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Real closed field
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21	ALGORITHMS IN REAL ALGEBRAIC GEOMETRY: A SURVEY SAUGATA BASU Abstract. We survey both old and new developments in the theory of algorithms in real algebraic geometry – starting from effective quantifier elimination in Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2011-07-21 09:04:59 Real algebraic geometry Field theory Algebraic geometry Cylindrical algebraic decomposition Real closed field Algebraic extension Algebraic variety Tarski–Seidenberg theorem Field Abstract algebra Mathematics Algebra
22	A COMPLEX ANALOGUE OF TODA’S THEOREM SAUGATA BASU Abstract. Toda [28] proved in 1989 that the (discrete) polynomial time hierarchy, PH, is contained in the class P#P , namely the class of languages that can be decided Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2011-09-22 08:25:51 Applied mathematics Constructible universe Polynomial Time hierarchy theorem Algebraic geometry Real closed field Karp–Lipton theorem Constructible number Mathematics Structural complexity theory Abstract algebra
23	/home/roy/.TeXmacs/system/tmp/tmp_349624716.ps Add to Reading List Source URL: perso.univ-rennes1.fr Language: English - Date: 2009-08-21 13:03:52 Field theory Polynomials Algebraic geometry Real algebraic geometry Discriminant Algebraic function Semialgebraic set Algebraic variety Algebraically closed field Abstract algebra Mathematics Algebra
24	Saugata Basu Department of Mathematics Purdue University Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2013-10-06 09:31:19 Cylindrical algebraic decomposition Algebraic geometry Computational mathematics Computational geometry Real closed field Discrete mathematics Theoretical computer science Algorithmic Number Theory Symposium Combinatorics Mathematics Real algebraic geometry Algebra
25	Introduction Ideas behind ETR and computing Euler-Poincaré Characteristic Algorithm for Computing the Euler-Poincaré characteristic Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2005-11-25 07:51:12 Topological graph theory Real algebraic geometry Betti number Euler characteristic Cylindrical algebraic decomposition Algorithm Leonhard Euler Real closed field Time complexity Mathematics Abstract algebra Algebraic topology
26	Introduction Quantitative Bounds Proof of the main theorem Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2008-06-12 16:23:19 Geometry Real closed field Semialgebraic set Betti number Algebraic variety Algorithm Abstract algebra Mathematics Real algebraic geometry
27	Bounds Algorithmic Results Techniques Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2005-11-25 07:51:12 Geometry Betti number Algorithm Algebraic variety Real closed field Pi Semialgebraic set Real number Polynomial Mathematics Abstract algebra Real algebraic geometry
28	Surreal Numbers – An Introduction Version 1.6 Add to Reading List Source URL: www.tondering.dk Language: English - Date: 2013-09-25 05:59:12 Infinity Logic Combinatorial game theory Real closed field Surreal number Vacuous truth Infinitesimal Number FO Mathematics Abstract algebra Mathematical logic
29	Symposium on the Add to Reading List Source URL: www.corelab.ntua.gr Language: English - Date: 2012-02-22 16:06:00 Field theory Formal systems Real algebraic geometry Algebraic structures Model theory Real closed field Axiom Field Peano axioms Mathematics Abstract algebra Mathematical logic
30	TMME, vol. 7, no. 1, p. 3 When is[removed]less than 1? Add to Reading List Source URL: www.math.umt.edu Language: English - Date: 2010-01-14 17:29:24 Calculus Abstract algebra Infinity Real closed field Criticism of non-standard analysis Infinitesimal Non-standard calculus 0.999... Standard part function Mathematics Mathematical analysis Non-standard analysis