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Signature method for counting point in semi-algebraic subsets. (English) Zbl 0874.14049

Summary: Theorems on counting root numbers of real polynomial endomorphism in an arbitrary semi-algebraic set are given and several cases are considered. An estimate for the computational complexity of counting root numbers is obtained. The mentioned facts generalize early results obtained by the author. Particularly the numbers of variables and equations are unrestricted.

MSC:

14P10 Semialgebraic sets and related spaces
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
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