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On the normalization of numbers and functions defined by radicals

✍ Scribed by Marc Rybowicz

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
249 KB
Volume
35
Category
Article
ISSN
0747-7171

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✦ Synopsis

Based on a criterion due to Kneser, we present new results for the degree of field extensions generated by finitely many radicals. We also improve an algorithm given by Zippel for computing a basis for such an extension field. This algorithm may be effectively used by computer algebra systems to normalize expressions involving radicals.

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✍ Gabriela Jeronimo; Juan Sabia πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 102 KB

We show that the known algorithms used to re-write any first order quantifierfree formula over an algebraically closed field into its normal disjunctive form are essentially optimal. This result follows from an estimate of the number of sets definable by equalities and inequalities of fixed polynomi