# zbMATH — the first resource for mathematics

## Basu, Saugata

Compute Distance To:
 Author ID: basu.saugata Published as: Basu, Saugata; Basu, S. Homepage: https://www.math.purdue.edu/~sbasu/ External Links: MGP · ResearchGate · dblp
 Documents Indexed: 85 Publications since 1994, including 4 Books
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#### Co-Authors

 21 single-authored 24 Roy, Marie-Françoise 20 Pollack, Richard M. 5 Riener, Cordian 5 Vorob’ëv, Nikolaĭ N. jun. 4 Gabrielov, Andrei 4 Zell, Thierry 3 Barone, Sal 3 Kettner, Michael 2 Lerario, Antonio 2 Parida, Laxmi 2 Pasechnik, Dmitrii V. 2 Patel, Deepam 1 Advaith, S. 1 Aronov, Boris 1 Bhatnagar, Nayantara 1 Carrieri, Anna Paola 1 Chaudhuri, Parimal Pal 1 Roy Chowdhury, Dipanwita 1 Dhandapani, Raghavan 1 Gonzalez-Vega, Laureano 1 Goodman, Jacob Eli 1 Gopalan, Parikshit 1 Holmsen, Andreas F. 1 Isik, Umut 1 Kuhn, David 1 Lipton, Richard J. 1 Lundberg, Erik 1 Mandal, Samir Ch. 1 Natarajan, Abhiram 1 Pach, János 1 Peterson, Chris 1 Raz, Orit E. 1 Rizzie, Anthony 1 Safey El Din, Mohab 1 Schost, Éric 1 Sen Gupta, Indranil 1 Sharir, Micha 1 Sombra, Martín 1 Tinaikar, Aashay 1 Utro, Filippo 1 Yorukoglu, Deniz
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#### Serials

 11 Discrete & Computational Geometry 6 Foundations of Computational Mathematics 4 Proceedings of the London Mathematical Society. Third Series 4 Journal of the European Mathematical Society (JEMS) 3 Computational Complexity 2 Journal of Symbolic Computation 2 Selecta Mathematica. New Series 2 Journal of the ACM 2 The Quarterly Journal of Mathematics 2 Algorithms and Computation in Mathematics 2 Transactions of A. Razmadze Mathematical Institute 1 Acta Mechanica 1 Journal of Fluid Mechanics 1 Advances in Mathematics 1 IEEE Transactions on Computers 1 Journal of Algebra 1 Journal of Computer and System Sciences 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Mathematische Annalen 1 Mathematika 1 Proceedings of the American Mathematical Society 1 Combinatorica 1 Journal of Complexity 1 Journal of the American Mathematical Society 1 IMRN. International Mathematics Research Notices 1 Expositiones Mathematicae 1 Zapiski Nauchnykh Seminarov POMI 1 Algorithms and Combinatorics 1 DIMACS. Series in Discrete Mathematics and Theoretical Computer Science 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Journal of Theoretical Biology 1 Forum of Mathematics, Sigma
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#### Fields

 63 Algebraic geometry (14-XX) 48 Computer science (68-XX) 8 Convex and discrete geometry (52-XX) 7 Mathematical logic and foundations (03-XX) 6 Commutative algebra (13-XX) 4 Algebraic topology (55-XX) 3 General and overarching topics; collections (00-XX) 3 Field theory and polynomials (12-XX) 3 Functional analysis (46-XX) 3 Manifolds and cell complexes (57-XX) 2 Group theory and generalizations (20-XX) 2 Probability theory and stochastic processes (60-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Category theory; homological algebra (18-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX)

#### Citations contained in zbMATH Open

70 Publications have been cited 676 times in 471 Documents Cited by Year
Algorithms in real algebraic geometry. 2nd ed. Zbl 1102.14041
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2006
On the combinatorial and algebraic complexity of quantifier elimination. Zbl 0885.68070
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1996
Algorithms in real algebraic geometry. Zbl 1031.14028
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2003
On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets. Zbl 0973.14033
Basu, S.
1999
New results on quantifier elimination over real closed fields and applications to constraint databases. Zbl 1065.03507
Basu, Saugata
1999
Refined bounds on the number of connected components of sign conditions on a variety. Zbl 1250.14039
Barone, Sal; Basu, Saugata
2012
Computing roadmaps of semi-algebraic sets on a variety. Zbl 0933.14037
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2000
On the number of cells defined by a family of polynomials on a variety. Zbl 0853.14028
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1996
A new algorithm to find a point in every cell defined by a family of polynomials. Zbl 0900.68278
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1998
Computing the first few Betti numbers of semi-algebraic sets in single exponential time. Zbl 1126.14065
Basu, Saugata
2006
Polynomial partitioning on varieties of codimension two and point-hypersurface incidences in four dimensions. Zbl 1332.13017
Basu, Saugata; Sombra, Martín
2016
On the Betti numbers of sign conditions. Zbl 1080.14068
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2005
On computing a set of points meeting every cell defined by a family of polynomials on a variety. Zbl 0872.68050
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1997
Computing roadmaps of semi-algebraic sets. (Extended abstract). Zbl 0917.14028
Basu, S.; Pollack, R.; Roy, M.-F.
1996
Different bounds on the different Betti numbers of semi-algebraic sets. Zbl 1073.14556
Basu, Saugata
2003
Polynomial hierarchy, Betti numbers, and a real analogue of Toda’s theorem. Zbl 1200.14108
Basu, Saugata; Zell, Thierry
2010
Algorithmic semi-algebraic geometry and topology – recent progress and open problems. Zbl 1145.14044
Basu, Saugata
2008
A sharper estimate on the Betti numbers of sets defined by quadratic inequalities. Zbl 1185.14051
Basu, Saugata; Kettner, Michael
2008
On a real analog of Bézout inequality and the number of connected components of sign conditions. Zbl 1347.14010
Barone, Sal; Basu, Saugata
2016
Bounding the Betti numbers and computing the Euler-Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials. Zbl 1218.14050
Basu, Saugata; Pasechnik, Dmitrii V.; Roy, Marie-Françoise
2010
Design of CAECC – cellular automata based error correcting code. Zbl 1068.68673
Chowdhury, Dipanwita Roy; Basu, Saugata; Gupta, Indranil Sen; Chaudhuri, Parimal Pal
1994
On the number of homotopy types of fibres of a definable map. Zbl 1131.14060
Basu, Saugata; Vorobjov, Nicolai
2007
Computing the first Betti number of a semi-algebraic set. Zbl 1142.14036
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2008
Semi-monotone sets. Zbl 1284.14081
Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai
2013
Computing the top Betti numbers of semialgebraic sets defined by quadratic inequalities in polynomial time. Zbl 1141.14034
Basu, Saugata
2008
A baby step-giant step roadmap algorithm for general algebraic sets. Zbl 1322.14090
Basu, S.; Roy, M.-F.; Safey El Din, M.; Schost, É.
2014
Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials. Zbl 1171.14040
Basu, Saugata; Pasechnik, Dmitrii V.; Roy, Marie-Françoise
2009
Betti number bounds, applications and algorithms. Zbl 1097.68152
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2005
Efficient algorithm for computing the Euler-Poincaré characteristic of a semi-algebraic set defined by few quadratic inequalities. Zbl 1103.14032
Basu, Saugata
2006
On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets. Zbl 0917.14029
Basu, Saugata
1996
Combinatorial complexity in o-minimal geometry. Zbl 1186.52017
Basu, Saugata
2010
An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions. Zbl 1212.14005
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2009
Computing the first Betti number and the connected components of semi-algebraic sets. Zbl 1192.14003
Basu, Saugata; Pollack, Richard; Roy, Marie-Francoise
2005
Bounding the radii of balls meeting every connected component of semi-algebraic sets. Zbl 1200.14107
Basu, Saugata; Roy, Marie-Françoise
2010
A complex analogue of Toda’s theorem. Zbl 1268.14016
Basu, Saugata
2012
Monotone functions and maps. Zbl 1273.14123
Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai
2013
Complexity of computing semi-algebraic descriptions of the connected components of a semialgebraic set. Zbl 0960.14033
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1998
A complexity theory of constructible functions and sheaves. Zbl 1349.68098
Basu, Saugata
2015
Random fields and the enumerative geometry of lines on real and complex hypersurfaces. Zbl 1423.14303
Basu, Saugata; Lerario, Antonio; Lundberg, Erik; Peterson, Chris
2019
Understanding evolution of vortex rings in viscous fluids. Zbl 1419.76169
Tinaikar, Aashay; Advaith, S.; Basu, S.
2018
Computing a set of points meeting every cell defined by a family of polynomials on a variety. Zbl 0829.14025
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1995
The combinatorial and topological complexity of a single cell. Zbl 1017.68056
Basu, Saugata
2003
Computing the Euler-Poincaré characteristics of sign conditions. Zbl 1077.14086
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2005
Computing the dimension of a semi-algebraic set. Zbl 1075.14053
Basu, S.; Pollack, R.; Roy, M.-F.
2004
Spectral sequences, exact couples and persistent homology of filtrations. Zbl 1381.55009
Basu, Saugata; Parida, Laxmi
2017
Combinatorial complexity in O-minimal geometry. Zbl 1232.68162
Basu, Saugata
2007
Topological signatures for population admixture. Zbl 1355.92077
Parida, Laxmi; Utro, Filippo; Yorukoglu, Deniz; Carrieri, Anna; Kuhn, David; Basu, Saugata
2015
Bounding the equivariant Betti numbers of symmetric semi-algebraic sets. Zbl 1423.14331
Basu, Saugata; Riener, Cordian
2017
An o-minimal Szemerédi-Trotter theorem. Zbl 06944973
Basu, Saugata; Raz, Orit E.
2018
Algorithms in real algebraic geometry: a survey. Zbl 1398.14062
Basu, Saugata
2017
Substrate stiffness and mechanical stress due to intercellular cooperativity guides tissue structure. Zbl 1406.92045
Basu, S.; Sutradhar, S.; Paul, R.
2018
Multi-degree bounds on the Betti numbers of real varieties and semi-algebraic sets and applications. Zbl 1401.14228
Basu, Saugata; Rizzie, Anthony
2018
On projections of semi-algebraic sets defined by few quadratic inequalities. Zbl 1137.14042
Basu, Saugata; Zell, Thierry
2008
The Hadwiger transversal theorem for pseudolines. Zbl 1112.52001
Basu, Saugata; Goodman, Jacob E.; Holmsen, Andreas; Pollack, Richard
2005
Computing the Betti numbers of arrangements in practice. Zbl 1169.68637
Basu, Saugata; Kettner, Michael
2005
Computing the Betti numbers of arrangements via spectral sequences. Zbl 1160.68606
Basu, Saugata
2003
Uniform quantifier elimination and constraint query processing. Zbl 0915.03031
Basu, Saugata
1997
Discrete and computational geometry. The Goodman-Pollack Festschrift. Zbl 1014.00040
Aronov, Boris (ed.); Basu, Saugata (ed.); Pach, János (ed.); Sharir, Micha (ed.)
2003
Algorithmic and quantitative real algebraic geometry. Proceedings of the DIMACS workshop on algorithmic and quantitative aspects of real algebraic geometry in mathematics and computer science, DIMACS Center, March 12–16, 2001. Zbl 1015.00018
Basu, Saugata (ed.); Gonzalez-Vega, Laureano (ed.)
2003
Polynomial time algorithm for computing the top Betti numbers of semi-algebraic sets defined by quadratic inequalities. Zbl 1192.14002
Basu, Saugata
2005
Polynomials that sign represent parity and Descartes’ rule of signs. Zbl 1188.68150
Basu, Saugata; Bhatnagar, Nayantara; Gopalan, Parikshit; Lipton, Richard J.
2008
Bounding the number of stable homotopy types of a parametrized family of semi-algebraic sets defined by quadratic inequalities. Zbl 1193.14072
Basu, Saugata; Kettner, Michael
2009
On the number of topological types occurring in a parameterized family of arrangements. Zbl 1159.52024
Basu, Saugata
2008
On projections of semi-algebraic sets defined by few quadratic inequalities. Reprinted from the journal Discrete & Computational Geometry 39, No. 1-3 (2008). Zbl 1177.14095
Basu, Saugata; Zell, Thierry
2009
On the isotypic decomposition of cohomology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities. Zbl 1453.14143
Basu, Saugata; Riener, Cordian
2020
A Helly-type theorem for semi-monotone sets and monotone maps. Zbl 1284.14082
Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai
2013
Abstract formulations of some theorems on nonmeasurable sets. Zbl 1428.28002
Basu, S.; Sen, D.
2017
Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets. Zbl 1390.14175
Basu, Saugata; Riener, Cordian
2017
Impact of a torsional load on a penny-shaped crack sandwiched between two elastic layers embedded in an elastic medium. Zbl 1390.74147
Karan, S.; Basu, S.; Mandal, S. C.
2018
Divide and conquer roadmap for algebraic sets. Zbl 1329.14109
Basu, Saugata; Roy, Marie-Françoise
2014
On the isotypic decomposition of cohomology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities. Zbl 1453.14143
Basu, Saugata; Riener, Cordian
2020
Random fields and the enumerative geometry of lines on real and complex hypersurfaces. Zbl 1423.14303
Basu, Saugata; Lerario, Antonio; Lundberg, Erik; Peterson, Chris
2019
Understanding evolution of vortex rings in viscous fluids. Zbl 1419.76169
Tinaikar, Aashay; Advaith, S.; Basu, S.
2018
An o-minimal Szemerédi-Trotter theorem. Zbl 06944973
Basu, Saugata; Raz, Orit E.
2018
Substrate stiffness and mechanical stress due to intercellular cooperativity guides tissue structure. Zbl 1406.92045
Basu, S.; Sutradhar, S.; Paul, R.
2018
Multi-degree bounds on the Betti numbers of real varieties and semi-algebraic sets and applications. Zbl 1401.14228
Basu, Saugata; Rizzie, Anthony
2018
Impact of a torsional load on a penny-shaped crack sandwiched between two elastic layers embedded in an elastic medium. Zbl 1390.74147
Karan, S.; Basu, S.; Mandal, S. C.
2018
Spectral sequences, exact couples and persistent homology of filtrations. Zbl 1381.55009
Basu, Saugata; Parida, Laxmi
2017
Bounding the equivariant Betti numbers of symmetric semi-algebraic sets. Zbl 1423.14331
Basu, Saugata; Riener, Cordian
2017
Algorithms in real algebraic geometry: a survey. Zbl 1398.14062
Basu, Saugata
2017
Abstract formulations of some theorems on nonmeasurable sets. Zbl 1428.28002
Basu, S.; Sen, D.
2017
Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets. Zbl 1390.14175
Basu, Saugata; Riener, Cordian
2017
Polynomial partitioning on varieties of codimension two and point-hypersurface incidences in four dimensions. Zbl 1332.13017
Basu, Saugata; Sombra, Martín
2016
On a real analog of Bézout inequality and the number of connected components of sign conditions. Zbl 1347.14010
Barone, Sal; Basu, Saugata
2016
A complexity theory of constructible functions and sheaves. Zbl 1349.68098
Basu, Saugata
2015
Topological signatures for population admixture. Zbl 1355.92077
Parida, Laxmi; Utro, Filippo; Yorukoglu, Deniz; Carrieri, Anna; Kuhn, David; Basu, Saugata
2015
A baby step-giant step roadmap algorithm for general algebraic sets. Zbl 1322.14090
Basu, S.; Roy, M.-F.; Safey El Din, M.; Schost, É.
2014
Divide and conquer roadmap for algebraic sets. Zbl 1329.14109
Basu, Saugata; Roy, Marie-Françoise
2014
Semi-monotone sets. Zbl 1284.14081
Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai
2013
Monotone functions and maps. Zbl 1273.14123
Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai
2013
A Helly-type theorem for semi-monotone sets and monotone maps. Zbl 1284.14082
Basu, Saugata; Gabrielov, Andrei; Vorobjov, Nicolai
2013
Refined bounds on the number of connected components of sign conditions on a variety. Zbl 1250.14039
Barone, Sal; Basu, Saugata
2012
A complex analogue of Toda’s theorem. Zbl 1268.14016
Basu, Saugata
2012
Polynomial hierarchy, Betti numbers, and a real analogue of Toda’s theorem. Zbl 1200.14108
Basu, Saugata; Zell, Thierry
2010
Bounding the Betti numbers and computing the Euler-Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials. Zbl 1218.14050
Basu, Saugata; Pasechnik, Dmitrii V.; Roy, Marie-Françoise
2010
Combinatorial complexity in o-minimal geometry. Zbl 1186.52017
Basu, Saugata
2010
Bounding the radii of balls meeting every connected component of semi-algebraic sets. Zbl 1200.14107
Basu, Saugata; Roy, Marie-Françoise
2010
Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials. Zbl 1171.14040
Basu, Saugata; Pasechnik, Dmitrii V.; Roy, Marie-Françoise
2009
An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions. Zbl 1212.14005
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2009
Bounding the number of stable homotopy types of a parametrized family of semi-algebraic sets defined by quadratic inequalities. Zbl 1193.14072
Basu, Saugata; Kettner, Michael
2009
On projections of semi-algebraic sets defined by few quadratic inequalities. Reprinted from the journal Discrete & Computational Geometry 39, No. 1-3 (2008). Zbl 1177.14095
Basu, Saugata; Zell, Thierry
2009
Algorithmic semi-algebraic geometry and topology – recent progress and open problems. Zbl 1145.14044
Basu, Saugata
2008
A sharper estimate on the Betti numbers of sets defined by quadratic inequalities. Zbl 1185.14051
Basu, Saugata; Kettner, Michael
2008
Computing the first Betti number of a semi-algebraic set. Zbl 1142.14036
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2008
Computing the top Betti numbers of semialgebraic sets defined by quadratic inequalities in polynomial time. Zbl 1141.14034
Basu, Saugata
2008
On projections of semi-algebraic sets defined by few quadratic inequalities. Zbl 1137.14042
Basu, Saugata; Zell, Thierry
2008
Polynomials that sign represent parity and Descartes’ rule of signs. Zbl 1188.68150
Basu, Saugata; Bhatnagar, Nayantara; Gopalan, Parikshit; Lipton, Richard J.
2008
On the number of topological types occurring in a parameterized family of arrangements. Zbl 1159.52024
Basu, Saugata
2008
On the number of homotopy types of fibres of a definable map. Zbl 1131.14060
Basu, Saugata; Vorobjov, Nicolai
2007
Combinatorial complexity in O-minimal geometry. Zbl 1232.68162
Basu, Saugata
2007
Algorithms in real algebraic geometry. 2nd ed. Zbl 1102.14041
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2006
Computing the first few Betti numbers of semi-algebraic sets in single exponential time. Zbl 1126.14065
Basu, Saugata
2006
Efficient algorithm for computing the Euler-Poincaré characteristic of a semi-algebraic set defined by few quadratic inequalities. Zbl 1103.14032
Basu, Saugata
2006
On the Betti numbers of sign conditions. Zbl 1080.14068
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2005
Betti number bounds, applications and algorithms. Zbl 1097.68152
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2005
Computing the first Betti number and the connected components of semi-algebraic sets. Zbl 1192.14003
Basu, Saugata; Pollack, Richard; Roy, Marie-Francoise
2005
Computing the Euler-Poincaré characteristics of sign conditions. Zbl 1077.14086
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2005
The Hadwiger transversal theorem for pseudolines. Zbl 1112.52001
Basu, Saugata; Goodman, Jacob E.; Holmsen, Andreas; Pollack, Richard
2005
Computing the Betti numbers of arrangements in practice. Zbl 1169.68637
Basu, Saugata; Kettner, Michael
2005
Polynomial time algorithm for computing the top Betti numbers of semi-algebraic sets defined by quadratic inequalities. Zbl 1192.14002
Basu, Saugata
2005
Computing the dimension of a semi-algebraic set. Zbl 1075.14053
Basu, S.; Pollack, R.; Roy, M.-F.
2004
Algorithms in real algebraic geometry. Zbl 1031.14028
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2003
Different bounds on the different Betti numbers of semi-algebraic sets. Zbl 1073.14556
Basu, Saugata
2003
The combinatorial and topological complexity of a single cell. Zbl 1017.68056
Basu, Saugata
2003
Computing the Betti numbers of arrangements via spectral sequences. Zbl 1160.68606
Basu, Saugata
2003
Discrete and computational geometry. The Goodman-Pollack Festschrift. Zbl 1014.00040
Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha
2003
Algorithmic and quantitative real algebraic geometry. Proceedings of the DIMACS workshop on algorithmic and quantitative aspects of real algebraic geometry in mathematics and computer science, DIMACS Center, March 12–16, 2001. Zbl 1015.00018
Basu, Saugata; Gonzalez-Vega, Laureano
2003
Computing roadmaps of semi-algebraic sets on a variety. Zbl 0933.14037
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
2000
On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets. Zbl 0973.14033
Basu, S.
1999
New results on quantifier elimination over real closed fields and applications to constraint databases. Zbl 1065.03507
Basu, Saugata
1999
A new algorithm to find a point in every cell defined by a family of polynomials. Zbl 0900.68278
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1998
Complexity of computing semi-algebraic descriptions of the connected components of a semialgebraic set. Zbl 0960.14033
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1998
On computing a set of points meeting every cell defined by a family of polynomials on a variety. Zbl 0872.68050
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1997
Uniform quantifier elimination and constraint query processing. Zbl 0915.03031
Basu, Saugata
1997
On the combinatorial and algebraic complexity of quantifier elimination. Zbl 0885.68070
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1996
On the number of cells defined by a family of polynomials on a variety. Zbl 0853.14028
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1996
Computing roadmaps of semi-algebraic sets. (Extended abstract). Zbl 0917.14028
Basu, S.; Pollack, R.; Roy, M.-F.
1996
On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets. Zbl 0917.14029
Basu, Saugata
1996
Computing a set of points meeting every cell defined by a family of polynomials on a variety. Zbl 0829.14025
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise
1995
Design of CAECC – cellular automata based error correcting code. Zbl 1068.68673
Chowdhury, Dipanwita Roy; Basu, Saugata; Gupta, Indranil Sen; Chaudhuri, Parimal Pal
1994
all top 5

#### Cited by 719 Authors

 33 Basu, Saugata 16 Roy, Marie-Françoise 13 Safey El Din, Mohab 13 Zahl, Joshua 10 Sharir, Micha 9 Heintz, Joos 8 Koiran, Pascal 7 Bank, Bernd 7 Giusti, Marc 7 Pach, János 7 Perrucci, Daniel 6 Cucker, Felipe 6 Fox, Jacob 6 Matoušek, Jiří 6 Pollack, Richard M. 6 Riener, Cordian 6 Rouillier, Fabrice 6 Sheffer, Adam 5 Batkhin, Alexandr B. 5 Davenport, James Harold 5 England, Matthew 5 Lasserre, Jean-Bernard 5 Schost, Éric 5 Suk, Andrew 5 Vorob’ëv, Nikolaĭ N. jun. 5 Xiao, ShuiJing 5 Zeng, Guangxing 4 Binyamini, Gal 4 Bourgain, Jean 4 Feliu, Elisenda 4 Gabrielov, Andrei 4 Grigor’ev, Dmitriĭ Yur’evich 4 Har-Peled, Sariel 4 Hong, Hoon 4 Jeronimo, Gabriela 4 Kerber, Michael 4 Pardo, Luis Miguel 4 Rojas, J. Maurice 4 Solomon, Noam 4 Starchenko, Sergei 4 Sturmfels, Bernd 4 Xia, Bican 4 Zell, Thierry 3 Aronov, Boris 3 Barone, Sal 3 Blondel, Vincent D. 3 Bukh, Boris 3 Bürgisser, Peter 3 Chen, Changbo 3 Chernikov, Artem 3 Drusvyatskiy, Dmitriy 3 Elbassioni, Khaled M. 3 Ezra, Esther E. 3 Fortuna, Elisabetta 3 Gianni, Patrizia M. 3 Henrion, Didier 3 Kaplan, Haim 3 Lerario, Antonio 3 Lucas, Salvador 3 Magron, Victor 3 Mateus, Paulo C. 3 Meer, Klaus 3 Naldi, Simone 3 Nie, Jiawang 3 Pasechnik, Dmitrii V. 3 Paulson, Lawrence Charles 3 Portier, Natacha 3 Sabia, Juan 3 Scheiblechner, Peter 3 Subramani, Krishnan 3 Tao, Terence 3 Wang, Wei-Min 3 Wu, Wenyuan 3 Yakovenko, Sergei 2 Ábrahám, Erika 2 Agarwal, Pankaj Kumar 2 Ahmadi, Amir Ali 2 Akin, Hasan 2 Alt, Helmut 2 Averkov, Gennadiy 2 Avigad, Jeremy 2 Baartse, Martijn 2 Băbălîc, Elena-Mirela 2 Bihan, Frédéric 2 Borralleras, Cristina 2 Bouzidi, Yacine 2 Bradford, Russell J. 2 Brown, Christopher W. 2 Casagrande, Alberto 2 Cheng, Jinsan 2 Choudhury, Pabitra Pal 2 Connelly, Robert 2 Diatta, Daouda Niang 2 Dickenstein, Alicia M. 2 Do, Thao T. 2 Drton, Mathias 2 Eirinakis, Pavlos 2 Emiris, Ioannis Z. 2 Fefferman, Charles Louis 2 Gaubert, Stéphane ...and 619 more Authors
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#### Cited in 162 Serials

 48 Discrete & Computational Geometry 34 Journal of Symbolic Computation 16 Journal of Complexity 16 Foundations of Computational Mathematics 15 Theoretical Computer Science 10 Mathematical Programming. Series A. Series B 8 SIAM Journal on Computing 8 Mathematics in Computer Science 7 Transactions of the American Mathematical Society 5 Artificial Intelligence 5 Communications in Mathematical Physics 5 Journal of Automated Reasoning 5 Computational Geometry 5 Applicable Algebra in Engineering, Communication and Computing 5 SIAM Journal on Optimization 5 Selecta Mathematica. New Series 5 Journal of the European Mathematical Society (JEMS) 5 Journal of Systems Science and Complexity 4 Journal of Pure and Applied Algebra 4 Mathematische Zeitschrift 4 Geometric and Functional Analysis. GAFA 4 Combinatorics, Probability and Computing 4 Mathematical Logic Quarterly (MLQ) 4 SIAM Journal on Applied Algebra and Geometry 3 Computers & Mathematics with Applications 3 Information Processing Letters 3 Mathematics of Computation 3 Bulletin of Mathematical Biology 3 The Annals of Statistics 3 Journal of Algebra 3 Journal of Computational and Applied Mathematics 3 Journal of Computer and System Sciences 3 Programming and Computer Software 3 Combinatorica 3 Chinese Annals of Mathematics. Series B 3 Algorithmica 3 Revista Matemática Iberoamericana 3 Journal of the American Mathematical Society 3 Computational Complexity 3 Economic Theory 3 Theory of Computing Systems 3 SIAM Journal on Applied Dynamical Systems 3 Science China. Mathematics 3 Forum of Mathematics, Sigma 2 Discrete Applied Mathematics 2 Israel Journal of Mathematics 2 Journal of Mathematical Physics 2 Acta Mathematica 2 Advances in Mathematics 2 Information Sciences 2 International Journal of Game Theory 2 Inventiones Mathematicae 2 Journal of Combinatorial Theory. Series A 2 The Journal of Symbolic Logic 2 Proceedings of the American Mathematical Society 2 Proceedings of the London Mathematical Society. Third Series 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Annals of Pure and Applied Logic 2 Information and Computation 2 Multidimensional Systems and Signal Processing 2 International Journal of Computer Mathematics 2 Archive for Mathematical Logic 2 Advances in Computational Mathematics 2 Annals of Mathematics and Artificial Intelligence 2 Journal of High Energy Physics 2 Computational Methods and Function Theory 2 Chebyshevskiĭ Sbornik 2 Computability 1 Acta Informatica 1 Indian Journal of Pure & Applied Mathematics 1 International Journal of Theoretical Physics 1 Journal of Mathematical Biology 1 Linear and Multilinear Algebra 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematische Semesterberichte 1 Acta Mathematica Vietnamica 1 Algebra and Logic 1 Algebra Universalis 1 Annales de l’Institut Fourier 1 Automatica 1 Commentarii Mathematici Helvetici 1 Compositio Mathematica 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics 1 Journal of Econometrics 1 Journal of the London Mathematical Society. Second Series 1 Kybernetika 1 Mathematische Annalen 1 Mathematics of Operations Research 1 Mathematika 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Nagoya Mathematical Journal 1 Synthese 1 Topology and its Applications 1 European Journal of Combinatorics 1 Advances in Applied Mathematics 1 Ergodic Theory and Dynamical Systems 1 Circuits, Systems, and Signal Processing 1 Acta Applicandae Mathematicae ...and 62 more Serials
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#### Cited in 53 Fields

 196 Computer science (68-XX) 165 Algebraic geometry (14-XX) 59 Mathematical logic and foundations (03-XX) 55 Convex and discrete geometry (52-XX) 49 Numerical analysis (65-XX) 49 Operations research, mathematical programming (90-XX) 48 Commutative algebra (13-XX) 41 Combinatorics (05-XX) 38 Field theory and polynomials (12-XX) 21 Number theory (11-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 16 Quantum theory (81-XX) 14 Real functions (26-XX) 13 Ordinary differential equations (34-XX) 13 Biology and other natural sciences (92-XX) 12 Dynamical systems and ergodic theory (37-XX) 12 Algebraic topology (55-XX) 12 Statistics (62-XX) 11 Geometry (51-XX) 10 Group theory and generalizations (20-XX) 10 Operator theory (47-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Functions of a complex variable (30-XX) 8 Several complex variables and analytic spaces (32-XX) 7 Partial differential equations (35-XX) 7 Systems theory; control (93-XX) 6 Manifolds and cell complexes (57-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Information and communication theory, circuits (94-XX) 5 Differential geometry (53-XX) 5 Probability theory and stochastic processes (60-XX) 4 Special functions (33-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 General topology (54-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Associative rings and algebras (16-XX) 3 Difference and functional equations (39-XX) 3 Functional analysis (46-XX) 3 Mechanics of particles and systems (70-XX) 2 General and overarching topics; collections (00-XX) 2 Topological groups, Lie groups (22-XX) 2 Approximations and expansions (41-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 $$K$$-theory (19-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Abstract harmonic analysis (43-XX) 1 Fluid mechanics (76-XX) 1 Mathematics education (97-XX)