Solving quadratic equations over polynomial rings of characteristic two
Cherly, Jorgen (Université de Bretagne Occidentale. Department of Mathematics)
Gallardo, Luis (Université de Bretagne Occidentale. Department of Mathematics)
Vaserstein, Leonid (Penn State University. Department of Mathematics)
Wheland, Ethel (University of Akron. Department of Mathematical Sciences)

Data:	1998
Resum:	We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation an tn + ··· + 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.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Publicat a:	Publicacions matemàtiques, V. 42 n. 1 (1998) p. 131-142, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/37927
DOI: 10.5565/PUBLMAT_42198_06

12 p, 162.5 KB

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