Edit Profile (opens in new tab) Davenport, James Harold Co-Author Distance Author ID: davenport.james-harold Published as: Davenport, James H.; Davenport, J. H.; Davenport, James; Davenport, James Harold; Davenport, H. James more...less Homepage: http://staff.bath.ac.uk/masjhd/ External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef Documents Indexed: 130 Publications since 1979, including 3 Books and 2 Additional arXiv Preprints 10 Contributions as Editor · 3 Further Contributions Co-Authors: 109 Co-Authors with 96 Joint Publications 2,553 Co-Co-Authors all top 5 Co-Authors 43 single-authored 28 England, Matthew 27 Bradford, Russell J. 14 Wilson, David J. 7 Chen, Changbo 7 Moreno Maza, Marc 6 Abbott, John A. 5 Sturm, Thomas 5 Xia, Bican 5 Xiao, Rong 4 Ábrahám, Erika 4 Beaumont, James C. 4 McCallum, Scott 4 Phisanbut, Nalina 4 Sankaran, Gregory Kumar 4 Urban, Josef 3 Bigatti, Anna Maria 3 Buchberger, Bruno 3 Corless, Robert Malcolm 3 Griggio, Alberto 3 Jeffrey, David J. 3 Nair, Akshar Sajive 3 Padget, Julian 3 Trager, Barry M. 3 Uncu, Ali Kemal 3 Watt, Stephen Michael 2 Becker, Bernd 2 Brain, Martin 2 Bridge, James P. 2 Brown, Christopher W. 2 Chen, Liqun 2 Cimatti, Alessandro 2 Coppersmith, Don 2 Cruz-Filipe, Luís 2 Errami, Hassan 2 Fontaine, Pascal 2 Forrest, Stephen 2 Gerdt, Vladimir Petrovich 2 Grigor’ev, Dmitriĭ Yur’evich 2 Helfgott, Harald Andrés 2 Hoyt, Charles Tapley 2 Huang, Zongyan 2 Hur, Namhyun 2 Košta, Marek 2 Kröning, Daniel 2 Labahn, George 2 May, John P. 2 Maynard, James 2 Paulson, Lawrence Charles 2 Poonen, Bjorn 2 Pring, Benjamin 2 Radulescu, Ovidiu 2 Seiler, Werner M. 2 Singer, Michael F. 2 Siret, Y. 2 Tiep Pham Huu 2 Weber, Andreas Günter 1 Adams, Andrew A. 1 Asperti, Andrea 1 Atkin, Arthur Oliver Lonsdale 1 Bennett, James P. 1 Bowyer, Adrian 1 Bronstein, Manuel Eric 1 Carette, Jacques 1 Cheb-Terrab, Edgardo S. 1 Coghlan, F. B. 1 Crouch, P. A. 1 Davenport, Harold 1 de Wolff, Timo 1 Dewar, Michael C. 1 Dupée, Brian J. 1 El Kaafarani, Ali 1 Elliott, C. James 1 Farmer, William M. 1 Faure, Christèle 1 Fisher, D. L. 1 Ghadafi, Essam M. 1 Gianni, Patrizia M. 1 Guy, Michael J. T. 1 Heintz, Joos 1 Holt, Andrew J. 1 Joswig, Michael 1 Kauers, Manuel 1 Khader, Dalia 1 Kohlhase, Michael 1 Kovács, Laura Ildikó 1 Kremer, Gereon 1 Kutsia, Temur 1 Lemaire, François 1 Libbrecht, Paul 1 Litt, Gurjeet 1 Locatelli, A. F. 1 Macmillan, R. J. 1 Mignotte, Maurice 1 Milne, Philip 1 Mulligan, Casey B. 1 Nalbach, Jasper 1 Norman, Arthur C. 1 Petit, Christophe 1 Rabe, Florian 1 Sadeghimanesh, AmirHosein ...and 17 more Co-Authors all top 5 Serials 13 Journal of Symbolic Computation 8 ACM Communications in Computer Algebra 7 Lecture Notes in Computer Science 6 Mathematics in Computer Science 5 SIGSAM Bulletin 2 Programming and Computer Software 2 Annales Mathematicae et Informaticae 1 Mathematics of Computation 1 ACM Transactions on Mathematical Software 1 Acta Arithmetica 1 Annales de l’Institut Fourier 1 The Computer Journal. Section A / Section B 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Philosophical Transactions of the Royal Society of London. Ser. A 1 SIAM Journal on Computing 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Applicable Algebra in Engineering, Communication and Computing 1 Euromath Bulletin 1 Integral Transforms and Special Functions 1 Annals of Mathematics and Artificial Intelligence 1 Journal of Logical and Algebraic Methods in Programming all top 5 Fields 116 Computer science (68-XX) 20 Number theory (11-XX) 20 Field theory and polynomials (12-XX) 20 Numerical analysis (65-XX) 17 Algebraic geometry (14-XX) 14 General and overarching topics; collections (00-XX) 11 Commutative algebra (13-XX) 9 Mathematical logic and foundations (03-XX) 6 Special functions (33-XX) 6 Ordinary differential equations (34-XX) 6 Information and communication theory, circuits (94-XX) 4 Real functions (26-XX) 3 Biology and other natural sciences (92-XX) 2 Functions of a complex variable (30-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Group theory and generalizations (20-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 96 Publications have been cited 653 times in 372 Documents Cited by ▼ Year ▼ Real quantifier elimination is doubly exponential. Zbl 0663.03015 Davenport, James H.; Heintz, Joos 87 1988 P-adic reconstruction of rational numbers. Zbl 0489.68032 Wang, Paul S.; Guy, M. J. T.; Davenport, James H. 40 1982 The complexity of quantifier elimination and cylindrical algebraic decomposition. Zbl 1190.68028 Brown, Christopher W.; Davenport, James H. 34 2007 Computer algebra. Systems and algorithms for algebraic computation. Translation from the French by A. Davenport and J. H. Davenport. Zbl 0679.68058 Davenport, J. H.; Siret, Y.; Tournier, G. 32 1988 Computer algebra. Systems and algorithms for algebraic computation. Transl. from the French by A. Davenport a. J. H. Davenport. 2nd ed. Zbl 0865.68064 Davenport, J. H.; Siret, Y.; Tournier, E. 24 1993 Truth table invariant cylindrical algebraic decomposition. Zbl 1351.68314 Bradford, Russell; Davenport, James H.; England, Matthew; McCallum, Scott; Wilson, David 22 2016 On the integration of algebraic functions. Zbl 0471.14009 Davenport, James Harold 20 1981 Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition. Zbl 1304.68224 Huang, Zongyan; England, Matthew; Wilson, David; Davenport, James H.; Paulson, Lawrence C.; Bridge, James 14 2014 Cylindrical algebraic decompositions for Boolean combinations. Zbl 1359.68327 Bradford, Russell; Davenport, James H.; England, Matthew; McCallum, Scott; Wilson, David 14 2013 Optimising problem formulation for cylindrical algebraic decomposition. Zbl 1390.68775 Bradford, Russell; Davenport, James H.; England, Matthew; Wilson, David 14 2013 Triangular decomposition of semi-algebraic systems. Zbl 1260.14070 Chen, Changbo; Davenport, James H.; May, John P.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong 14 2013 SC\(^2\): satisfiability checking meets symbolic computation. (Project paper). Zbl 1344.68198 Ábrahám, Erika; Abbott, John; Becker, Bernd; Bigatti, Anna M.; Brain, Martin; Buchberger, Bruno; Cimatti, Alessandro; Davenport, James H.; England, Matthew; Fontaine, Pascal; Forrest, Stephen; Griggio, Alberto; Kroening, Daniel; Seiler, Werner M.; Sturm, Thomas 13 2016 A case study on the parametric occurrence of multiple steady states. Zbl 1444.92034 Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas 13 2017 Improving the use of equational constraints in cylindrical algebraic decomposition. Zbl 1346.68283 England, Matthew; Bradford, Russell; Davenport, James H. 12 2015 The Risch differential equation problem. Zbl 0632.65091 Davenport, J. H. 11 1986 The higher arithmetic. An introduction to the theory of numbers. Editing and additional material by James H. Davenport. 8th revised ed. Zbl 1204.11002 Davenport, Harold 11 2008 Truth table invariant cylindrical algebraic decomposition by regular chains. Zbl 1350.68293 Bradford, Russell; Chen, Changbo; Davenport, James H.; England, Matthew; Moreno Maza, Marc; Wilson, David 10 2014 Using machine learning to improve cylindrical algebraic decomposition. Zbl 1474.68464 Huang, Zongyan; England, Matthew; Wilson, David J.; Bridge, James; Davenport, James H.; Paulson, Lawrence C. 10 2019 Cylindrical algebraic decomposition with equational constraints. Zbl 1432.68599 England, Matthew; Bradford, Russell; Davenport, James H. 10 2020 Triangular decomposition of semi-algebraic systems. Zbl 1321.68526 Chen, Changbo; Davenport, James H.; May, John P.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong 9 2010 On the parallel Risch algorithm. II. Zbl 0606.68032 Davenport, J. H.; Trager, B. M. 9 1985 Cylindrical algebraic sub-decompositions. Zbl 1309.68232 Wilson, D. J.; Bradford, R. J.; Davenport, J. H.; England, M. 9 2014 Identifying the parametric occurrence of multiple steady states for some biological networks. Zbl 1442.92056 Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas 9 2020 Using the Regular Chains library to build cylindrical algebraic decompositions by projecting and lifting. Zbl 1437.14008 England, Matthew; Wilson, David; Bradford, Russell; Davenport, James H. 8 2014 Deciding the consistency of non-linear real arithmetic constraints with a conflict driven search using cylindrical algebraic coverings. Zbl 1509.68243 Ábrahám, Erika; Davenport, James H.; England, Matthew; Kremer, Gereon 8 2021 Intelligent computer mathematics. International conference, CICM 2014, Coimbra, Portugal, July 7–11, 2014. Proceedings. Zbl 1293.68035 7 2014 Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. Zbl 1304.68223 England, Matthew; Bradford, Russell; Chen, Changbo; Davenport, James H.; Maza, Marc Moreno; Wilson, David 7 2014 Elementary and Liouvillian solutions of linear differential equations. Zbl 0652.12016 Davenport, J. H.; Singer, M. F. 7 1986 The complexity of cylindrical algebraic decomposition with respect to polynomial degree. Zbl 1453.13079 England, Matthew; Davenport, James H. 6 2016 Fast recognition of alternating and symmetric Galois groups. Zbl 0960.11053 Davenport, J. H.; Smith, G. C. 6 2000 TheoryGuru: a Mathematica package to apply quantifier elimination technology to economics. Zbl 1395.68350 Mulligan, Casey B.; Davenport, James H.; England, Matthew 6 2018 Polynomials whose powers are sparse. Zbl 0729.11015 Coppersmith, Don; Davenport, James 6 1991 Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. Zbl 1350.68294 England, Matthew; Bradford, Russell; Davenport, James H.; Wilson, David 6 2014 Integration in closed form. Zbl 0661.26006 Davenport, J. H. 6 1988 Intégration algorithmique des fonctions élémentairement transcendantes sur une courbe algébrique. Zbl 0506.34002 Davenport, James H. 6 1983 Towards better simplification of elementary functions. Zbl 1072.68651 Bradford, Russell; Davenport, James H. 6 2002 Reasoning about the elementary functions of complex analysis. Zbl 1007.30001 Bradford, Russell; Corless, Robert M.; Davenport, James H.; Jeffrey, David J.; Watt, Stephen M. 5 2002 On finding the largest root of a polynomial. Zbl 0715.65033 Davenport, J. H.; Mignotte, M. 5 1990 Computing with semi-algebraic sets represented by triangular decomposition. Zbl 1323.14029 Chen, Changbo; Davenport, James H.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong 5 2011 Symbolic integration - the dust settles? Zbl 0399.68056 Norman, A. C.; Davenport, James H. 5 1979 Factorization over finitely generated fields. Zbl 0481.68040 Davenport, James H.; Trager, Barry M. 5 1981 Speeding up cylindrical algebraic decomposition by Gröbner bases. Zbl 1360.68959 Wilson, David J.; Bradford, Russell J.; Davenport, James H. 5 2012 Scratchpad’s view of algebra. II: A categorical view of factorization. Zbl 0921.13011 Davenport, J. H.; Gianni, P.; Trager, B. M. 4 1991 A repository for CAD examples. Zbl 1322.68294 Wilson, David J.; Bradford, Russell J.; Davenport, James H. 4 2012 Improvements to quantum search techniques for block-ciphers, with applications to AES. Zbl 1485.94078 Davenport, James H.; Pring, Benjamin 4 2021 Editorial: Symbolic computation and satisfiability checking. Zbl 1444.68006 4 2020 Algebraic properties of the Lambert \(W\) function from a result of Rosenlicht and of Liouville. Zbl 1156.33004 Bronstein, Manuel; Corless, Robert M.; Davenport, James H.; Jeffrey, D. J. 4 2008 Equality in computer algebra and beyond. Zbl 1037.68161 Davenport, James H. 4 2002 Algorithms for the integration of algebraic functions. Zbl 0411.34002 Davenport, James H. 3 1979 Geometry of branch cuts. Zbl 1305.68367 Phisanbut, Nalina; Bradford, Russell J.; Davenport, James H. 3 2010 HEUGCD: How elementary upperbounds generate cheaper data. Zbl 0603.68037 Davenport, James; Padget, Julian 3 1985 A ”Piano movers” problem. Zbl 0623.68036 Davenport, J. H. 3 1986 Integration - what do we want from the theory? Zbl 0556.68008 Davenport, James H. 3 1983 The parallel Risch algorithm. I. Zbl 0538.68024 Davenport, James H. 3 1982 On the parallel Risch algorithm. III: Use of tangents. Zbl 0538.68025 Davenport, James H. 3 1982 Understanding branch cuts of expressions. Zbl 1390.68777 England, Matthew; Bradford, Russell; Davenport, James H.; Wilson, David 3 2013 Unit knowledge management. Zbl 1166.68360 Stratford, Jonathan; Davenport, James H. 3 2008 The freedom to extend OpenMath and its utility. Zbl 1173.00301 Davenport, James H.; Libbrecht, Paul 3 2008 Curtains in CAD: why are they a problem and how do we fix them? Zbl 1503.68314 Nair, Akshar; Davenport, James; Sankaran, Gregory 3 2020 Computing with semi-algebraic sets: relaxation techniques and effective boundaries. Zbl 1277.13021 Chen, Changbo; Davenport, James H.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong 3 2013 What does “without loss of generality” mean, and how do we detect it. Zbl 1425.68464 Davenport, James H. 2 2017 Need polynomial systems be doubly-exponential? Zbl 1434.68702 Davenport, James H.; England, Matthew 2 2016 An exact real algebraic arithmetic with equality determination. Zbl 1326.68357 Hur, Namhyun; Davenport, James H. 2 2000 Abstract data types in computer algebra. Zbl 0996.68866 Davenport, James H. 2 2000 A poly-algorithmic approach to simplifying elementary functions. Zbl 1134.68594 Beaumont, James C.; Bradford, Russell J.; Davenport, James H.; Phisanbut, Nalina 2 2004 Computer algebra applied to itself. Zbl 0651.68043 Davenport, J. H. 2 1988 Copyright issues for MKM. Zbl 1108.68581 Adams, Andrew A.; Davenport, James H. 2 2004 Reasoning about the elementary functions of complex analysis. Zbl 1042.68128 Corless, Robert M.; Davenport, James H.; Jeffrey, David J.; Litt, Gurjeet; Watt, Stephen M. 2 2001 Unifying math ontologies: a tale of two standards. Zbl 1247.68268 Davenport, James H.; Kohlhase, Michael 2 2009 Better simplification of elementary functions through power series. Zbl 1072.68646 Beaumont, James; Bradford, Russell; Davenport, James H. 2 2003 Intelligent computer mathematics. 18th symposium, Calculemus 2011, and 10th international conference, MKM 2011, Bertinoro, Italy, July 18–23, 2011. Proceedings. Zbl 1218.68014 2 2011 Mathematical knowledge management. Second international conference, MKM 2003, Bertinoro, Italy, February 16–18, 2003. Proceedings. Zbl 1015.00029 2 2003 Machine-assisted proofs. Zbl 1452.68262 Davenport, James; Poonen, Bjorn; Maynard, James; Helfgott, Harald; Tiep, Pham Huu; Cruz-Filipe, Luís 2 2018 Solving computational problems in real algebra/geometry. Zbl 1340.14001 Davenport, H. James 1 2015 Primality testing revisited. Zbl 0921.11069 Davenport, J. H. 1 1992 Recent advances in real geometric reasoning. Zbl 1434.68701 Davenport, James H.; England, Matthew 1 2015 A generic root operation for exact real arithmetic. Zbl 0985.65042 Hur, Namhyun; Davenport, James H. 1 2001 The potential and challenges of CAD with equational constraints for SC-square. Zbl 1497.68583 Davenport, James H.; England, Matthew 1 2017 Branch cuts in Maple 17. Zbl 1369.68358 England, M.; Cheb-Terrab, E.; Bradford, R.; Davenport, J. H.; Wilson, D. 1 2014 A remark on factorisation. Zbl 0601.12003 Abbott, J. A.; Bradford, R. J.; Davenport, J. H. 1 1985 An application of factoring. Zbl 0601.68033 Coppersmith, D.; Davenport, J. H. 1 1985 Elementary and Liouvillian solutions of linear differential equations. Zbl 0609.12024 Singer, M. F.; Davenport, J. H. 1 1985 Adherence is better than adjacency: computing the Riemann index using CAD. Zbl 1360.14140 Beaumont, James C.; Bradford, Russell J.; Davenport, James H.; Phisanbut, Nalina 1 2005 Closed form solutions of ordinary differential equations. Zbl 0642.65059 Davenport, J. H. 1 1985 Computer algebra approaches to enzyme kinetics. Zbl 0785.92014 Bennett, J. P.; Davenport, J. H.; Dewar, M. C.; Fisher, D. L.; Grinfeld, M.; Sauro, H. M. 1 1991 Computer algebra – past, present and future. Zbl 0938.68973 Davenport, J. H. 1 1994 Effective mathematics - the computer algebra viewpoint. Zbl 0482.03029 Davenport, James H. 1 1981 Effective set membership in computer algebra and beyond. Zbl 1166.68371 Davenport, James H. 1 2008 Lazard’s CAD exploiting equality constraints. Zbl 07640868 Nair, Akshar; Davenport, James; Sankaran, Gregory; McCallum, Scott 1 2019 The DEWCAD project: pushing back the doubly exponential wall of cylindrical algebraic decomposition. Zbl 07581910 Bradford, R.; Davenport, J. H.; England, M.; Sadeghimanesh, A.; Uncu, A. 1 2021 Numerical tables on elliptic curves. Prepared by H. P. F. Swinnerton-Dyer, N. M. Stephens, James Davenport, J. Vélu, F. B. Coghlan, A. O. L. Atkin and D. J. Tingley. Zbl 1214.11006 1 1975 Testing elementary function identities using CAD. Zbl 1142.68618 Beaumont, James C.; Bradford, Russell J.; Davenport, James H.; Phisanbut, Nalina 1 2007 EUROCAL ’87. European Conference on Computer Algebra, Leipzig, GDR, June 2–5, 1987. Proceedings. Zbl 1209.00079 1 1989 Polynomial factorisation: an exploration of Lenstra’s algorithm. Zbl 1209.13032 Abbott, John A.; Davenport, James H. 1 1989 MKM from book to computer: A case study. Zbl 1022.68118 Davenport, James H. 1 2003 The challenges of multivalued “functions”. Zbl 1286.68516 Davenport, James H. 1 2010 Deciding the consistency of non-linear real arithmetic constraints with a conflict driven search using cylindrical algebraic coverings. Zbl 1509.68243 Ábrahám, Erika; Davenport, James H.; England, Matthew; Kremer, Gereon 8 2021 Improvements to quantum search techniques for block-ciphers, with applications to AES. Zbl 1485.94078 Davenport, James H.; Pring, Benjamin 4 2021 The DEWCAD project: pushing back the doubly exponential wall of cylindrical algebraic decomposition. Zbl 07581910 Bradford, R.; Davenport, J. H.; England, M.; Sadeghimanesh, A.; Uncu, A. 1 2021 Cylindrical algebraic decomposition with equational constraints. Zbl 1432.68599 England, Matthew; Bradford, Russell; Davenport, James H. 10 2020 Identifying the parametric occurrence of multiple steady states for some biological networks. Zbl 1442.92056 Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas 9 2020 Editorial: Symbolic computation and satisfiability checking. Zbl 1444.68006 4 2020 Curtains in CAD: why are they a problem and how do we fix them? Zbl 1503.68314 Nair, Akshar; Davenport, James; Sankaran, Gregory 3 2020 Using machine learning to improve cylindrical algebraic decomposition. Zbl 1474.68464 Huang, Zongyan; England, Matthew; Wilson, David J.; Bridge, James; Davenport, James H.; Paulson, Lawrence C. 10 2019 Lazard’s CAD exploiting equality constraints. Zbl 07640868 Nair, Akshar; Davenport, James; Sankaran, Gregory; McCallum, Scott 1 2019 TheoryGuru: a Mathematica package to apply quantifier elimination technology to economics. Zbl 1395.68350 Mulligan, Casey B.; Davenport, James H.; England, Matthew 6 2018 Machine-assisted proofs. Zbl 1452.68262 Davenport, James; Poonen, Bjorn; Maynard, James; Helfgott, Harald; Tiep, Pham Huu; Cruz-Filipe, Luís 2 2018 A case study on the parametric occurrence of multiple steady states. Zbl 1444.92034 Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas 13 2017 What does “without loss of generality” mean, and how do we detect it. Zbl 1425.68464 Davenport, James H. 2 2017 The potential and challenges of CAD with equational constraints for SC-square. Zbl 1497.68583 Davenport, James H.; England, Matthew 1 2017 Truth table invariant cylindrical algebraic decomposition. Zbl 1351.68314 Bradford, Russell; Davenport, James H.; England, Matthew; McCallum, Scott; Wilson, David 22 2016 SC\(^2\): satisfiability checking meets symbolic computation. (Project paper). Zbl 1344.68198 Ábrahám, Erika; Abbott, John; Becker, Bernd; Bigatti, Anna M.; Brain, Martin; Buchberger, Bruno; Cimatti, Alessandro; Davenport, James H.; England, Matthew; Fontaine, Pascal; Forrest, Stephen; Griggio, Alberto; Kroening, Daniel; Seiler, Werner M.; Sturm, Thomas 13 2016 The complexity of cylindrical algebraic decomposition with respect to polynomial degree. Zbl 1453.13079 England, Matthew; Davenport, James H. 6 2016 Need polynomial systems be doubly-exponential? Zbl 1434.68702 Davenport, James H.; England, Matthew 2 2016 Improving the use of equational constraints in cylindrical algebraic decomposition. Zbl 1346.68283 England, Matthew; Bradford, Russell; Davenport, James H. 12 2015 Solving computational problems in real algebra/geometry. Zbl 1340.14001 Davenport, H. James 1 2015 Recent advances in real geometric reasoning. Zbl 1434.68701 Davenport, James H.; England, Matthew 1 2015 Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition. Zbl 1304.68224 Huang, Zongyan; England, Matthew; Wilson, David; Davenport, James H.; Paulson, Lawrence C.; Bridge, James 14 2014 Truth table invariant cylindrical algebraic decomposition by regular chains. Zbl 1350.68293 Bradford, Russell; Chen, Changbo; Davenport, James H.; England, Matthew; Moreno Maza, Marc; Wilson, David 10 2014 Cylindrical algebraic sub-decompositions. Zbl 1309.68232 Wilson, D. J.; Bradford, R. J.; Davenport, J. H.; England, M. 9 2014 Using the Regular Chains library to build cylindrical algebraic decompositions by projecting and lifting. Zbl 1437.14008 England, Matthew; Wilson, David; Bradford, Russell; Davenport, James H. 8 2014 Intelligent computer mathematics. International conference, CICM 2014, Coimbra, Portugal, July 7–11, 2014. Proceedings. Zbl 1293.68035 7 2014 Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. Zbl 1304.68223 England, Matthew; Bradford, Russell; Chen, Changbo; Davenport, James H.; Maza, Marc Moreno; Wilson, David 7 2014 Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. Zbl 1350.68294 England, Matthew; Bradford, Russell; Davenport, James H.; Wilson, David 6 2014 Branch cuts in Maple 17. Zbl 1369.68358 England, M.; Cheb-Terrab, E.; Bradford, R.; Davenport, J. H.; Wilson, D. 1 2014 Cylindrical algebraic decompositions for Boolean combinations. Zbl 1359.68327 Bradford, Russell; Davenport, James H.; England, Matthew; McCallum, Scott; Wilson, David 14 2013 Optimising problem formulation for cylindrical algebraic decomposition. Zbl 1390.68775 Bradford, Russell; Davenport, James H.; England, Matthew; Wilson, David 14 2013 Triangular decomposition of semi-algebraic systems. Zbl 1260.14070 Chen, Changbo; Davenport, James H.; May, John P.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong 14 2013 Understanding branch cuts of expressions. Zbl 1390.68777 England, Matthew; Bradford, Russell; Davenport, James H.; Wilson, David 3 2013 Computing with semi-algebraic sets: relaxation techniques and effective boundaries. Zbl 1277.13021 Chen, Changbo; Davenport, James H.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong 3 2013 Speeding up cylindrical algebraic decomposition by Gröbner bases. Zbl 1360.68959 Wilson, David J.; Bradford, Russell J.; Davenport, James H. 5 2012 A repository for CAD examples. Zbl 1322.68294 Wilson, David J.; Bradford, Russell J.; Davenport, James H. 4 2012 Computing with semi-algebraic sets represented by triangular decomposition. Zbl 1323.14029 Chen, Changbo; Davenport, James H.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong 5 2011 Intelligent computer mathematics. 18th symposium, Calculemus 2011, and 10th international conference, MKM 2011, Bertinoro, Italy, July 18–23, 2011. Proceedings. Zbl 1218.68014 2 2011 Triangular decomposition of semi-algebraic systems. Zbl 1321.68526 Chen, Changbo; Davenport, James H.; May, John P.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong 9 2010 Geometry of branch cuts. Zbl 1305.68367 Phisanbut, Nalina; Bradford, Russell J.; Davenport, James H. 3 2010 The challenges of multivalued “functions”. Zbl 1286.68516 Davenport, James H. 1 2010 Unifying math ontologies: a tale of two standards. Zbl 1247.68268 Davenport, James H.; Kohlhase, Michael 2 2009 The higher arithmetic. An introduction to the theory of numbers. Editing and additional material by James H. Davenport. 8th revised ed. Zbl 1204.11002 Davenport, Harold 11 2008 Algebraic properties of the Lambert \(W\) function from a result of Rosenlicht and of Liouville. Zbl 1156.33004 Bronstein, Manuel; Corless, Robert M.; Davenport, James H.; Jeffrey, D. J. 4 2008 Unit knowledge management. Zbl 1166.68360 Stratford, Jonathan; Davenport, James H. 3 2008 The freedom to extend OpenMath and its utility. Zbl 1173.00301 Davenport, James H.; Libbrecht, Paul 3 2008 Effective set membership in computer algebra and beyond. Zbl 1166.68371 Davenport, James H. 1 2008 The complexity of quantifier elimination and cylindrical algebraic decomposition. Zbl 1190.68028 Brown, Christopher W.; Davenport, James H. 34 2007 Testing elementary function identities using CAD. Zbl 1142.68618 Beaumont, James C.; Bradford, Russell J.; Davenport, James H.; Phisanbut, Nalina 1 2007 Adherence is better than adjacency: computing the Riemann index using CAD. Zbl 1360.14140 Beaumont, James C.; Bradford, Russell J.; Davenport, James H.; Phisanbut, Nalina 1 2005 A poly-algorithmic approach to simplifying elementary functions. Zbl 1134.68594 Beaumont, James C.; Bradford, Russell J.; Davenport, James H.; Phisanbut, Nalina 2 2004 Copyright issues for MKM. Zbl 1108.68581 Adams, Andrew A.; Davenport, James H. 2 2004 Better simplification of elementary functions through power series. Zbl 1072.68646 Beaumont, James; Bradford, Russell; Davenport, James H. 2 2003 Mathematical knowledge management. Second international conference, MKM 2003, Bertinoro, Italy, February 16–18, 2003. Proceedings. Zbl 1015.00029 2 2003 MKM from book to computer: A case study. Zbl 1022.68118 Davenport, James H. 1 2003 Towards better simplification of elementary functions. Zbl 1072.68651 Bradford, Russell; Davenport, James H. 6 2002 Reasoning about the elementary functions of complex analysis. Zbl 1007.30001 Bradford, Russell; Corless, Robert M.; Davenport, James H.; Jeffrey, David J.; Watt, Stephen M. 5 2002 Equality in computer algebra and beyond. Zbl 1037.68161 Davenport, James H. 4 2002 Reasoning about the elementary functions of complex analysis. Zbl 1042.68128 Corless, Robert M.; Davenport, James H.; Jeffrey, David J.; Litt, Gurjeet; Watt, Stephen M. 2 2001 A generic root operation for exact real arithmetic. Zbl 0985.65042 Hur, Namhyun; Davenport, James H. 1 2001 Fast recognition of alternating and symmetric Galois groups. Zbl 0960.11053 Davenport, J. H.; Smith, G. C. 6 2000 An exact real algebraic arithmetic with equality determination. Zbl 1326.68357 Hur, Namhyun; Davenport, James H. 2 2000 Abstract data types in computer algebra. Zbl 0996.68866 Davenport, James H. 2 2000 Computer algebra – past, present and future. Zbl 0938.68973 Davenport, J. H. 1 1994 Computer algebra. Systems and algorithms for algebraic computation. Transl. from the French by A. Davenport a. J. H. Davenport. 2nd ed. Zbl 0865.68064 Davenport, J. H.; Siret, Y.; Tournier, E. 24 1993 Primality testing revisited. Zbl 0921.11069 Davenport, J. H. 1 1992 Polynomials whose powers are sparse. Zbl 0729.11015 Coppersmith, Don; Davenport, James 6 1991 Scratchpad’s view of algebra. II: A categorical view of factorization. Zbl 0921.13011 Davenport, J. H.; Gianni, P.; Trager, B. M. 4 1991 Computer algebra approaches to enzyme kinetics. Zbl 0785.92014 Bennett, J. P.; Davenport, J. H.; Dewar, M. C.; Fisher, D. L.; Grinfeld, M.; Sauro, H. M. 1 1991 On finding the largest root of a polynomial. Zbl 0715.65033 Davenport, J. H.; Mignotte, M. 5 1990 EUROCAL ’87. European Conference on Computer Algebra, Leipzig, GDR, June 2–5, 1987. Proceedings. Zbl 1209.00079 1 1989 Polynomial factorisation: an exploration of Lenstra’s algorithm. Zbl 1209.13032 Abbott, John A.; Davenport, James H. 1 1989 Real quantifier elimination is doubly exponential. Zbl 0663.03015 Davenport, James H.; Heintz, Joos 87 1988 Computer algebra. Systems and algorithms for algebraic computation. Translation from the French by A. Davenport and J. H. Davenport. Zbl 0679.68058 Davenport, J. H.; Siret, Y.; Tournier, G. 32 1988 Integration in closed form. Zbl 0661.26006 Davenport, J. H. 6 1988 Computer algebra applied to itself. Zbl 0651.68043 Davenport, J. H. 2 1988 The Risch differential equation problem. Zbl 0632.65091 Davenport, J. H. 11 1986 Elementary and Liouvillian solutions of linear differential equations. Zbl 0652.12016 Davenport, J. H.; Singer, M. F. 7 1986 A ”Piano movers” problem. Zbl 0623.68036 Davenport, J. H. 3 1986 On the parallel Risch algorithm. II. Zbl 0606.68032 Davenport, J. H.; Trager, B. M. 9 1985 HEUGCD: How elementary upperbounds generate cheaper data. Zbl 0603.68037 Davenport, James; Padget, Julian 3 1985 A remark on factorisation. Zbl 0601.12003 Abbott, J. A.; Bradford, R. J.; Davenport, J. H. 1 1985 An application of factoring. Zbl 0601.68033 Coppersmith, D.; Davenport, J. H. 1 1985 Elementary and Liouvillian solutions of linear differential equations. Zbl 0609.12024 Singer, M. F.; Davenport, J. H. 1 1985 Closed form solutions of ordinary differential equations. Zbl 0642.65059 Davenport, J. H. 1 1985 Intégration algorithmique des fonctions élémentairement transcendantes sur une courbe algébrique. Zbl 0506.34002 Davenport, James H. 6 1983 Integration - what do we want from the theory? Zbl 0556.68008 Davenport, James H. 3 1983 P-adic reconstruction of rational numbers. Zbl 0489.68032 Wang, Paul S.; Guy, M. J. T.; Davenport, James H. 40 1982 The parallel Risch algorithm. I. Zbl 0538.68024 Davenport, James H. 3 1982 On the parallel Risch algorithm. III: Use of tangents. Zbl 0538.68025 Davenport, James H. 3 1982 On the integration of algebraic functions. Zbl 0471.14009 Davenport, James Harold 20 1981 Factorization over finitely generated fields. Zbl 0481.68040 Davenport, James H.; Trager, Barry M. 5 1981 Effective mathematics - the computer algebra viewpoint. Zbl 0482.03029 Davenport, James H. 1 1981 Symbolic integration - the dust settles? Zbl 0399.68056 Norman, A. C.; Davenport, James H. 5 1979 Algorithms for the integration of algebraic functions. Zbl 0411.34002 Davenport, James H. 3 1979 Numerical tables on elliptic curves. Prepared by H. P. F. Swinnerton-Dyer, N. M. Stephens, James Davenport, J. Vélu, F. B. Coghlan, A. O. L. Atkin and D. J. Tingley. Zbl 1214.11006 1 1975 all cited Publications top 5 cited Publications all top 5 Cited by 606 Authors 31 Davenport, James Harold 19 England, Matthew 18 Romanovskiĭ, Valeriĭ Georgievich 14 Sturm, Thomas 13 Giné, Jaume 8 Chen, Changbo 7 Bradford, Russell J. 6 Abbott, John A. 6 Ábrahám, Erika 6 Brown, Christopher W. 6 Xia, Bican 5 Bright, Curtis 5 Bronstein, Manuel Eric 5 da Mota, Luis Antonio Campinho Pereira 5 Duarte, L. G. S. 5 Eirinakis, Pavlos 5 Fernandes, Wilker 5 Ganesh, Vijay 5 Griggio, Alberto 5 Kohlhase, Michael 5 Kotsireas, Ilias S. 5 Moreno Maza, Marc 5 Oliveira, Regilene D. S. 5 Seiler, Werner M. 5 Singer, Michael F. 5 Subramani, Krishnan 5 Weber, Andreas Günter 5 Wilson, David J. 5 Wojciechowski, Piotr J. 4 Avellar, J. 4 Cimatti, Alessandro 4 Feliu, Elisenda 4 Ferčec, Brigita 4 Hong, Hoon 4 Kremer, Gereon 4 Sadeghimanesh, AmirHosein 4 Safey El Din, Mohab 4 Wu, Wenyuan 3 Anai, Hirokazu 3 Bigatti, Anna Maria 3 Duarte, Sergio Eduardo Silva 3 Fontaine, Pascal 3 Grigor’ev, Dmitriĭ Yur’evich 3 Heintz, Joos 3 Iwane, Hidenao 3 Jackson, Paul B. 3 Jeffrey, David J. 3 Kreinovich, Vladik Yakovlevich 3 Marco García, Ana 3 Martínez, José-Javier 3 McCallum, Scott 3 Platzer, André 3 Rabe, Florian 3 Rahkooy, Hamid 3 Roy, Marie-Françoise 3 Ruggieri, Salvatore 3 Sankaran, Gregory Kumar 3 Tang, Xiaoxian 3 Tinelli, Cesare 3 Wang, Dongming 3 Zhan, Naijun 2 Abdel-Rahman, Essam Othman 2 Algaba, Antonio 2 Anand, Ravi 2 Barrett, Clark W. 2 Becker, Bernd 2 Berry, Thomas G. 2 Brain, Martin 2 Bridge, James P. 2 Buchberger, Bruno 2 Cheung, Kevin K. H. 2 Chèze, Guillaume 2 Collins, George E. 2 Eraşcu, Mădălina 2 Errami, Hassan 2 Feng, Ruyong 2 Feng, Yong 2 Florescu, Dorian 2 Flynn, Eugene Victor 2 Forrest, Stephen 2 Gao, Xiaoshan 2 García, Cristóbal 2 Huang, Zongyan 2 Iosif, Alexandru 2 Jaroschek, Maximilian 2 Kleist, Linda 2 Korniłowicz, Artur 2 Kovács, Zoltán 2 Kröning, Daniel 2 Labahn, George 2 Lecerf, Grégoire 2 Li, Ziming 2 Liu, Yirong 2 Matsuzaki, Takuya 2 Mencinger, Matej 2 Mignotte, Maurice 2 Miltzow, Tillmann 2 Mitsch, Stefan 2 Müller, Dennis 2 Nair, Akshar Sajive ...and 506 more Authors all top 5 Cited in 115 Serials 72 Journal of Symbolic Computation 14 Mathematics in Computer Science 12 Theoretical Computer Science 8 Applied Mathematics and Computation 8 Applicable Algebra in Engineering, Communication and Computing 7 Journal of Computational and Applied Mathematics 6 Journal of Pure and Applied Algebra 6 Annals of Mathematics and Artificial Intelligence 5 Journal of Systems Science and Complexity 4 Computers & Mathematics with Applications 4 Journal of Mathematical Analysis and Applications 4 Mathematics of Computation 4 Bulletin of Mathematical Biology 4 Programming and Computer Software 4 Computer Aided Geometric Design 4 Discrete & Computational Geometry 4 Formal Methods in System Design 3 Computer Physics Communications 3 Journal of Differential Equations 3 Journal of Complexity 3 Journal of Automated Reasoning 3 Cybernetics and Systems Analysis 3 Foundations of Computational Mathematics 2 American Mathematical Monthly 2 Automatica 2 Journal of the London Mathematical Society. Second Series 2 Journal of Number Theory 2 Mathematics and Computers in Simulation 2 Advances in Applied Mathematics 2 Computational Geometry 2 Journal of Dynamics and Differential Equations 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Nonlinear Dynamics 2 Qualitative Theory of Dynamical Systems 2 SIAM Journal on Applied Dynamical Systems 2 Quantum Information Processing 1 Artificial Intelligence 1 Bulletin of the Australian Mathematical Society 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal of General Systems 1 International Journal of Systems Science 1 International Journal of Theoretical Physics 1 Journal of Computational Physics 1 Journal of Statistical Physics 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Chaos, Solitons and Fractals 1 The Mathematical Intelligencer 1 Annales de l’Institut Fourier 1 Archiv der Mathematik 1 BIT 1 Bulletin de la Société Mathématique de France 1 Compositio Mathematica 1 Functional Analysis and its Applications 1 International Journal of Mathematics and Mathematical Sciences 1 Inventiones Mathematicae 1 Journal of Optimization Theory and Applications 1 Journal of Soviet Mathematics 1 Memoirs of the American Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Synthese 1 Systems & Control Letters 1 Acta Applicandae Mathematicae 1 Annals of Pure and Applied Logic 1 Physica D 1 Information and Computation 1 International Journal of Intelligent Systems 1 Mathematical and Computer Modelling 1 SIAM Journal on Discrete Mathematics 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Cryptology 1 AI Communications 1 Random Structures & Algorithms 1 Applied Mathematical Modelling 1 European Journal of Operational Research 1 Linear Algebra and its Applications 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 RAIRO. Informatique Théorique et Applications 1 Journal of Nonlinear Science 1 Combinatorics, Probability and Computing 1 Journal of Mathematical Sciences (New York) 1 Advances in Applied Clifford Algebras 1 Integral Transforms and Special Functions 1 Applied Mathematical Finance 1 Reliable Computing 1 Journal of Difference Equations and Applications 1 Constraints 1 Journal of Mathematical Chemistry 1 Doklady Mathematics 1 Journal of Inequalities and Applications 1 Journal of the European Mathematical Society (JEMS) 1 Physical Review Letters 1 Nonlinear Analysis. Real World Applications 1 Discrete and Continuous Dynamical Systems. Series B 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Communications on Pure and Applied Analysis 1 Computer Languages, Systems & Structures 1 Oberwolfach Reports 1 Groups, Geometry, and Dynamics 1 Journal of Physics A: Mathematical and Theoretical ...and 15 more Serials all top 5 Cited in 42 Fields 220 Computer science (68-XX) 59 Ordinary differential equations (34-XX) 56 Algebraic geometry (14-XX) 50 Commutative algebra (13-XX) 47 Field theory and polynomials (12-XX) 45 Numerical analysis (65-XX) 39 Mathematical logic and foundations (03-XX) 30 Number theory (11-XX) 20 Biology and other natural sciences (92-XX) 16 Operations research, mathematical programming (90-XX) 15 Dynamical systems and ergodic theory (37-XX) 14 Combinatorics (05-XX) 9 Real functions (26-XX) 9 Systems theory; control (93-XX) 7 Quantum theory (81-XX) 7 Information and communication theory, circuits (94-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Functions of a complex variable (30-XX) 6 Special functions (33-XX) 5 General and overarching topics; collections (00-XX) 5 Geometry (51-XX) 5 Mechanics of particles and systems (70-XX) 4 History and biography (01-XX) 4 Group theory and generalizations (20-XX) 4 Mathematics education (97-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Partial differential equations (35-XX) 3 Approximations and expansions (41-XX) 3 Convex and discrete geometry (52-XX) 3 Probability theory and stochastic processes (60-XX) 3 Statistics (62-XX) 3 Fluid mechanics (76-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Difference and functional equations (39-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Mechanics of deformable solids (74-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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