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Chistov, Alexander Leonidovich
Statistics Math-Net.Ru
Total publications: 44
Scientific articles: 44
Talks: 1

Number of views:
This page:3157
Abstract pages:24948
Full texts:8059
Talk pages:740
Senior Researcher
Doctor of physico-mathematical sciences
E-mail:

https://www.mathnet.ru/eng/person33642
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/211087

Publications in Math-Net.Ru Citations
2025
1. A. L. Chistov, “Complexity of constructing the roots of a polynomial in the field of multiple formal fractional power series in zero characteristic”, Zap. Nauchn. Sem. POMI, 543 (2025),  191–221  mathnet
2023
2. A. L. Chistov, “An algorithm for factoring polynomials in the ring of multivariable formal power series in zero–characteristic. II”, Zap. Nauchn. Sem. POMI, 528 (2023),  261–290  mathnet 1
2022
3. A. L. Chistov, “An algorithm for factoring polynomials in the ring of multivariable formal power series in zero–characteristic”, Zap. Nauchn. Sem. POMI, 517 (2022),  268–290  mathnet 2
2021
4. A. L. Chistov, “An efficient algorithm for testing the solvability for a system of polynomial equations over $p$-adic integers”, Algebra i Analiz, 33:6 (2021),  162–196  mathnet; St. Petersburg Math. J., 33:6 (2022), 1011–1033
5. A. L. Chistov, “An effective construction of a small number of equations defining an algebraic variety”, Zap. Nauchn. Sem. POMI, 507 (2021),  140–156  mathnet
2020
6. A. L. Chistov, “Subexponential-time computation of isolated primary components of a polynomial ideal”, Zap. Nauchn. Sem. POMI, 498 (2020),  64–74  mathnet 1
7. A. L. Chistov, “Efficient estimation of roots from the field of fractional power series of a given polynomial in nonzero characteristic”, Zap. Nauchn. Sem. POMI, 498 (2020),  55–63  mathnet
2019
8. A. L. Chistov, “Systems with parameters, or efficiently solving systems of polynomial equations 33 years later”, Zap. Nauchn. Sem. POMI, 481 (2019),  146–177  mathnet 1
2018
9. A. L. Chistov, “Systems with parameters, or efficiently solving systems of polynomial equations: 33 years later. II”, Zap. Nauchn. Sem. POMI, 468 (2018),  138–176  mathnet; J. Math. Sci. (N. Y.), 240:5 (2019), 594–616  scopus 4
2017
10. A. L. Chistov, “Systems with parameters, or efficiently solving systems of polynomial equations: 33 years later. I”, Zap. Nauchn. Sem. POMI, 462 (2017),  122–166  mathnet; J. Math. Sci. (N. Y.), 232:2 (2018), 177–203  scopus 5
2016
11. A. L. Chistov, “Extension of the Newton–Puiseux algorithm to the case of a nonzero characteristic ground field. I”, Algebra i Analiz, 28:6 (2016),  147–188  mathnet  elib; St. Petersburg Math. J., 28:6 (2017), 825–853  isi  scopus 2
12. A. L. Chistov, “Efficient absolute factorization of polynomials with parametric coefficients”, Zap. Nauchn. Sem. POMI, 448 (2016),  286–325  mathnet  mathscinet; J. Math. Sci. (N. Y.), 224:2 (2017), 360–384  scopus 4
2015
13. A. L. Chistov, “Computations with parameters: a theoretical background”, Zap. Nauchn. Sem. POMI, 436 (2015),  219–239  mathnet  mathscinet; J. Math. Sci. (N. Y.), 215:6 (2016), 769–781  scopus 4
14. A. L. Chistov, “A deterministic polynomial-time algorithm for the first Bertini theorem. III”, Zap. Nauchn. Sem. POMI, 432 (2015),  297–323  mathnet; J. Math. Sci. (N. Y.), 209:6 (2015), 1005–1019  scopus
2014
15. A. L. Chistov, “A deterministic polynomial-time algorithm for the first Bertini theorem. II”, Zap. Nauchn. Sem. POMI, 421 (2014),  214–249  mathnet; J. Math. Sci. (N. Y.), 200:6 (2014), 769–784  scopus 1
2013
16. A. L. Chistov, “A deterministic polynomial-time algorithm for the first Bertini theorem. I”, Zap. Nauchn. Sem. POMI, 411 (2013),  191–239  mathnet  mathscinet; J. Math. Sci. (N. Y.), 196:2 (2014), 223–243  scopus 2
2012
17. A. L. Chistov, “Estimating the power of a system of equations that determines a variety of reducible polynomials”, Algebra i Analiz, 24:3 (2012),  199–222  mathnet  mathscinet  zmath  elib; St. Petersburg Math. J., 24:3 (2013), 513–528  isi  elib  scopus 10
18. A. L. Chistov, “An effective version of the first Bertini theorem in nonzero characteristic and its applications”, Zap. Nauchn. Sem. POMI, 403 (2012),  172–196  mathnet  mathscinet; J. Math. Sci. (N. Y.), 190:3 (2013), 503–514  scopus
2011
19. A. L. Chistov, “An improvement of the complexity bound for solving systems of polynomial equations”, Zap. Nauchn. Sem. POMI, 390 (2011),  299–306  mathnet; J. Math. Sci. (N. Y.), 181:6 (2012), 921–924  scopus 11
20. A. L. Chistov, “Effective construction of a nonsingular in codimension one algebraic variety over a zero-characteristic ground field”, Zap. Nauchn. Sem. POMI, 387 (2011),  167–188  mathnet; J. Math. Sci. (N. Y.), 179:6 (2011), 729–740  scopus 4
2010
21. A. L. Chistov, “Polynomial-time algorithms for a new model of representation of algebraic varieties (in characteristic zero)”, Zap. Nauchn. Sem. POMI, 378 (2010),  133–170  mathnet; J. Math. Sci. (N. Y.), 174:1 (2011), 71–89  scopus 3
2009
22. A. L. Chistov, “Эффективная нормализация неособого в коразмерности один алгебраического многообразия”, Dokl. Akad. Nauk, 427:5 (2009),  605–608  mathnet; Dokl. Math., 80:1 (2009), 577–580  isi  scopus 3
23. A. L. Chistov, “An overview of effective normalization of a nonsingular in codimension one projective algebraic variety”, Zap. Nauchn. Sem. POMI, 373 (2009),  295–317  mathnet; J. Math. Sci. (N. Y.), 168:3 (2010), 478–490  scopus 3
2008
24. A. L. Chistov, “Double-exponential lower bound for the degree of any system of generators of a polynomial prime ideal”, Algebra i Analiz, 20:6 (2008),  186–213  mathnet  mathscinet  zmath; St. Petersburg Math. J., 20:6 (2009), 983–1001  isi 13
25. D. Yu. Grigoriev, A. L. Chistov, “Complexity of the Standard Basis of a $D$-Module”, Algebra i Analiz, 20:5 (2008),  41–82  mathnet  mathscinet  zmath; St. Petersburg Math. J., 20:5 (2009), 709–736  isi 8
26. A. L. Chistov, “Polynomial-time computation of the degree of a dominant morphism in zero characteristic. IV”, Zap. Nauchn. Sem. POMI, 360 (2008),  260–294  mathnet  zmath; J. Math. Sci. (N. Y.), 158:6 (2009), 912–927  scopus 4
2007
27. A. L. Chistov, “Inequalities for Hilbert functions and primary decompositions”, Algebra i Analiz, 19:6 (2007),  143–172  mathnet  mathscinet  zmath  elib; St. Petersburg Math. J., 19:6 (2008), 975–994  isi 1
28. A. L. Chistov, “Polynomial-time computation of the degree of a dominant morphism in zero characteristic. III”, Zap. Nauchn. Sem. POMI, 344 (2007),  203–239  mathnet  mathscinet; J. Math. Sci. (N. Y.), 147:6 (2007), 7234–7250  scopus 5
2005
29. A. L. Chistov, “Efficient construction of local parameters of irreducible components of an algebraic variety in nonzero characteristic”, Zap. Nauchn. Sem. POMI, 326 (2005),  248–278  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 140:3 (2007), 480–496  scopus 2
30. A. L. Chistov, “Polynomial-time computation of the degree of a dominant morphism in zero characteristic. II”, Zap. Nauchn. Sem. POMI, 325 (2005),  181–224  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 138:3 (2006), 5733–5752  scopus 6
2004
31. A. L. Chistov, “Polynomial-time computation of the degree of a dominant morphism in characteristic zero. I”, Zap. Nauchn. Sem. POMI, 307 (2004),  189–235  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 131:2 (2005), 5547–5568 8
2002
32. A. L. Chistov, “Monodromy and irreducibility criteria with algorithmic applications in zero characteristic”, Zap. Nauchn. Sem. POMI, 292 (2002),  130–152  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 126:2 (2005), 1117–1127 10
2000
33. A. L. Chistov, “Efficient smooth stratification of an algebraic variety in zero characteristic and its applications”, Zap. Nauchn. Sem. POMI, 266 (2000),  254–311  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 113:5 (2003), 689–717 12
1999
34. A. L. Chistov, “Polynomial-time computation of degrees of algebraic varieties in zero-characteristic and its applications”, Zap. Nauchn. Sem. POMI, 258 (1999),  7–59  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 108:6 (2002), 897–933 10
35. A. L. Chistov, “Strong version of the basic deciding algorithm for the existential theory of real fields”, Zap. Nauchn. Sem. POMI, 256 (1999),  168–211  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 107:5 (2001), 4265–4295 9
1991
36. A. L. Chistov, “Polynomial-time factoring polynomials over local fields”, Zap. Nauchn. Sem. LOMI, 192 (1991),  112–148  mathnet  mathscinet  zmath; J. Math. Sci., 70:4 (1994), 1912–1933 10
1989
37. A. L. Chistov, “The complexity of the construction of the ring of integers of a global field”, Dokl. Akad. Nauk SSSR, 306:5 (1989),  1063–1067  mathnet  mathscinet  zmath; Dokl. Math., 39:3 (1989), 597–600 1
38. A. L. Chistov, “Polynomial-time algorithms for computational problems in the theory of algebraic curves”, Zap. Nauchn. Sem. LOMI, 176 (1989),  127–150  mathnet  mathscinet  zmath; J. Soviet Math., 59:3 (1992), 855–867 1
1987
39. A. L. Chistov, “Efficient factorization of polynomials over local fields”, Dokl. Akad. Nauk SSSR, 293:5 (1987),  1073–1077  mathnet  mathscinet  zmath 1
1984
40. D. Yu. Grigor'ev, A. L. Chistov, “Fast factorization of polynomials into irreducible ones and the solution of systems of algebraic equations”, Dokl. Akad. Nauk SSSR, 275:6 (1984),  1302–1306  mathnet  mathscinet  zmath
41. A. L. Chistov, “Polynomial-time factoring of polynomials and finding the compounds of a variety within the aubexponential time”, Zap. Nauchn. Sem. LOMI, 137 (1984),  124–188  mathnet  mathscinet  zmath 28
1978
42. A. L. Chistov, “On the number of generators of a semigroup of classes of algebraic tori relative to stable equivalence”, Dokl. Akad. Nauk SSSR, 242:5 (1978),  1027–1029  mathnet  mathscinet  zmath 1
43. M. I. Bashmakov, A. L. Chistov, “Rationality of a class of tori”, Trudy Mat. Inst. Steklov., 148 (1978),  27–29  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 148 (1980), 23–25 2
1976
44. A. L. Chistov, “Birational equivalence of tori with a cyclic splitting field”, Zap. Nauchn. Sem. LOMI, 64 (1976),  153–158  mathnet  mathscinet  zmath; J. Soviet Math., 17:2 (1981), 1819–1823 2

Presentations in Math-Net.Ru
1. The problem of solving systems of algebraic equations and complexity theory. The survey of results
Alexander Chistov
General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences
May 18, 2006

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