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Re: Working with polynomials in Z/23

• To: mathgroup at smc.vnet.net
• Subject: [mg106619] Re: Working with polynomials in Z/23
• From: dh <dh at metrohm.com>
• Date: Mon, 18 Jan 2010 05:40:23 -0500 (EST)
• References: <his6ug$l6a$1@smc.vnet.net>

Hi Bob,

simple follow PolynomialMod by a corresponding rule. E.g.:

PolynomialMod[poly] /. x^n_ -> x^Mod[n, 23]

Also note that you made a small mistake: Mod[25,23]->2 not 3

Daniel



me13013 wrote:

> I'm exploring polynomials over integer values modulo 23 (i.e. 'x' in

> the polynomial can only take integer values, and my polynomials only

> have integer coefficients). I know that I can reduce the polynomial

> coefficients mod 23 using PolynomialMod.  However, I also want to

> reduce the exponents for the identity x^23 = x.  Is there an easy way

> to do that?

> 

> For example, if I have the polynomial P(x) = x^5 + 2x.  Then

> P(P(x)) = x^25 + 10x^21 + 40x^17 + 80x^13 + 80x^9 + 34x^5 + 4x.

> PolynomialMod will reduce this to

> P(P(x)) = x^25 + 10x^21 + 17x^17 + 11x^13 + 11x^9 + 11x^5 + 4x.

> But since x^25 = x^3, the answer I want is

> P(P(x)) = 10x^21 + 17x^17 + 11x^13 + 11x^9 + 11x^5 + x^3 + 4x.

> 

> I tried to figure out a way to do this using CoefficientList, but I'm

> not proficient enough as an occasional Mathematica user to figure out

> how to sort of "fold" the list onto itsefl and sum the columns.

> 

> Any help would be appreciated,

> Bob H

>