# Solving quadratic equations over polynomial rings of characteristic two.

Jorgen Cherly; Luis Gallardo; Leonid Vaserstein; Ethel Wheland

Publicacions Matemàtiques (1998)

- Volume: 42, Issue: 1, page 131-142
- ISSN: 0214-1493

## Access Full Article

top## Abstract

top## How to cite

topCherly, Jorgen, et al. "Solving quadratic equations over polynomial rings of characteristic two.." Publicacions Matemàtiques 42.1 (1998): 131-142. <http://eudml.org/doc/41332>.

@article{Cherly1998,

abstract = {We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A.We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain a finite algorithm for solving a polynomial equation over A when A is F[x1, ..., xN] or F(x1, ..., xN) for any finite field F and any number N of variables.The case of quadratic equations in characteristic two is studied in detail.},

author = {Cherly, Jorgen, Gallardo, Luis, Vaserstein, Leonid, Wheland, Ethel},

journal = {Publicacions Matemàtiques},

keywords = {Ecuaciones polinómicas; Anillos de polinomios; Grupos finitos; quadratic equation; finite fields; rings of characteristic two; polynomial equation},

language = {eng},

number = {1},

pages = {131-142},

title = {Solving quadratic equations over polynomial rings of characteristic two.},

url = {http://eudml.org/doc/41332},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Cherly, Jorgen

AU - Gallardo, Luis

AU - Vaserstein, Leonid

AU - Wheland, Ethel

TI - Solving quadratic equations over polynomial rings of characteristic two.

JO - Publicacions Matemàtiques

PY - 1998

VL - 42

IS - 1

SP - 131

EP - 142

AB - We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A.We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain a finite algorithm for solving a polynomial equation over A when A is F[x1, ..., xN] or F(x1, ..., xN) for any finite field F and any number N of variables.The case of quadratic equations in characteristic two is studied in detail.

LA - eng

KW - Ecuaciones polinómicas; Anillos de polinomios; Grupos finitos; quadratic equation; finite fields; rings of characteristic two; polynomial equation

UR - http://eudml.org/doc/41332

ER -

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.