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texto impreso
Using some model-theoretic arguments applied to the theory of real valuations, we obtain a sufficient condition based on elementary properties of , K any real closed field, for ƒ to be sum of 2mth powers of rational functions in K(x).texto impreso
Using some elementary theory of convex sets we prove a necessary and a sufficient condition for f ? R[x„ . . ., x„](R being the real numbers) to be a finite sum of 2m-th powers of rational functions in x1, . . ., x n over R[i.e.f ? ? R(x)2 m]texto impreso
texto impreso
"In this paper the authors discuss the representation of a polynomial as a sum of 2mth powers of rational functions. Of course, it is known that the number of rational functions involved can be bounded in terms of m, but also that the degrees of[...]texto impreso
"The paper deals with representation of polynomials in several variables over a real closed field as sums of 2mth powers of rational functions. It has been proved by A. Prestel that even in one variable over R, the set of polynomials of given de[...]
