Abstract.
We provide an explicit algorithm of computing the mapping degree of a rational mapping from the real projective line to itself. As a corollary we prove Sturm’s theorem and a number of its generalizations. These generalizations are used to prove Tarski’s theorem about real semialgebraic sets. Similarly a version of Tarski’s theorem can be proved for an arbitrary algebraically closed field.
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To V. I. Arnold on the occasion of his 70th birthday
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Khovanskii, A., Burda, Y. Degree of rational mappings, and the theorems of Sturm and Tarski. J. fixed point theory appl. 3, 79–93 (2008). https://doi.org/10.1007/s11784-008-0065-6
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DOI: https://doi.org/10.1007/s11784-008-0065-6