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A bibliography of quantifier elimination for real closed fields. (English) Zbl 0646.03024
A list of papers on quantifier elimination for real closed fields are referred with comments on their destination (e.g. tutorial, research etc.). It seems to be complete, but unfortunately short summaries and comparisons of different algorithms fail, what yields difficulties for the novice in this area. Also it is regretable that the supporting algorithms such as polynomial factoring and solving systems of algebraic equations tightly connected with the subject under discussion are absent.
Reviewer: D.Yu.Grigor’ev

MSC:
03C10 Quantifier elimination, model completeness and related topics
12L12 Model theory of fields
68W30 Symbolic computation and algebraic computation
00A15 Bibliographies for mathematics in general
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[32] Collins, G.E., Quantifier elimlnatlon for real closed fields by cylindrical algebraic decomposition - a synopsis, ACM SIGSAM bull., 10, 1, 10-12, (1976), (CollinsAlgorithm, Exposition)
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[39] Davenport, J.; Heintz, J., Real quantifier elimination is doubly exponential, J. symb. comp., 5, (1988), (this issue). (ComplexityResult, ResearchResult) · Zbl 0663.03015
[40] Delzell, C., A finiteness theorem for open semi-algebraic sets, with applications to Hilbert’s 17th problem, (), 79-97, (RealAlgebraicGeometry, ResearchResult) · Zbl 0495.14013
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[46] (), (RealAlgebraicGeometry, ResesrchResult, Exposition)
[47] (), (RealAlgebraicGeometry, ResearchResult, Exposition)
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[57] Heintz, J., Definability and fast quantifier elimination in algebraically closed fields, Theoretical comput. sci., 24, 239-277, (1983), (ComplexityResult, ResearchResult) · Zbl 0546.03017
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