An effective implementation of symbolic–numeric cylindrical algebraic decomposition for quantifier elimination
With many applications in engineering and scientific fields, quantifier elimination (QE) has received increasing attention. Cylindrical algebraic decomposition (CAD) is used as a basis for a general QE algorithm. In this paper we present an effective symbolic–numeric cylindrical algebraic decomposit...
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| Vydané v: | Theoretical computer science Ročník 479; s. 43 - 69 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
01.04.2013
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | With many applications in engineering and scientific fields, quantifier elimination (QE) has received increasing attention. Cylindrical algebraic decomposition (CAD) is used as a basis for a general QE algorithm. In this paper we present an effective symbolic–numeric cylindrical algebraic decomposition (SNCAD) algorithm for QE incorporating several new devices, which we call “quick tests”. The simple quick tests are run beforehand to detect an unnecessary procedure that might be skipped without violating the correctness of results and they thus considerably reduce the computing time. The effectiveness of the SNCAD algorithm is examined in a number of experiments including practical engineering problems, which also reveal the quality of the implementation. Experimental results show that our implementation has significantly improved efficiency compared with our previous work. |
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| AbstractList | With many applications in engineering and scientific fields, quantifier elimination (QE) has received increasing attention. Cylindrical algebraic decomposition (CAD) is used as a basis for a general QE algorithm. In this paper we present an effective symbolic–numeric cylindrical algebraic decomposition (SNCAD) algorithm for QE incorporating several new devices, which we call “quick tests”. The simple quick tests are run beforehand to detect an unnecessary procedure that might be skipped without violating the correctness of results and they thus considerably reduce the computing time. The effectiveness of the SNCAD algorithm is examined in a number of experiments including practical engineering problems, which also reveal the quality of the implementation. Experimental results show that our implementation has significantly improved efficiency compared with our previous work. |
| Author | Anai, Hirokazu Yokoyama, Kazuhiro Iwane, Hidenao Yanami, Hitoshi |
| Author_xml | – sequence: 1 givenname: Hidenao surname: Iwane fullname: Iwane, Hidenao email: iwane@jp.fujitsu.com organization: Fujitsu Laboratories Ltd., 4-1-1 Kamikodanaka, Nakahara-ku, Kawasaki 211-8588, Japan – sequence: 2 givenname: Hitoshi surname: Yanami fullname: Yanami, Hitoshi email: yanami@labs.fujitsu.com organization: Fujitsu Laboratories Ltd., 4-1-1 Kamikodanaka, Nakahara-ku, Kawasaki 211-8588, Japan – sequence: 3 givenname: Hirokazu surname: Anai fullname: Anai, Hirokazu email: anai@jp.fujitsu.com organization: Fujitsu Laboratories Ltd., 4-1-1 Kamikodanaka, Nakahara-ku, Kawasaki 211-8588, Japan – sequence: 4 givenname: Kazuhiro surname: Yokoyama fullname: Yokoyama, Kazuhiro email: kazuhiro@rikkyo.ac.jp organization: Rikkyo University, 3-34-1 Nishi Ikebukuro, Toshima-ku, Tokyo 171-8501, Japan |
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| Cites_doi | 10.1006/jsco.2001.0463 10.1006/jsco.2002.0547 10.1023/A:1011818803494 10.1016/S0747-7171(88)80004-X 10.1007/978-3-7091-9459-1_19 10.1137/S1052623400366802 10.1109/ACC.2000.876713 10.1006/jsco.1997.0122 10.1109/CCA.2004.1387594 10.1016/j.jsc.2011.05.014 10.1145/2331684.2331712 10.1006/jsco.1996.0042 10.1016/S0747-7171(88)80003-8 10.1007/s002000050055 10.1007/BF02234767 10.1023/A:1014785518570 10.1016/j.jsc.2006.06.004 10.1145/309831.309890 10.1006/jsco.1999.0327 10.1007/978-3-7091-9459-1_12 10.1145/1577190.1577203 10.1093/comjnl/36.5.450 10.1016/S0747-7171(08)80152-6 10.1006/jsco.1994.1057 10.1137/050647098 10.1023/A:1009924521389 10.1093/comjnl/36.5.432 10.1145/968708.968710 |
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| Keywords | Quantifier elimination Cylindrical algebraic decomposition Symbolic–numeric computation |
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| References | Wilson, Cappelleri, Simpson, Frecker (br000265) 2001; 2 Weispfenning (br000260) 1997; 24 Rump (br000210) 2005 Davenport, Heintz (br000070) 1988; 5 Hong, Safey El Din (br000125) 2011; 47 Rump (br000205) 1988; vol. 296 Brown (br000040) 2001; 32 Dolzmann, Sturm, Weispfenning (br000085) 1998 Collins, Johnson, Krandick (br000065) 2002; 34 Safey El~Din (br000215) 2008 McCallum (br000175) 1999 Della~Dora, Dicrescenzo, Duval (br000080) 1985 S. McCallum, An improved projection operator for cylindrical algebraic decomposition, in: Caviness and Johnson Pistikopoulos, Georgiadis, Dua (br000195) 2007; vol. 1 Strzeboński (br000240) 2006; 41 Schweighofer (br000225) 2006; 17 H. Anai, P. Parrilo, Convex quantifier elimination for semidefinite programming, in: Proceedings of the International Workshop on Computer Algebra in Scientific Computing, CASC 2003, Sept. 2003, pp. 3–11. Hong (br000115) 1993 Lampinen (br000150) 2000 Schattman (br000220) Kaltofen, Li, Yang, Zhi (br000140) 2008 Hong (br000120) 1996 McCallum (br000180) 2001 Basu, Pollack, Roy (br000025) 2006 Deb (br000075) 2001 Strzeboński (br000230) 1999; 5 Weispfenning (br000250) 1988; 5 Brown (br000035) 2000 L. González-Vega, A combinatorial algorithm solving some quantifier elimination problems, in: Caviness and Johnson Ratschan (br000200) 2002; 8 Strzeboński (br000235) 2000; 29 Lasserre (br000155) 2001; 11 H. Iwane, H. Yanami, H. Anai, K. Yokoyama, An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for quantifier elimination, in: Proceedings of the 2009 International Workshop on Symbolic-Numeric Computation, vol. 1, 2009, pp. 55–64. Winkler (br000270) 1996 Parrilo, Sturmfels (br000190) 2001 Collins (br000055) 1975; vol. 32 Brown (br000045) 2003; 37 Loos, Weispfenning (br000160) 1993; 36 H. Anai, H. Yanami, S. Hara, K. Sakabe, Fixed-structure robust controller synthesis based on symbolic-numeric computation: design algorithms with a CACSD toolbox, in: Proceedings of CCA/ISIC/CACSD 2004 (Taipei, Taiwan), vol. 2 (9) 2004, pp. 1540–1545,. T. Sturm, V. Weispfenning, Rounding and blending of solids by a real elimination method, in: Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling, and Applied Mathematics, IMACS 97, 1997, pp. 727–732. Anai, Yokoyama (br000020) 2005 (br000050) 1998 Collins, Hong (br000060) 1991; 12 C.W. Brown, Solution formula construction for truth invariant cad’s. Ph.D. Thesis, University of Delaware Newark, 1999. 1998, pp. 365–375. pp. 242–268. Guo, Safey, Din, Zhi (br000105) 2010 P.A. Parrilo, S. Lall, Semidefinite programming relaxations and algebraic optimization in control, Mini-course on Polynomial Equations and Inequalities I and II, 2006. Weispfenning (br000255) 1993; 8 H. Anai, S. Hara, Fixed-structure robust controller synthesis based on sign definite condition by a special quantifier elimination, in: Proceedings of American Control Conference, 2000, vol. 2, 2000, pp. 1312–1316. McCallum (br000165) 1993 González-Vega (br000095) 1996; 22 H. Iwane, H. Yanami, H. Anai, An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for optimization problems, in: Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation, vol. 1, 2011, pp. 168–177. Duval (br000090) 1994; 18 Krawczyk (br000145) 1969 Hong (br000110) 1990 Kaltofen (10.1016/j.tcs.2012.10.020_br000140) 2008 Pistikopoulos (10.1016/j.tcs.2012.10.020_br000195) 2007; vol. 1 Lampinen (10.1016/j.tcs.2012.10.020_br000150) 2000 Lasserre (10.1016/j.tcs.2012.10.020_br000155) 2001; 11 Weispfenning (10.1016/j.tcs.2012.10.020_br000250) 1988; 5 10.1016/j.tcs.2012.10.020_br000185 Collins (10.1016/j.tcs.2012.10.020_br000060) 1991; 12 10.1016/j.tcs.2012.10.020_br000100 Strzeboński (10.1016/j.tcs.2012.10.020_br000230) 1999; 5 Strzeboński (10.1016/j.tcs.2012.10.020_br000240) 2006; 41 Loos (10.1016/j.tcs.2012.10.020_br000160) 1993; 36 Hong (10.1016/j.tcs.2012.10.020_br000125) 2011; 47 Wilson (10.1016/j.tcs.2012.10.020_br000265) 2001; 2 McCallum (10.1016/j.tcs.2012.10.020_br000175) 1999 González-Vega (10.1016/j.tcs.2012.10.020_br000095) 1996; 22 McCallum (10.1016/j.tcs.2012.10.020_br000165) 1993 Davenport (10.1016/j.tcs.2012.10.020_br000070) 1988; 5 Guo (10.1016/j.tcs.2012.10.020_br000105) 2010 Collins (10.1016/j.tcs.2012.10.020_br000065) 2002; 34 Anai (10.1016/j.tcs.2012.10.020_br000020) 2005 Hong (10.1016/j.tcs.2012.10.020_br000110) 1990 10.1016/j.tcs.2012.10.020_br000030 Rump (10.1016/j.tcs.2012.10.020_br000205) 1988; vol. 296 Krawczyk (10.1016/j.tcs.2012.10.020_br000145) 1969 Schweighofer (10.1016/j.tcs.2012.10.020_br000225) 2006; 17 Basu (10.1016/j.tcs.2012.10.020_br000025) 2006 Brown (10.1016/j.tcs.2012.10.020_br000045) 2003; 37 Winkler (10.1016/j.tcs.2012.10.020_br000270) 1996 (10.1016/j.tcs.2012.10.020_br000050) 1998 10.1016/j.tcs.2012.10.020_br000245 10.1016/j.tcs.2012.10.020_br000005 Weispfenning (10.1016/j.tcs.2012.10.020_br000255) 1993; 8 Della~Dora (10.1016/j.tcs.2012.10.020_br000080) 1985 Strzeboński (10.1016/j.tcs.2012.10.020_br000235) 2000; 29 McCallum (10.1016/j.tcs.2012.10.020_br000180) 2001 Brown (10.1016/j.tcs.2012.10.020_br000040) 2001; 32 Dolzmann (10.1016/j.tcs.2012.10.020_br000085) 1998 Ratschan (10.1016/j.tcs.2012.10.020_br000200) 2002; 8 Brown (10.1016/j.tcs.2012.10.020_br000035) 2000 Hong (10.1016/j.tcs.2012.10.020_br000120) 1996 Schattman (10.1016/j.tcs.2012.10.020_br000220) 10.1016/j.tcs.2012.10.020_br000170 10.1016/j.tcs.2012.10.020_br000130 Safey El~Din (10.1016/j.tcs.2012.10.020_br000215) 2008 10.1016/j.tcs.2012.10.020_br000010 10.1016/j.tcs.2012.10.020_br000015 Duval (10.1016/j.tcs.2012.10.020_br000090) 1994; 18 10.1016/j.tcs.2012.10.020_br000135 Deb (10.1016/j.tcs.2012.10.020_br000075) 2001 Parrilo (10.1016/j.tcs.2012.10.020_br000190) 2001 Weispfenning (10.1016/j.tcs.2012.10.020_br000260) 1997; 24 Rump (10.1016/j.tcs.2012.10.020_br000210) 2005 Collins (10.1016/j.tcs.2012.10.020_br000055) 1975; vol. 32 Hong (10.1016/j.tcs.2012.10.020_br000115) 1993 |
| References_xml | – year: 2001 ident: br000075 publication-title: Multi-Objective Optimization using Evolutionary Algorithms – volume: 22 start-page: 83 year: 1996 end-page: 103 ident: br000095 article-title: Applying quantifier elimination to the Birkhoff interpolation problem publication-title: Journal of Symbolic Computation – start-page: 48 year: 2000 end-page: 53 ident: br000035 article-title: Improved projection for CAD’s of publication-title: Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation – reference: H. Anai, P. Parrilo, Convex quantifier elimination for semidefinite programming, in: Proceedings of the International Workshop on Computer Algebra in Scientific Computing, CASC 2003, Sept. 2003, pp. 3–11. – start-page: 432 year: 1993 end-page: 438 ident: br000165 article-title: Solving polynomial strict inequalities using cylindrical algebraic decomposition publication-title: The Computer Journal – reference: H. Anai, S. Hara, Fixed-structure robust controller synthesis based on sign definite condition by a special quantifier elimination, in: Proceedings of American Control Conference, 2000, vol. 2, 2000, pp. 1312–1316. – volume: 12 start-page: 299 year: 1991 end-page: 328 ident: br000060 article-title: Partial cylindrical algebraic decomposition for quantifier elimination publication-title: Journal of Symbolic Computation – volume: 47 start-page: 883 year: 2011 end-page: 901 ident: br000125 article-title: Variant quantifier elimination publication-title: Journal of Symbolic Computation – start-page: 571 year: 1996 end-page: 582 ident: br000120 article-title: An efficient method for analyzing the topology of plane real algebraic curves publication-title: Selected Papers Presented at the International IMACS Symposium on Symbolic Computation, New Trends and Developments – volume: 11 start-page: 796 year: 2001 end-page: 817 ident: br000155 article-title: Global optimization with polynomials and the problem of moments publication-title: SIAM Journal on Optimization – start-page: 264 year: 1993 end-page: 274 ident: br000115 article-title: Quantifier elimination for formulas constrained by quadratic equations publication-title: Proceedings of the 1993 International Symposium on Symbolic and Algebraic Computation – reference: , 1998, pp. 365–375. – reference: S. McCallum, An improved projection operator for cylindrical algebraic decomposition, in: Caviness and Johnson – start-page: 145 year: 1999 end-page: 149 ident: br000175 article-title: On projection in CAD-based quantifier elimination with equational constraint publication-title: Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation – volume: 5 start-page: 29 year: 1988 end-page: 35 ident: br000070 article-title: Real quantifier elimination is doubly exponential publication-title: Journal of Symbolic Computation – volume: 5 start-page: 337 year: 1999 end-page: 346 ident: br000230 article-title: A real polynomial decision algorithm using arbitrary-precision floating point arithmetic publication-title: Reliable Computing – start-page: 223 year: 2001 end-page: 231 ident: br000180 article-title: On propagation of equational constraints in CAD-based quantifier elimination publication-title: Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation – reference: C.W. Brown, Solution formula construction for truth invariant cad’s. Ph.D. Thesis, University of Delaware Newark, 1999. – volume: 8 start-page: 85 year: 1993 end-page: 101 ident: br000255 article-title: Quantifier elimination for real algebra — the quadratic case and beyond publication-title: AAECC – volume: 8 start-page: 21 year: 2002 end-page: 42 ident: br000200 article-title: Approximate quantified constraint solving by cylindrical box decomposition publication-title: Reliable Computing – start-page: 187 year: 1969 end-page: 201 ident: br000145 article-title: Newton-algorithmen zur bestimmung von nullstellen mit fehlerschranken publication-title: Computing – start-page: 71 year: 2008 end-page: 78 ident: br000215 article-title: Computing the global optimum of a multivariate polynomial over the reals publication-title: Proceedings of the Twenty-first International Symposium on Symbolic and Algebraic Computation – year: 2000 ident: br000150 article-title: Multiobjective Nonlinear Pareto-Optimization – start-page: 261 year: 1990 end-page: 264 ident: br000110 article-title: An improvement of the projection operator in cylindrical algebraic decomposition publication-title: Proceedings of the International Symposium on Symbolic and Algebraic Computation – volume: 17 start-page: 920 year: 2006 end-page: 942 ident: br000225 article-title: Global optimization of polynomials using gradient tentacles and sums of squares publication-title: SIAM J. on Optimization – reference: H. Iwane, H. Yanami, H. Anai, An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for optimization problems, in: Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation, vol. 1, 2011, pp. 168–177. – reference: H. Iwane, H. Yanami, H. Anai, K. Yokoyama, An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for quantifier elimination, in: Proceedings of the 2009 International Workshop on Symbolic-Numeric Computation, vol. 1, 2009, pp. 55–64. – start-page: 107 year: 2010 end-page: 114 ident: br000105 article-title: Global optimization of polynomials using generalized critical values and sums of squares publication-title: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation – volume: 5 start-page: 3 year: 1988 end-page: 27 ident: br000250 article-title: The complexity of linear problems in fields publication-title: Journal of Symbolic Computation – volume: 18 start-page: 429 year: 1994 end-page: 445 ident: br000090 article-title: Algebraic numbers: an example of dynamic evaluation publication-title: Journal of Symbolic Computation – start-page: 221 year: 1998 end-page: 247 ident: br000085 article-title: Real quantifier elimination in practice publication-title: Algorithmic Algebra and Number Theory – start-page: 25 year: 2005 end-page: 30 ident: br000020 article-title: Cylindrical algebraic decomposition via numerical computation with validated symbolic reconstruction publication-title: Algorithmic Algebra and Logic – reference: P.A. Parrilo, S. Lall, Semidefinite programming relaxations and algebraic optimization in control, Mini-course on Polynomial Equations and Inequalities I and II, 2006. – volume: vol. 1 year: 2007 ident: br000195 article-title: Multi-parametric programming: theory, algorithms, and applications publication-title: Multi-Parametric Programming – reference: T. Sturm, V. Weispfenning, Rounding and blending of solids by a real elimination method, in: Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling, and Applied Mathematics, IMACS 97, 1997, pp. 727–732. – start-page: 289 year: 1985 end-page: 290 ident: br000080 article-title: About a new method for computing in algebraic number fields publication-title: Research Contributions from the European Conference on Computer Algebra, vol. 2 – reference: L. González-Vega, A combinatorial algorithm solving some quantifier elimination problems, in: Caviness and Johnson – volume: vol. 32 year: 1975 ident: br000055 article-title: Quantifier elimination for real closed fields by cylindrical algebraic decomposition publication-title: LNCS – start-page: 155 year: 2008 end-page: 164 ident: br000140 article-title: Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars publication-title: Proceedings of the Twenty-first International Symposium on Symbolic and Algebraic Computation – year: 1996 ident: br000270 publication-title: Polynomial Algorithms in Computer Algebra – year: 2006 ident: br000025 article-title: Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics) – volume: 41 start-page: 1021 year: 2006 end-page: 1038 ident: br000240 article-title: Cylindrical algebraic decomposition using validated numerics publication-title: Journal of Symbolic Computation – volume: 24 start-page: 189 year: 1997 end-page: 208 ident: br000260 article-title: Simulation and optimization by quantifier elimination publication-title: Journal of Symbolic Computation – volume: 32 start-page: 447 year: 2001 end-page: 465 ident: br000040 article-title: Improved projection for cylindrical algebraic decomposition publication-title: Journal of Symbolic Computation – year: 2005 ident: br000210 article-title: Computer-Assisted Proofs and Self-Validating Methods, vol. 18 (chapter~10), pp. 195–240 – volume: 37 start-page: 97 year: 2003 end-page: 108 ident: br000045 article-title: QEPCAD B: a program for computing with semi-algebraic sets using CADs publication-title: SIGSAM BULLETIN – volume: 36 start-page: 450 year: 1993 end-page: 462 ident: br000160 article-title: Applying linear quantifier elimination publication-title: The Computer Journal – ident: br000220 article-title: Portfolio optimization under nonconvex transaction costs with the global optimization toolbox – volume: vol. 296 start-page: 177 year: 1988 end-page: 197 ident: br000205 article-title: Algebraic computation, numerical computation and verified inclusions publication-title: Trends in Computer Algebra – volume: 29 start-page: 471 year: 2000 end-page: 480 ident: br000235 article-title: Solving systems of strict polynomial inequalities publication-title: Journal of Symbolic Computation – start-page: 83 year: 2001 end-page: 99 ident: br000190 article-title: Minimizing polynomial functions publication-title: Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, vol. 60 – volume: 2 start-page: 31 year: 2001 end-page: 50 ident: br000265 article-title: Efficient Pareto frontier exploration using surrogate approximations publication-title: Optimization and Engineering – volume: 34 start-page: 145 year: 2002 end-page: 157 ident: br000065 article-title: Interval arithmetic in cylindrical algebraic decomposition publication-title: Journal of Symbolic Computation – reference: H. Anai, H. Yanami, S. Hara, K. Sakabe, Fixed-structure robust controller synthesis based on symbolic-numeric computation: design algorithms with a CACSD toolbox, in: Proceedings of CCA/ISIC/CACSD 2004 (Taipei, Taiwan), vol. 2 (9) 2004, pp. 1540–1545,. – reference: , pp. 242–268. – year: 1998 ident: br000050 article-title: Quantifier elimination and cylindrical algebraic decomposition publication-title: Texts and Monographs in Symbolic Computation – year: 2006 ident: 10.1016/j.tcs.2012.10.020_br000025 – volume: 32 start-page: 447 issue: 5 year: 2001 ident: 10.1016/j.tcs.2012.10.020_br000040 article-title: Improved projection for cylindrical algebraic decomposition publication-title: Journal of Symbolic Computation doi: 10.1006/jsco.2001.0463 – start-page: 223 year: 2001 ident: 10.1016/j.tcs.2012.10.020_br000180 article-title: On propagation of equational constraints in CAD-based quantifier elimination – volume: 34 start-page: 145 issue: 2 year: 2002 ident: 10.1016/j.tcs.2012.10.020_br000065 article-title: Interval arithmetic in cylindrical algebraic decomposition publication-title: Journal of Symbolic Computation doi: 10.1006/jsco.2002.0547 – volume: 2 start-page: 31 year: 2001 ident: 10.1016/j.tcs.2012.10.020_br000265 article-title: Efficient Pareto frontier exploration using surrogate approximations publication-title: Optimization and Engineering doi: 10.1023/A:1011818803494 – start-page: 155 year: 2008 ident: 10.1016/j.tcs.2012.10.020_br000140 article-title: Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars – start-page: 25 year: 2005 ident: 10.1016/j.tcs.2012.10.020_br000020 article-title: Cylindrical algebraic decomposition via numerical computation with validated symbolic reconstruction – volume: 5 start-page: 29 issue: 1/2 year: 1988 ident: 10.1016/j.tcs.2012.10.020_br000070 article-title: Real quantifier elimination is doubly exponential publication-title: Journal of Symbolic Computation doi: 10.1016/S0747-7171(88)80004-X – volume: vol. 1 year: 2007 ident: 10.1016/j.tcs.2012.10.020_br000195 article-title: Multi-parametric programming: theory, algorithms, and applications – ident: 10.1016/j.tcs.2012.10.020_br000010 – ident: 10.1016/j.tcs.2012.10.020_br000100 doi: 10.1007/978-3-7091-9459-1_19 – year: 2001 ident: 10.1016/j.tcs.2012.10.020_br000075 – year: 1998 ident: 10.1016/j.tcs.2012.10.020_br000050 article-title: Quantifier elimination and cylindrical algebraic decomposition – year: 1996 ident: 10.1016/j.tcs.2012.10.020_br000270 – start-page: 107 year: 2010 ident: 10.1016/j.tcs.2012.10.020_br000105 article-title: Global optimization of polynomials using generalized critical values and sums of squares – volume: vol. 296 start-page: 177 year: 1988 ident: 10.1016/j.tcs.2012.10.020_br000205 article-title: Algebraic computation, numerical computation and verified inclusions – start-page: 221 year: 1998 ident: 10.1016/j.tcs.2012.10.020_br000085 article-title: Real quantifier elimination in practice – volume: 11 start-page: 796 issue: 3 year: 2001 ident: 10.1016/j.tcs.2012.10.020_br000155 article-title: Global optimization with polynomials and the problem of moments publication-title: SIAM Journal on Optimization doi: 10.1137/S1052623400366802 – ident: 10.1016/j.tcs.2012.10.020_br000185 – ident: 10.1016/j.tcs.2012.10.020_br000005 doi: 10.1109/ACC.2000.876713 – volume: 24 start-page: 189 issue: August year: 1997 ident: 10.1016/j.tcs.2012.10.020_br000260 article-title: Simulation and optimization by quantifier elimination publication-title: Journal of Symbolic Computation doi: 10.1006/jsco.1997.0122 – volume: vol. 32 year: 1975 ident: 10.1016/j.tcs.2012.10.020_br000055 article-title: Quantifier elimination for real closed fields by cylindrical algebraic decomposition – ident: 10.1016/j.tcs.2012.10.020_br000015 doi: 10.1109/CCA.2004.1387594 – volume: 47 start-page: 883 issue: 7 year: 2011 ident: 10.1016/j.tcs.2012.10.020_br000125 article-title: Variant quantifier elimination publication-title: Journal of Symbolic Computation doi: 10.1016/j.jsc.2011.05.014 – ident: 10.1016/j.tcs.2012.10.020_br000130 doi: 10.1145/2331684.2331712 – start-page: 571 year: 1996 ident: 10.1016/j.tcs.2012.10.020_br000120 article-title: An efficient method for analyzing the topology of plane real algebraic curves – volume: 22 start-page: 83 issue: July year: 1996 ident: 10.1016/j.tcs.2012.10.020_br000095 article-title: Applying quantifier elimination to the Birkhoff interpolation problem publication-title: Journal of Symbolic Computation doi: 10.1006/jsco.1996.0042 – volume: 5 start-page: 3 issue: February year: 1988 ident: 10.1016/j.tcs.2012.10.020_br000250 article-title: The complexity of linear problems in fields publication-title: Journal of Symbolic Computation doi: 10.1016/S0747-7171(88)80003-8 – ident: 10.1016/j.tcs.2012.10.020_br000245 – ident: 10.1016/j.tcs.2012.10.020_br000220 – volume: 8 start-page: 85 year: 1993 ident: 10.1016/j.tcs.2012.10.020_br000255 article-title: Quantifier elimination for real algebra — the quadratic case and beyond publication-title: AAECC doi: 10.1007/s002000050055 – start-page: 187 year: 1969 ident: 10.1016/j.tcs.2012.10.020_br000145 article-title: Newton-algorithmen zur bestimmung von nullstellen mit fehlerschranken publication-title: Computing doi: 10.1007/BF02234767 – volume: 8 start-page: 21 issue: 1 year: 2002 ident: 10.1016/j.tcs.2012.10.020_br000200 article-title: Approximate quantified constraint solving by cylindrical box decomposition publication-title: Reliable Computing doi: 10.1023/A:1014785518570 – volume: 41 start-page: 1021 issue: 9 year: 2006 ident: 10.1016/j.tcs.2012.10.020_br000240 article-title: Cylindrical algebraic decomposition using validated numerics publication-title: Journal of Symbolic Computation doi: 10.1016/j.jsc.2006.06.004 – ident: 10.1016/j.tcs.2012.10.020_br000030 doi: 10.1145/309831.309890 – volume: 29 start-page: 471 issue: March year: 2000 ident: 10.1016/j.tcs.2012.10.020_br000235 article-title: Solving systems of strict polynomial inequalities publication-title: Journal of Symbolic Computation doi: 10.1006/jsco.1999.0327 – start-page: 145 year: 1999 ident: 10.1016/j.tcs.2012.10.020_br000175 article-title: On projection in CAD-based quantifier elimination with equational constraint – ident: 10.1016/j.tcs.2012.10.020_br000170 doi: 10.1007/978-3-7091-9459-1_12 – ident: 10.1016/j.tcs.2012.10.020_br000135 doi: 10.1145/1577190.1577203 – start-page: 48 year: 2000 ident: 10.1016/j.tcs.2012.10.020_br000035 article-title: Improved projection for CAD’s of R3 – volume: 36 start-page: 450 issue: 5 year: 1993 ident: 10.1016/j.tcs.2012.10.020_br000160 article-title: Applying linear quantifier elimination publication-title: The Computer Journal doi: 10.1093/comjnl/36.5.450 – start-page: 261 year: 1990 ident: 10.1016/j.tcs.2012.10.020_br000110 article-title: An improvement of the projection operator in cylindrical algebraic decomposition – start-page: 289 year: 1985 ident: 10.1016/j.tcs.2012.10.020_br000080 article-title: About a new method for computing in algebraic number fields – start-page: 71 year: 2008 ident: 10.1016/j.tcs.2012.10.020_br000215 article-title: Computing the global optimum of a multivariate polynomial over the reals – start-page: 264 year: 1993 ident: 10.1016/j.tcs.2012.10.020_br000115 article-title: Quantifier elimination for formulas constrained by quadratic equations – volume: 12 start-page: 299 issue: 3 year: 1991 ident: 10.1016/j.tcs.2012.10.020_br000060 article-title: Partial cylindrical algebraic decomposition for quantifier elimination publication-title: Journal of Symbolic Computation doi: 10.1016/S0747-7171(08)80152-6 – year: 2000 ident: 10.1016/j.tcs.2012.10.020_br000150 – volume: 18 start-page: 429 issue: 5 year: 1994 ident: 10.1016/j.tcs.2012.10.020_br000090 article-title: Algebraic numbers: an example of dynamic evaluation publication-title: Journal of Symbolic Computation doi: 10.1006/jsco.1994.1057 – start-page: 83 year: 2001 ident: 10.1016/j.tcs.2012.10.020_br000190 article-title: Minimizing polynomial functions – volume: 17 start-page: 920 issue: September year: 2006 ident: 10.1016/j.tcs.2012.10.020_br000225 article-title: Global optimization of polynomials using gradient tentacles and sums of squares publication-title: SIAM J. on Optimization doi: 10.1137/050647098 – volume: 5 start-page: 337 issue: 3 year: 1999 ident: 10.1016/j.tcs.2012.10.020_br000230 article-title: A real polynomial decision algorithm using arbitrary-precision floating point arithmetic publication-title: Reliable Computing doi: 10.1023/A:1009924521389 – start-page: 432 year: 1993 ident: 10.1016/j.tcs.2012.10.020_br000165 article-title: Solving polynomial strict inequalities using cylindrical algebraic decomposition publication-title: The Computer Journal doi: 10.1093/comjnl/36.5.432 – year: 2005 ident: 10.1016/j.tcs.2012.10.020_br000210 – volume: 37 start-page: 97 year: 2003 ident: 10.1016/j.tcs.2012.10.020_br000045 article-title: QEPCAD B: a program for computing with semi-algebraic sets using CADs publication-title: SIGSAM BULLETIN doi: 10.1145/968708.968710 |
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| Title | An effective implementation of symbolic–numeric cylindrical algebraic decomposition for quantifier elimination |
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