# Solving quadratic equations over polynomial rings of characteristic two.

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

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## Abstract

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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.

## How to cite

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Cherly, 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 -

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