Quadratic modules of polynomials in two variables
Copyright policy )Quadratic modules of polynomials in two variables
AbstractLeth1,…,hs∈ ℝ[X, Y] and assume that the setW(h) := {(a, b) ∈ ℝ2|hi(a, b) ≥ 0 for all 1 ≤i≤s} is compact and non-empty. We give an effective method to decide from the knowledge ofh1,…,hswhether every polynomialf∈ ℝ[X, Y], strictly positive onW(h), has a representationf=σ0+h1σ1+···+hsσswith eachσibeing a sum of squares in ℝ[X, Y].
Real algebra, algebraic curves, valuation theory, effectivity in semialgebraic geometry, Henselization, archimedian quadratic module, quadratic forms, sums of squares, Real algebraic sets, Schmuedgen's representation theorem, Effectivity, complexity and computational aspects of algebraic geometry, Valued fields, Witt's Local Global Principle
Real algebra, algebraic curves, valuation theory, effectivity in semialgebraic geometry, Henselization, archimedian quadratic module, quadratic forms, sums of squares, Real algebraic sets, Schmuedgen's representation theorem, Effectivity, complexity and computational aspects of algebraic geometry, Valued fields, Witt's Local Global Principle
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