
>
> Out[257]= -1 + (-(3/2) - (I*Sqrt[23])/2)*x + (3/2 - (I*Sqrt[23])/2)*
>    x^2 + x^3
>
> In[272]:= PolynomialQuotientRemainder[p1, m1, x]
>
> Out[272]= {-1 + (-(3/2) + (I*Sqrt[23])/2)*x + (3/2 + (I*Sqrt[23])/2)*
>     x^2 + x^3, 0}
>
> Daniel Lichtblau
> Wolfram Research
>




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