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## Chistov, Alexandre L.

Compute Distance To:
 Author ID: chistov.alexandre-l Published as: Chistov, A. L.; Chistov, Alexander; Chistov, Alexander L.; Chistov, Alexandre L.
 Documents Indexed: 57 Publications since 1976, including 1 Book
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#### Co-Authors

 48 single-authored 4 Grigor’ev, Dmitriĭ Yur’evich 2 Bashmakov, M. I. 2 Fournier, Hervé 2 Koiran, Pascal 1 Gurvits, Leonid 1 Ivanyos, Gábor 1 Karpinski, Marek 1 Perifel, Sylvain
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#### Serials

 21 Journal of Mathematical Sciences (New York) 5 St. Petersburg Mathematical Journal 4 Soviet Mathematics. Doklady 4 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 3 Journal of Soviet Mathematics 3 Zapiski Nauchnykh Seminarov POMI 2 Doklady Mathematics 1 Journal of Pure and Applied Algebra 1 Journal of Symbolic Computation 1 Linear Algebra and its Applications 1 Foundations of Computational Mathematics 1 Proceedings of the Steklov Institute of Mathematics 1 Trudy Matematicheskogo Instituta Imeni V. A. Steklova
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#### Fields

 38 Algebraic geometry (14-XX) 25 Computer science (68-XX) 19 Field theory and polynomials (12-XX) 10 Commutative algebra (13-XX) 9 Number theory (11-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 History and biography (01-XX) 3 Numerical analysis (65-XX) 2 Associative rings and algebras (16-XX) 2 Functions of a complex variable (30-XX) 1 Mathematical logic and foundations (03-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Manifolds and cell complexes (57-XX)

#### Citations contained in zbMATH Open

44 Publications have been cited 272 times in 154 Documents Cited by Year
An algorithm of polynomial complexity for factoring polynomials, and determination of the components of a variety in subexponential time. Zbl 0561.12010
Chistov, A. L.
1984
Algorithm of polynomial complexity for factoring polynomials and finding the components of varieties in subexponential time. Zbl 0596.12022
Chistov, A. L.
1986
Polynomial time algorithms for modules over finite dimensional algebras. Zbl 0918.16001
Chistov, Alexander; Ivanyos, Gábor; Karpinski, Marek
1997
Polynomial-time factoring of the multivariable polynomials over a global field. Zbl 0509.68029
Chistov, A. L.; Grigor’ev, D. Yu.
1982
Vandermonde matrices, NP-completeness and transversal subspaces. Zbl 1050.15001
Chistov, Alexander; Fournier, Hervé; Gurvits, Leonid; Koiran, Pascal
2003
Complexity of quantifier elimination in the theory of algebraically closed fields. Zbl 0562.03015
Chistov, A. L.; Grigor’ev, D. Yu.
1984
Polynomial complexity of the Newton-Puiseux algorithm. Zbl 0636.65043
Chistov, A. L.
1986
Polynomial-time computation of the dimensions of components of algebraic varieties in zero-characteristic. Zbl 0893.14020
Chistov, Alexander L.
1997
Fast parallel calculation of the rank of matrices over a field of arbitrary characteristic. Zbl 0591.65035
Chistov, A. L.
1985
The complexity of constructing the ring of integers of a global field. Zbl 0698.12001
Chistov, A. L.
1989
Fast decomposition of polynomials into irreducible ones and the solution of systems of algebraic equations. Zbl 0596.12021
Grigor’ev, D. Yu.; Chistov, A. L.
1984
Efficient smooth stratification of an algebraic variety in zero characteristic and its applications. Zbl 1027.14007
Chistov, A. L.
2000
Efficient factoring polynomials over local fields and its applications. Zbl 0761.11045
Chistov, Alexandre L.
1991
Monodromy and irreducibility criteria with algorithmic applications in characteristic zero. Zbl 1111.14054
Chistov, A. L.
2002
Efficient factorization of polynomials over local fields. Zbl 0636.12010
Chistov, A. L.
1987
Complexity of a standard basis of a $$D$$-module. Zbl 1206.16050
Grigoriev, D. Yu.; Chistov, A. L.
2009
The polynomial-time computation of the degree of a dominant morphism in characteristic zero. I. Zbl 1078.14538
Chistov, A. L.
2005
Polynomial-time computation of the degree of algebraic varieties in zero characteristic and its applications. Zbl 1081.14527
Chistov, A. L.
1999
Strong version of the basic deciding algorithm for the existential theory of real fields. Zbl 0980.14034
Chistov, A. L.
1999
Polynomial-time computation of the dimension of algebraic varieties in zero-characteristic. Zbl 0889.14027
Chistov, Alexander L.
1996
A deterministic polynomial-time algorithm for the first Bertini theorem. I. Zbl 1304.14076
Chistov, A. L.
2014
A bound for the degree of a system of equations determining the variety of reducible polynomials. Zbl 1283.14026
Chistov, A. L.
2013
Computations with parameters: a theoretical background. Zbl 1357.68301
Chistov, A. L.
2016
Effective construction of local parameters of irreducible components of an algebraic variety. Zbl 1086.14511
Chistov, A. L.
2001
Algorithm of polynomial complexity for factoring polynomials over local fields. Zbl 0835.11047
Chistov, A. L.
1991
On the rationality of a class of tori. Zbl 0453.14009
Bashmakov, M. I.; Chistov, A. L.
1978
On the birational equivalence of tori with a cyclic decomposition field. Zbl 0358.14017
Chistov, A. L.
1976
Systems with parameters, or efficiently solving systems of polynomial equations: 33 years later. I. Zbl 1405.13050
Chistov, A. L.
2018
Efficient absolute factorization of polynomials with parametric coefficients. Zbl 1381.13008
Chistov, A. L.
2017
Polynomial-time computation of the degree of a dominant morphism in zero characteristic. IV. Zbl 1173.14347
Chistov, A. L.
2009
On the construction of a family of transversal subspaces over finite fields. Zbl 1143.15002
Chistov, Alexander; Fournier, Hervé; Koiran, Pascal; Perifel, Sylvain
2008
Efficient construction of local parameters of irreducible components of an algebraic variety in nonzero characteristic. Zbl 1082.14530
Chistov, A. L.
2005
Polynomial-time computation of the degree of a dominant morphism in zero characteristic. II. Zbl 1080.14548
Chistov, A. L.
2005
Calculation of the Galois group over a function field of characteristic zero with algebraically closed field of constants in polynomial time. Zbl 0806.12006
Chistov, A. L.
1990
Algorithms of polynomial complexity for computational problems of the theory of algebraic curves. Zbl 0755.14017
Chistov, A. L.
1989
Birational equivalence of tori with a cyclic splitting field. Zbl 0462.14005
Chistov, A. L.
1981
Extension of the Newton-Puiseux algorithm to the case of a nonzero characteristic ground field. I. Zbl 1383.14016
Chistov, A. L.
2017
A deterministic polynomial-time algorithm for the first Bertini theorem. II. Zbl 1326.14140
Chistov, A. L.
2014
An improvement of the complexity bound for solving systems of polynomial equations. Zbl 1322.12003
Chistov, A. L.
2012
Double-exponential lower bound for the degree of any system of generators of a polynomial prime ideal. Zbl 1206.13031
Chistov, A. L.
2009
Effective normalization of a nonsingular in codimension one algebraic variety. Zbl 1184.14091
Chistov, A. L.
2009
Efficient algorithms in zero-characteristic for a new model of representation of algebraic varieties. Zbl 1185.14055
Chistov, Alexander L.
2006
An algorithm of polynomial complexity for factoring polynomials over local fields. Zbl 0761.11046
Chistov, A. L.
1991
The rationality of a class of tori. Zbl 0467.14003
Bashmakov, M. I.; Chistov, A. L.
1980
Systems with parameters, or efficiently solving systems of polynomial equations: 33 years later. I. Zbl 1405.13050
Chistov, A. L.
2018
Efficient absolute factorization of polynomials with parametric coefficients. Zbl 1381.13008
Chistov, A. L.
2017
Extension of the Newton-Puiseux algorithm to the case of a nonzero characteristic ground field. I. Zbl 1383.14016
Chistov, A. L.
2017
Computations with parameters: a theoretical background. Zbl 1357.68301
Chistov, A. L.
2016
A deterministic polynomial-time algorithm for the first Bertini theorem. I. Zbl 1304.14076
Chistov, A. L.
2014
A deterministic polynomial-time algorithm for the first Bertini theorem. II. Zbl 1326.14140
Chistov, A. L.
2014
A bound for the degree of a system of equations determining the variety of reducible polynomials. Zbl 1283.14026
Chistov, A. L.
2013
An improvement of the complexity bound for solving systems of polynomial equations. Zbl 1322.12003
Chistov, A. L.
2012
Complexity of a standard basis of a $$D$$-module. Zbl 1206.16050
Grigoriev, D. Yu.; Chistov, A. L.
2009
Polynomial-time computation of the degree of a dominant morphism in zero characteristic. IV. Zbl 1173.14347
Chistov, A. L.
2009
Double-exponential lower bound for the degree of any system of generators of a polynomial prime ideal. Zbl 1206.13031
Chistov, A. L.
2009
Effective normalization of a nonsingular in codimension one algebraic variety. Zbl 1184.14091
Chistov, A. L.
2009
On the construction of a family of transversal subspaces over finite fields. Zbl 1143.15002
Chistov, Alexander; Fournier, Hervé; Koiran, Pascal; Perifel, Sylvain
2008
Efficient algorithms in zero-characteristic for a new model of representation of algebraic varieties. Zbl 1185.14055
Chistov, Alexander L.
2006
The polynomial-time computation of the degree of a dominant morphism in characteristic zero. I. Zbl 1078.14538
Chistov, A. L.
2005
Efficient construction of local parameters of irreducible components of an algebraic variety in nonzero characteristic. Zbl 1082.14530
Chistov, A. L.
2005
Polynomial-time computation of the degree of a dominant morphism in zero characteristic. II. Zbl 1080.14548
Chistov, A. L.
2005
Vandermonde matrices, NP-completeness and transversal subspaces. Zbl 1050.15001
Chistov, Alexander; Fournier, Hervé; Gurvits, Leonid; Koiran, Pascal
2003
Monodromy and irreducibility criteria with algorithmic applications in characteristic zero. Zbl 1111.14054
Chistov, A. L.
2002
Effective construction of local parameters of irreducible components of an algebraic variety. Zbl 1086.14511
Chistov, A. L.
2001
Efficient smooth stratification of an algebraic variety in zero characteristic and its applications. Zbl 1027.14007
Chistov, A. L.
2000
Polynomial-time computation of the degree of algebraic varieties in zero characteristic and its applications. Zbl 1081.14527
Chistov, A. L.
1999
Strong version of the basic deciding algorithm for the existential theory of real fields. Zbl 0980.14034
Chistov, A. L.
1999
Polynomial time algorithms for modules over finite dimensional algebras. Zbl 0918.16001
Chistov, Alexander; Ivanyos, Gábor; Karpinski, Marek
1997
Polynomial-time computation of the dimensions of components of algebraic varieties in zero-characteristic. Zbl 0893.14020
Chistov, Alexander L.
1997
Polynomial-time computation of the dimension of algebraic varieties in zero-characteristic. Zbl 0889.14027
Chistov, Alexander L.
1996
Efficient factoring polynomials over local fields and its applications. Zbl 0761.11045
Chistov, Alexandre L.
1991
Algorithm of polynomial complexity for factoring polynomials over local fields. Zbl 0835.11047
Chistov, A. L.
1991
An algorithm of polynomial complexity for factoring polynomials over local fields. Zbl 0761.11046
Chistov, A. L.
1991
Calculation of the Galois group over a function field of characteristic zero with algebraically closed field of constants in polynomial time. Zbl 0806.12006
Chistov, A. L.
1990
The complexity of constructing the ring of integers of a global field. Zbl 0698.12001
Chistov, A. L.
1989
Algorithms of polynomial complexity for computational problems of the theory of algebraic curves. Zbl 0755.14017
Chistov, A. L.
1989
Efficient factorization of polynomials over local fields. Zbl 0636.12010
Chistov, A. L.
1987
Algorithm of polynomial complexity for factoring polynomials and finding the components of varieties in subexponential time. Zbl 0596.12022
Chistov, A. L.
1986
Polynomial complexity of the Newton-Puiseux algorithm. Zbl 0636.65043
Chistov, A. L.
1986
Fast parallel calculation of the rank of matrices over a field of arbitrary characteristic. Zbl 0591.65035
Chistov, A. L.
1985
An algorithm of polynomial complexity for factoring polynomials, and determination of the components of a variety in subexponential time. Zbl 0561.12010
Chistov, A. L.
1984
Complexity of quantifier elimination in the theory of algebraically closed fields. Zbl 0562.03015
Chistov, A. L.; Grigor’ev, D. Yu.
1984
Fast decomposition of polynomials into irreducible ones and the solution of systems of algebraic equations. Zbl 0596.12021
Grigor’ev, D. Yu.; Chistov, A. L.
1984
Polynomial-time factoring of the multivariable polynomials over a global field. Zbl 0509.68029
Chistov, A. L.; Grigor’ev, D. Yu.
1982
Birational equivalence of tori with a cyclic splitting field. Zbl 0462.14005
Chistov, A. L.
1981
The rationality of a class of tori. Zbl 0467.14003
Bashmakov, M. I.; Chistov, A. L.
1980
On the rationality of a class of tori. Zbl 0453.14009
Bashmakov, M. I.; Chistov, A. L.
1978
On the birational equivalence of tori with a cyclic decomposition field. Zbl 0358.14017
Chistov, A. L.
1976
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#### Cited by 166 Authors

 23 Chistov, Alexandre L. 12 Grigor’ev, Dmitriĭ Yur’evich 8 von zur Gathen, Joachim 8 Vorob’ëv, Nikolaĭ N. jun. 5 Ivanyos, Gábor 5 Tung, Shih-Ping 4 Koiran, Pascal 4 Qiao, Youming 3 Heintz, Joos 3 Karpinski, Marek 3 Krick, Teresa 3 Rojas, J. Maurice 3 Shparlinski, Igor E. 3 Voskresenskii, Valentin Evgen’evich 2 Avendano, Martin 2 Ayad, Ali 2 Brooksbank, Peter A. 2 Díaz-Toca, Gema María 2 Escolar, Emerson G. 2 Fitchas, Noaï 2 Giusti, Marc 2 Hiraoka, Yasuaki 2 Kaltofen, Erich L. 2 Lenstra, Hendrik W. jun. 2 Morgenstern, Jacques 2 Mourrain, Bernard 2 Pan, Victor Yakovlevich 2 Rónyai, Lajos 2 Sabia, Juan 2 Saxena, Nitin 2 Scheiblechner, Peter 2 Solernó, Pablo 2 Sutherland, Nicole 2 Volčič, Jurij 2 Walsh, Gary 1 Abdeljaoued, Jounaïdi 1 Absil, Pierre-Antoine 1 Abu Salem, Fatima K. 1 Acciaro, Vincenzo 1 Adleman, Leonard Max 1 Amzallag, Eli 1 Andreev, Alexander E. 1 Asashiba, Hideto 1 Aschenbrenner, Matthias 1 Ayad, A. M. 1 Barone, Sal 1 Barvinok, Alexander I. 1 Basu, Saugata 1 Berthomieu, Jérémy 1 Buchmann, Johannes A. 1 Bürgisser, Peter 1 Busé, Laurent 1 Cai, Jin-Yi 1 Cai, Meixiang 1 Cambier, Léopold 1 Caniglia, Leandro 1 Caviness, Bob F. 1 Charles, Zachary B. 1 Chattopadhyay, Arkadev 1 Codenotti, Bruno 1 Cortiñas, Guillermo H. 1 Danón, Silvia 1 Davydow, Alex 1 Derksen, Harm 1 Dickenstein, Alicia M. 1 Dowbor, Piotr 1 Doyle, John R. 1 Dwivedi, Ashish 1 Eaves, B. Curtis 1 Elkadi, Mohamed 1 Elliott, Jesse 1 Emiris, Ioannis Z. 1 Evdokimov, Sergeĭ Alekseevich 1 Fancsali, Szabolcs L. 1 Faugère, Jean-Charles 1 Feng, Erbao 1 Fournier, Hervé 1 Galligo, André 1 Gao, Shuhong 1 Garrity, Thomas A. 1 Gerdt, Vladimir P. 1 Gonzalez-Vega, Laureano 1 Grenet, Bruno 1 Grochow, Joshua A. 1 Gurvits, Leonid 1 Gustavson, Richard 1 Hajja, Mowaffaq 1 Heinle, Albert 1 Helton, John William 1 Herrero, María Isabel 1 Heß, Friedrich 1 Hirsch, Edward A. 1 Huang, Ming-Deh A. 1 Ibrahim, Ashraf S. 1 Jeronimo, Gabriela 1 Jin, Jinbi 1 Klep, Igor 1 Kopp, Leann 1 Krumm, David 1 Kudryavtsev, Valeriĭ Borisovich ...and 66 more Authors
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#### Cited in 41 Serials

 30 Journal of Symbolic Computation 25 Journal of Mathematical Sciences (New York) 9 Mathematics of Computation 7 Journal of Algebra 7 Journal of Pure and Applied Algebra 7 Journal of Soviet Mathematics 6 Journal of Computer and System Sciences 5 Journal of Complexity 5 Discrete & Computational Geometry 5 Computational Complexity 4 Theoretical Computer Science 4 Applicable Algebra in Engineering, Communication and Computing 3 Information and Computation 3 Journal de Théorie des Nombres de Bordeaux 2 Discrete Applied Mathematics 2 SIAM Journal on Computing 2 Linear Algebra and its Applications 2 St. Petersburg Mathematical Journal 1 Computers & Mathematics with Applications 1 Mathematical Notes 1 Advances in Mathematics 1 Computing 1 The Journal of Symbolic Logic 1 Transactions of the American Mathematical Society 1 Advances in Applied Mathematics 1 Annals of Pure and Applied Logic 1 Computer Aided Geometric Design 1 Annals of Operations Research 1 Japan Journal of Industrial and Applied Mathematics 1 Designs, Codes and Cryptography 1 Bulletin of the American Mathematical Society. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Computational Optimization and Applications 1 SIAM Journal on Scientific Computing 1 Applied Mathematics. Series B (English Edition) 1 Numerical Linear Algebra with Applications 1 Finite Fields and their Applications 1 Doklady Mathematics 1 Discrete Dynamics in Nature and Society 1 Foundations of Computational Mathematics 1 JP Journal of Algebra, Number Theory and Applications
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#### Cited in 29 Fields

 81 Computer science (68-XX) 51 Algebraic geometry (14-XX) 45 Field theory and polynomials (12-XX) 33 Number theory (11-XX) 33 Commutative algebra (13-XX) 22 Numerical analysis (65-XX) 14 Associative rings and algebras (16-XX) 12 Mathematical logic and foundations (03-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 5 Combinatorics (05-XX) 5 Information and communication theory, circuits (94-XX) 4 Group theory and generalizations (20-XX) 4 Operations research, mathematical programming (90-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Ordinary differential equations (34-XX) 3 Operator theory (47-XX) 2 Functions of a complex variable (30-XX) 2 Geometry (51-XX) 2 Convex and discrete geometry (52-XX) 2 Algebraic topology (55-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 General and overarching topics; collections (00-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Differential geometry (53-XX) 1 Quantum theory (81-XX) 1 Systems theory; control (93-XX)