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Solving quadratic equations over polynomial rings of characteristic two. (English) Zbl 0915.13017

The authors are concerned with the problem of solving a polynomial equation with coefficients in a ring of polynomials over a commutative domain \(B\). First it is shown that this problem can be reduced to the solution of a finite system of polynomial equations in one variable over \(B\) and bounds are given for the degrees and number of these equations. The quadratic case is considered more closely and an algorithm is presented for solving a quadratic equation in one variable over the ring of polynomials in several variables over a finite field of characteristic two.

MSC:

13P05 Polynomials, factorization in commutative rings
12E12 Equations in general fields
13B25 Polynomials over commutative rings
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
11T06 Polynomials over finite fields
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