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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:
13P05Polynomials, factorization
12E12Algebraic equations
13B25Polynomials over commutative rings
13F20Polynomial rings and ideals
11T06Polynomials over finite fields or rings
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