Re: Finding Roots of Polynomials over Polynomial Quotient Rings

*To*: mathgroup at smc.vnet.net*Subject*: [mg93502] Re: Finding Roots of Polynomials over Polynomial Quotient Rings*From*: Julian <julianhaw at gmail.com>*Date*: Wed, 12 Nov 2008 06:46:02 -0500 (EST)*References*: <200811091025.FAA20508@smc.vnet.net> <gf8ree$pmh$1@smc.vnet.net>

On Nov 10, 3:30 am, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote: > On 9 Nov 2008, at 19:25, Julian wrote: > > > Hi all, > > > Just wondering how I would go about finding roots of an polynomial, > > say t^2 +2, over a quotient ring, say Z/5Z[x] / <x^2+2>, in > > Mathematica? The modulus option in Reduce is only for integers, and > > I've had trouble finding anything relevant in the finite fields > > package... anyone know if this can be done in Mathematica? > > > Thanks, > > Julian > > Since a finite field has only finitely many elements and since the > FiniteFields package lets you perform arithmetic on these elements, > you can always find the roots of a polynomial simply by substituting > all the field elements into the polynomial and selecting those that > satisfy it. Or am I misunderstanding your question? > > Andrzej Kozlowski Yep it worked! Thanks. I made a function to list all the elements in the field, then simply substituted each one

**References**:**Finding Roots of Polynomials over Polynomial Quotient Rings***From:*Julian <julianhaw@gmail.com>