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Abstract: We give a survey of three implemented real quantifier elimination methods: partial cylindrical algebraic decomposition, virtual substitution of test terms, and a combination of Gröbner basis computations with multivariate real root counting. We examine the scope of these implementations for applications in various fields of science, engineering, and economics. (Update)
Context of citations to this paper: More
.... quantifiers (# and #) and the evaluation of the modal operators can be performed using quantifier elimination tools such as Redlog [14] or Qepcad although the quantifier elimination algorithm implemented in those tools has been significantly improved [9] Using such...
.... improves the version of Collins cylindrical algebraic decomposition currently implemented in the computer algebra tool REDLOG [88]) the number of arithmetical operations required to perform this QElim procedure is bounded by , when the body of the argument formula is...
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BibTeX entry: (Update)
Andreas Dolzmann, Thomas Sturm, and Volker Weispfenning. Real quantifier elimination in practice. Technical Report MIP9720, FMI, Universitat Passau, D-94030 Passau, Germany, December 1997. http://citeseer.ist.psu.edu/dolzmann98real.html More
@techreport{ dolzmann97real,
author = "A. Dolzmann and T. Sturm and V. Weispfenning",
title = "Real quantifier elimination in practice",
number = "MIP9720",
institution = "FMI, Universitat Passau, D-94030 Passau, Germany",
month = dec,
year = "1997",
url = "citeseer.ist.psu.edu/dolzmann98real.html" }
Citations (may not include all citations):229 A decision method for elementary algebra and geometry (context) - Tarski - 1948
110 the computational complexity and geometry of the firstorder .. (context) - Renegar - 1992
76 Partial cylindrical algebraic decomposition for quantifier e.. (context) - Collins, Hong - 1991
72 the combinatorial and algebraic complexity of quantifier eli.. - Basu, Pollack et al. - 1994
71 Ein Algorithmus zum Auffinden der Basiselemente des Restklas.. (context) - Buchberger - 1965
53 Undergraduate Texts in Mathematics (context) - Cox, Little et al. - 1992
42 Redlog: Computer algebra meets computer logic - Dolzmann, Sturm - 1997
42 Cylindrical algebraic decomposition I: The basic algorithm (context) - Arnon, Collins et al. - 1984
35 The complexity of linear problems in fields (context) - Weispfenning - 1988
24 An improvement of the projection operator in cylindrical alg.. (context) - Hong - 1990
24 Simple solution formula construction in cylindrical algebrai.. (context) - Hong - 1992
23 A new approach for automatic theorem proving in real geometr.. - Dolzmann, Sturm et al. - 1996
20 Robust multi-objective feedback design by quantifier elimina.. (context) - Dorato, Yang et al. - 1997
19 Comprehensive Grobner bases (context) - Weispfenning - 1992
19 Quantifier elimination for real algebra---the quadratic case.. - Weispfenning - 1997
19 Algorithms and Applications (context) - de Berg, van Kreveld et al. - 1997
18 Parametric linear and quadratic optimization by elimination - Weispfenning - 1994
15 Maximization of a linear function of variables subject to li.. (context) - Dantzig - 1951
15 A new approach to quantifier elimination for real algebra (context) - Weispfenning - 1993
15 Real quantifier elimination is doubly exponential (context) - Davenport, Heintz - 1988
13 Quantifier elimination for real algebra---the cubic case - Weispfenning - 1994
13 Offsetting operations in solid modelling (context) - Rossignac, Requicha - 1986
13 Technical Report MIP (context) - Dolzmann, Sturm et al. - 1996
13 Computational geometry problems in Redlog - Sturm, Weispfenning - 1997
13 Simplification of quantifier-free formulae over ordered fiel.. (context) - Dolzmann, Sturm - 1997
12 Simulation and optimization by quantifier elimination - Weispfenning - 1997
12 Communications of the ACM (context) - Colmerauer - 1990
12 Quantifier elimination for formulas constrained by quadratic.. (context) - Hong - 1993
12 Special issue on computational quantifier elimination (context) - Loos, Weispfenning et al. - 1993
12 Quantifier elimination for formulas constrained by quadratic.. (context) - Hong - 1993
10 Testing stability by quantifier elimination - Hong, Liska et al. - 1997
9 Cylindrical algebraic decomposition II: An adjacency algorit.. (context) - Arnon, Collins et al. - 1984
9 Applications of quantifier elimination theory to control sys.. - Abdallah, Dorato et al. - 1996
9 Reasoning over networks by symbolic methods - Sturm - 1997
9 Counting real zeroes in the multivariate case (context) - Pedersen, Roy et al. - 1993
8 An improved projection operation for cylindrical algebraic d.. (context) - McCallum - 1988
7 Rounding and blending of solids by a real elimination method - Sturm, Weispfenning - 1997
5 Reelle Quantorenelimination durch parametrisches Zahlen von .. (context) - Dolzmann - 1994
5 Nonlinear control system design by quantifier elimination - Jirtsrand - 1997
3 Implementierung eines Algorithmus zur Quantorenelimination f.. (context) - Burhenne - 1990
3 Computer Graphics and Geometric Modeling (context) - Hoffmann, Solid - 1989
3 Beitrage zur Theorie der linearen Ungleichungen (context) - Motzkin - 1936
2 College of Engineering and Applied Science (context) - Rossignac, Offsetting et al. - 1985
2 University of Cantabria (context) - Gonz'alez-Vega, algorithm et al. - 1993
2 Continuous Optimization Models (context) - Eiselt, Pederzoli et al. - 1987
2 Partial solution to path finding problems using the CAD meth.. (context) - McCallum - 1995
2 M'emoire sur la r'esolution des 'equations num'eriques (context) - Fran, Sturm
2 Implementierung eines Verfahrens zum Zahlen reeller Nullstel.. (context) - Lippold - 1993
1 Nouvelle m'ethode pour la r'esolution des 'equations num'eri.. (context) - Fran, Budan
1 Analyse des 'equations d'etermin'ees (context) - Joseph
1 La g'eometrie---livre III (context) - Descartes - 1973
1 a theory of the syzegetic relations of two rational integral.. (context) - Sylvester
1 Parametrische Grobnerbasen im Computeralgebrasystem ALDES/SA.. (context) - Schonfeld - 1991
1 Remarques sur le th'eor`eme de M (context) - Hermite - 1905
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.fmi.uni-passau.de/~redlog/references.html): More
Applying Linear Quantifier Elimination - Loos, Weispfenning (1993) (Correct)
Quantifier Elimination for Real Algebra - the Cubic Case - Weispfenning (1994) (Correct)
Redlog User Manual - Reduce Logic (Correct)
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