Edit Profile (opens in new tab) Xia, Bican Compute Distance To: Compute Author ID: xia.bican Published as: Xia, Bican; Xia, BiCan; Xia, B. C. more...less Documents Indexed: 60 Publications since 1998, including 1 Book Co-Authors: 50 Co-Authors with 59 Joint Publications 1,959 Co-Co-Authors all top 5 Co-Authors 1 single-authored 15 Yang, Lu 12 Zhan, Naijun 10 Dai, Liyun 7 Moreno Maza, Marc 7 Xiao, Rong 6 Chen, Changbo 5 Davenport, James Harold 5 Gan, Ting 5 Zheng, Zhiming 4 She, Zhikun 4 Tang, Xiaoxian 4 Zhang, Zhihai 3 Chen, Mingshuai 3 Chen, Zhenghong 3 Han, Jingjun 3 Hou, Xiaorong 3 Li, Haokun 2 Chen, Yinghua 2 Hong, Hoon 2 Li, Yangjia 2 May, John P. 2 Wang, Yu 2 Wu, Wenyuan 2 Xue, Bai 2 Zhang, Ting 2 Zheng, Tao 2 Zhou, Chaochen 1 Chen, Min 1 Fan, Zhe 1 Fang, Tian 1 Feng, Yijun 1 Guan, Qiang 1 Jansen, David N. 1 Jin, Zhi 1 Kapur, Deepak 1 Lemaire, François 1 Li, Haoyang 1 Li, Yinglin 1 Ning, Shucheng 1 Shen, Fei 1 Wang, Dongming 1 Wang, Jie 1 Wang, Long 1 Wang, Qiuye 1 Xie, Yuzhen 1 Yu, Wensheng 1 Zeng, Zhenbing 1 Zhang, Hanwen 1 Zhang, Huiying 1 Zhang, Lijun all top 5 Serials 10 Journal of Symbolic Computation 4 Journal of Systems Science and Complexity 3 Computers & Mathematics with Applications 2 Journal of Sichuan University. Natural Science Edition 2 Science in China. Series F 2 Mathematics in Computer Science 2 Science China. Information Sciences 1 IEEE Transactions on Automatic Control 1 Journal of Computational and Applied Mathematics 1 Acta Mathematicae Applicatae Sinica 1 Journal of Systems Science and Mathematical Sciences 1 Formal Aspects of Computing 1 Journal of Global Optimization 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Nonlinear Analysis. Hybrid Systems 1 ACM Communications in Computer Algebra 1 Scientia Sinica. Mathematica 1 Frontiers of Computer Science in China all top 5 Fields 44 Computer science (68-XX) 11 Numerical analysis (65-XX) 10 Algebraic geometry (14-XX) 10 Operations research, mathematical programming (90-XX) 9 Mathematical logic and foundations (03-XX) 9 Field theory and polynomials (12-XX) 7 Commutative algebra (13-XX) 6 Systems theory; control (93-XX) 5 Real functions (26-XX) 3 Ordinary differential equations (34-XX) 3 Biology and other natural sciences (92-XX) 2 Functions of a complex variable (30-XX) 2 Geometry (51-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 43 Publications have been cited 302 times in 185 Documents Cited by ▼ Year ▼ A complete algorithm for automated discovering of a class of inequality-type theorems. Zbl 1125.68406Yang, Lu; Hou, Xiaorong; Xia, Bican 31 2001 Computing cylindrical algebraic decomposition via triangular decomposition. Zbl 1237.14068Chen, Changbo; Moreno Maza, Marc; Xia, Bican; Yang, Lu 27 2009 An algorithm for isolating the real solutions of semi-algebraic systems. Zbl 1027.68150Xia, Bican; Yang, Lu 24 2002 Stability analysis of biological systems with real solution classification. Zbl 1360.92048Wang, Dongming; Xia, Bican 17 2005 Real solution isolation using interval arithmetic. Zbl 1131.65041Xia, Bican; Zhang, Ting 16 2006 Triangular decomposition of semi-algebraic systems. Zbl 1260.14070Chen, Changbo; Davenport, James H.; May, John P.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong 14 2013 Barrier certificates revisited. Zbl 1357.68110Dai, Liyun; Gan, Ting; Xia, Bican; Zhan, Naijun 11 2017 Constructing fewer open cells by GCD computation in CAD projection. Zbl 1325.68286Han, Jingjun; Dai, Liyun; Xia, Bican 10 2014 A complete algorithm for counting real solutions of polynomial systems of equations and inequalities. Zbl 1035.65054Xia, Bican; Hou, Xiaorong 10 2002 Discovering non-linear ranking functions by solving semi-algebraic systems. Zbl 1147.68442Chen, Yinghua; Xia, Bican; Yang, Lu; Zhan, Naijun; Zhou, Chaochen 10 2007 Discovering polynomial Lyapunov functions for continuous dynamical systems. Zbl 1338.37025She, Zhikun; Li, Haoyang; Xue, Bai; Zheng, Zhiming; Xia, Bican 9 2013 Triangular decomposition of semi-algebraic systems. Zbl 1321.68526Chen, Changbo; Davenport, James H.; May, John P.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong 8 2010 Termination of linear programs with nonlinear constraints. Zbl 1208.68151Xia, Bican; Zhang, Zhihai 8 2010 A semi-algebraic approach for asymptotic stability analysis. Zbl 1217.93153She, Zhikun; Xia, Bican; Xiao, Rong; Zheng, Zhiming 8 2009 Generating polynomial invariants with DISCOVERER and QEPCAD. Zbl 1151.68366Chen, Yinghua; Xia, Bican; Yang, Lu; Zhan, Naijun 7 2007 Reachability analysis for solvable dynamical systems. Zbl 1423.93057Gan, Ting; Chen, Mingshuai; Li, Yangjia; Xia, Bican; Zhan, Naijun 6 2018 Recent advances in program verification through computer algebra. Zbl 1267.68099Yang, Lu; Zhou, Chaochen; Zhan, Naijun; Xia, Bican 6 2010 Generating non-linear interpolants by semidefinite programming. Zbl 1503.68181Dai, Liyun; Xia, Bican; Zhan, Naijun 6 2013 Special algorithm for stability analysis of multistable biological regulatory systems. Zbl 1328.92028Hong, Hoon; Tang, Xiaoxian; Xia, Bican 5 2015 Proving inequalities and solving global optimization problems via simplified CAD projection. Zbl 1337.90052Han, Jingjun; Jin, Zhi; Xia, Bican 5 2016 Automated inequality proving and discovering. Zbl 1362.26001Xia, Bican; Yang, Lu 5 2016 A new sparse SOS decomposition algorithm based on term sparsity. Zbl 1467.68234Wang, Jie; Li, Haokun; Xia, Bican 5 2019 Automated discovering and proving for geometric inequalities. Zbl 0947.03017Yang, Lu; Hou, Xiaorong; Xia, Bican 5 1999 Symbolic decision procedure for termination of linear programs. Zbl 1216.68077Xia, Bican; Yang, Lu; Zhan, Naijun; Zhang, Zhihai 5 2011 Interpolant synthesis for quadratic polynomial inequalities and combination with EUF. Zbl 1475.03072Gan, Ting; Dai, Liyun; Xia, Bican; Zhan, Naijun; Kapur, Deepak; Chen, Mingshuai 4 2016 Computing with semi-algebraic sets represented by triangular decomposition. Zbl 1323.14029Chen, Changbo; Davenport, James H.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong 4 2011 Real root isolation of polynomial equations based on hybrid computation. Zbl 1336.65080Shen, Fei; Wu, Wenyuan; Xia, Bican 3 2014 Computing with semi-algebraic sets: relaxation techniques and effective boundaries. Zbl 1277.13021Chen, Changbo; Davenport, James H.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong 3 2013 Decidability of the reachability for a family of linear vector fields. Zbl 1476.68147Gan, Ting; Chen, Mingshuai; Dai, Liyun; Xia, Bican; Zhan, Naijun 3 2015 Generic regular decompositions for parametric polynomial systems. Zbl 1327.93101Chen, Zhenghong; Tang, Xiaoxian; Xia, Bican 3 2015 Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems. Zbl 1420.68244Wang, Qiuye; Li, Yangjia; Xia, Bican; Zhan, Naijun 3 2017 On solving parametric polynomial systems. Zbl 1274.13047Maza, Marc Moreno; Xia, Bican; Xiao, Rong 3 2012 Finding polynomial loop invariants for probabilistic programs. Zbl 1495.68042Feng, Yijun; Zhang, Lijun; Jansen, David N.; Zhan, Naijun; Xia, Bican 3 2017 Open weak CAD and its applications. Zbl 1410.68410Han, Jingjun; Dai, Liyun; Hong, Hoon; Xia, Bican 2 2017 Nonlinear Craig interpolant generation. Zbl 1478.68159Gan, Ting; Xia, Bican; Xue, Bai; Zhan, Naijun; Dai, Liyun 2 2020 An effective framework for constructing exponent lattice basis of nonzero algebraic numbers. Zbl 1462.11113Zheng, Tao; Xia, Bican 2 2019 Condition number based complexity estimate for solving polynomial systems. Zbl 1211.65059She, Zhikun; Xia, Bican; Zheng, Zhiming 2 2011 Some properties of the discrimination matrix of polynomials with applications. Zbl 1051.15010Xia, Bican; Yang, Lu 2 2003 A special homotopy continuation method for a class of polynomial systems. Zbl 1455.65079Wang, Yu; Wu, Wenyuan; Xia, Bican 1 2017 Real solution isolation with multiplicity of zero-dimensional triangular systems. Zbl 1218.65046Zhang, ZhiHai; Fang, Tian; Xia, BiCan 1 2011 Solution to the generalized champagne problem on simultaneous stabilization of linear systems. Zbl 1124.93030Guan, Qiang; Wang, Long; Xia, Bican; Yang, Lu; Yu, Wensheng; Zeng, Zhenbing 1 2007 A new method for real root isolation of univariate polynomials. Zbl 1132.68074Zhang, Ting; Xia, Bican 1 2007 Automated deduction in real geometry. Zbl 1082.65054Yang, Lu; Xia, Bican 1 2004 Nonlinear Craig interpolant generation. Zbl 1478.68159Gan, Ting; Xia, Bican; Xue, Bai; Zhan, Naijun; Dai, Liyun 2 2020 A new sparse SOS decomposition algorithm based on term sparsity. Zbl 1467.68234Wang, Jie; Li, Haokun; Xia, Bican 5 2019 An effective framework for constructing exponent lattice basis of nonzero algebraic numbers. Zbl 1462.11113Zheng, Tao; Xia, Bican 2 2019 Reachability analysis for solvable dynamical systems. Zbl 1423.93057Gan, Ting; Chen, Mingshuai; Li, Yangjia; Xia, Bican; Zhan, Naijun 6 2018 Barrier certificates revisited. Zbl 1357.68110Dai, Liyun; Gan, Ting; Xia, Bican; Zhan, Naijun 11 2017 Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems. Zbl 1420.68244Wang, Qiuye; Li, Yangjia; Xia, Bican; Zhan, Naijun 3 2017 Finding polynomial loop invariants for probabilistic programs. Zbl 1495.68042Feng, Yijun; Zhang, Lijun; Jansen, David N.; Zhan, Naijun; Xia, Bican 3 2017 Open weak CAD and its applications. Zbl 1410.68410Han, Jingjun; Dai, Liyun; Hong, Hoon; Xia, Bican 2 2017 A special homotopy continuation method for a class of polynomial systems. Zbl 1455.65079Wang, Yu; Wu, Wenyuan; Xia, Bican 1 2017 Proving inequalities and solving global optimization problems via simplified CAD projection. Zbl 1337.90052Han, Jingjun; Jin, Zhi; Xia, Bican 5 2016 Automated inequality proving and discovering. Zbl 1362.26001Xia, Bican; Yang, Lu 5 2016 Interpolant synthesis for quadratic polynomial inequalities and combination with EUF. Zbl 1475.03072Gan, Ting; Dai, Liyun; Xia, Bican; Zhan, Naijun; Kapur, Deepak; Chen, Mingshuai 4 2016 Special algorithm for stability analysis of multistable biological regulatory systems. Zbl 1328.92028Hong, Hoon; Tang, Xiaoxian; Xia, Bican 5 2015 Decidability of the reachability for a family of linear vector fields. Zbl 1476.68147Gan, Ting; Chen, Mingshuai; Dai, Liyun; Xia, Bican; Zhan, Naijun 3 2015 Generic regular decompositions for parametric polynomial systems. Zbl 1327.93101Chen, Zhenghong; Tang, Xiaoxian; Xia, Bican 3 2015 Constructing fewer open cells by GCD computation in CAD projection. Zbl 1325.68286Han, Jingjun; Dai, Liyun; Xia, Bican 10 2014 Real root isolation of polynomial equations based on hybrid computation. Zbl 1336.65080Shen, Fei; Wu, Wenyuan; Xia, Bican 3 2014 Triangular decomposition of semi-algebraic systems. Zbl 1260.14070Chen, Changbo; Davenport, James H.; May, John P.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong 14 2013 Discovering polynomial Lyapunov functions for continuous dynamical systems. Zbl 1338.37025She, Zhikun; Li, Haoyang; Xue, Bai; Zheng, Zhiming; Xia, Bican 9 2013 Generating non-linear interpolants by semidefinite programming. Zbl 1503.68181Dai, Liyun; Xia, Bican; Zhan, Naijun 6 2013 Computing with semi-algebraic sets: relaxation techniques and effective boundaries. Zbl 1277.13021Chen, Changbo; Davenport, James H.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong 3 2013 On solving parametric polynomial systems. Zbl 1274.13047Maza, Marc Moreno; Xia, Bican; Xiao, Rong 3 2012 Symbolic decision procedure for termination of linear programs. Zbl 1216.68077Xia, Bican; Yang, Lu; Zhan, Naijun; Zhang, Zhihai 5 2011 Computing with semi-algebraic sets represented by triangular decomposition. Zbl 1323.14029Chen, Changbo; Davenport, James H.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong 4 2011 Condition number based complexity estimate for solving polynomial systems. Zbl 1211.65059She, Zhikun; Xia, Bican; Zheng, Zhiming 2 2011 Real solution isolation with multiplicity of zero-dimensional triangular systems. Zbl 1218.65046Zhang, ZhiHai; Fang, Tian; Xia, BiCan 1 2011 Triangular decomposition of semi-algebraic systems. Zbl 1321.68526Chen, Changbo; Davenport, James H.; May, John P.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong 8 2010 Termination of linear programs with nonlinear constraints. Zbl 1208.68151Xia, Bican; Zhang, Zhihai 8 2010 Recent advances in program verification through computer algebra. Zbl 1267.68099Yang, Lu; Zhou, Chaochen; Zhan, Naijun; Xia, Bican 6 2010 Computing cylindrical algebraic decomposition via triangular decomposition. Zbl 1237.14068Chen, Changbo; Moreno Maza, Marc; Xia, Bican; Yang, Lu 27 2009 A semi-algebraic approach for asymptotic stability analysis. Zbl 1217.93153She, Zhikun; Xia, Bican; Xiao, Rong; Zheng, Zhiming 8 2009 Discovering non-linear ranking functions by solving semi-algebraic systems. Zbl 1147.68442Chen, Yinghua; Xia, Bican; Yang, Lu; Zhan, Naijun; Zhou, Chaochen 10 2007 Generating polynomial invariants with DISCOVERER and QEPCAD. Zbl 1151.68366Chen, Yinghua; Xia, Bican; Yang, Lu; Zhan, Naijun 7 2007 Solution to the generalized champagne problem on simultaneous stabilization of linear systems. Zbl 1124.93030Guan, Qiang; Wang, Long; Xia, Bican; Yang, Lu; Yu, Wensheng; Zeng, Zhenbing 1 2007 A new method for real root isolation of univariate polynomials. Zbl 1132.68074Zhang, Ting; Xia, Bican 1 2007 Real solution isolation using interval arithmetic. Zbl 1131.65041Xia, Bican; Zhang, Ting 16 2006 Stability analysis of biological systems with real solution classification. Zbl 1360.92048Wang, Dongming; Xia, Bican 17 2005 Automated deduction in real geometry. Zbl 1082.65054Yang, Lu; Xia, Bican 1 2004 Some properties of the discrimination matrix of polynomials with applications. Zbl 1051.15010Xia, Bican; Yang, Lu 2 2003 An algorithm for isolating the real solutions of semi-algebraic systems. Zbl 1027.68150Xia, Bican; Yang, Lu 24 2002 A complete algorithm for counting real solutions of polynomial systems of equations and inequalities. Zbl 1035.65054Xia, Bican; Hou, Xiaorong 10 2002 A complete algorithm for automated discovering of a class of inequality-type theorems. Zbl 1125.68406Yang, Lu; Hou, Xiaorong; Xia, Bican 31 2001 Automated discovering and proving for geometric inequalities. Zbl 0947.03017Yang, Lu; Hou, Xiaorong; Xia, Bican 5 1999 all cited Publications top 5 cited Publications all top 5 Cited by 325 Authors 24 Xia, Bican 14 England, Matthew 11 Davenport, James Harold 10 Chen, Changbo 10 Zhan, Naijun 8 Moreno Maza, Marc 8 She, Zhikun 7 Tang, Xiaoxian 6 Niu, Wei 6 Wang, Dongming 5 Bradford, Russell J. 5 Chen, Mingshuai 5 Huang, Bo 5 Wilson, David J. 5 Wu, Wenyuan 5 Yang, Lu 5 Zhang, Zhihai 5 Zhao, Hengjun 4 Dai, Liyun 4 Feng, Yong 4 Gao, Xiaoshan 4 Kapur, Deepak 4 Wang, Jie 4 Zheng, Zhiming 3 Boulier, François 3 Cheng, Jinsan 3 Han, Jingjun 3 Katoen, Joost-Pieter 3 Lai, Yisheng 3 Lemaire, François 3 Li, Yi 3 Magron, Victor 3 Mou, Chenqi 3 Sturm, Thomas 3 Sun, Xianbo 3 Wang, Jihua 3 Wang, Qiuye 3 Wang, Renhong 3 Wu, Jinming 3 Wu, Min 3 Xu, Ming 3 Xue, Bai 3 Yang, Zhengfeng 3 Yu, Pei 3 Zeng, Zhenbing 3 Zhi, Lihong 2 Ábrahám, Erika 2 Bridge, James P. 2 Chen, Zhenghong 2 Florescu, Dorian 2 Giesl, Peter 2 Hafstein, Sigurður Freyr 2 Hong, Hoon 2 Hou, Xiaorong 2 Huang, Chengchao 2 Huang, Zongyan 2 Jamiołkowski, Andrzej 2 Jiang, Xin 2 Kazemi, Mahsa 2 Lasserre, Jean-Bernard 2 Li, Xiaoliang 2 Li, Zhibin 2 Lichtblau, Daniel A. 2 Lin, Wang 2 Liu, Jiang 2 Lu, Junjie 2 Ouaknine, Joel O. 2 Pastuszak, Grzegorz 2 Paulson, Lawrence Charles 2 Platzer, André 2 Poteaux, Adrien 2 Safey El Din, Mohab 2 Seiler, Werner M. 2 Skowyrski, Adam 2 Sogokon, Andrew 2 Strzeboński, Adam Wojciech 2 Tan, Yong Kiam 2 Wang, Chu 2 Wang, Long 2 Weber, Andreas Günter 2 Worrell, James B. 2 Xiao, Rong 2 Yang, Zhihong 2 Yap, Chee-Keng 2 Yu, Wensheng 2 Yu, Zhiheng 2 Zhang, Jingzhong 2 Zheng, Tao 1 Abánades, Miguel Angel 1 Abate, Alessandro 1 Abbott, John A. 1 Abdel-Rahman, Essam Othman 1 Ahmed, Daniele 1 Almagor, Shaull 1 Althoff, Matthias 1 Alvandi, Parisa 1 An, Jie 1 Ataei, Masoud 1 Backeman, Peter 1 Baldi, Simone ...and 225 more Authors all top 5 Cited in 55 Serials 31 Journal of Symbolic Computation 18 Journal of Systems Science and Complexity 10 Mathematics in Computer Science 6 Computers & Mathematics with Applications 5 Journal of Computational and Applied Mathematics 5 Theoretical Computer Science 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Discrete and Continuous Dynamical Systems. Series B 4 SIAM Journal on Applied Dynamical Systems 4 Nonlinear Analysis. Hybrid Systems 3 Applied Mathematics and Computation 3 Formal Aspects of Computing 3 Science China. Information Sciences 2 Journal of Mathematical Analysis and Applications 2 Chaos, Solitons and Fractals 2 Automatica 2 Science in China. Series A 2 SIAM Journal on Optimization 2 Formal Methods in System Design 2 Journal of Difference Equations and Applications 1 International Journal of Systems Science 1 Bulletin of Mathematical Biology 1 Journal of Mathematical Economics 1 Journal of Optimization Theory and Applications 1 Le Matematiche 1 SIAM Journal on Control and Optimization 1 Systems & Control Letters 1 Information and Computation 1 Journal of Automated Reasoning 1 Computational Geometry 1 Journal of Global Optimization 1 International Journal of Computer Mathematics 1 Mathematical Programming. Series A. Series B 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 Computational Complexity 1 Computational Optimization and Applications 1 Bulletin des Sciences Mathématiques 1 Abstract and Applied Analysis 1 Journal of Inequalities and Applications 1 Annals of Combinatorics 1 Chaos 1 Acta Mathematica Sinica. English Series 1 Communications in Nonlinear Science and Numerical Simulation 1 Communications in Contemporary Mathematics 1 Qualitative Theory of Dynamical Systems 1 Journal of the Australian Mathematical Society 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Quantum Information Processing 1 Science in China. Series F 1 Electronic Journal of Statistics 1 Frontiers of Computer Science in China 1 Frontiers of Computer Science 1 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 SIAM Journal on Applied Algebra and Geometry all top 5 Cited in 30 Fields 101 Computer science (68-XX) 34 Algebraic geometry (14-XX) 30 Commutative algebra (13-XX) 29 Numerical analysis (65-XX) 24 Ordinary differential equations (34-XX) 21 Systems theory; control (93-XX) 17 Mathematical logic and foundations (03-XX) 17 Field theory and polynomials (12-XX) 16 Biology and other natural sciences (92-XX) 15 Dynamical systems and ergodic theory (37-XX) 15 Operations research, mathematical programming (90-XX) 6 Real functions (26-XX) 4 Number theory (11-XX) 4 Geometry (51-XX) 3 Combinatorics (05-XX) 2 Functions of a complex variable (30-XX) 2 Difference and functional equations (39-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 2 Mechanics of particles and systems (70-XX) 2 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year