Geodesic
Polynomial-time algorithms for a new model of representation of algebraic varieties (in characteristic zero)
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Tome 378 (2010), pp. 133-170 Cet article a éte moissonné depuis la source Math-Net.Ru

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We suggest a model of representation of algebraic varieties based on representative systems of points of their irreducible components. Deterministic polynomial-time algorithms that substantiate this model are described in characteristic zero. The main result here is a construction of the intersection of algebraic varieties. As applications, we obtain efficient algorithms for constructing the smooth stratification and smooth cover of an algebraic variety suggested by the author earlier. Bibl. 16 titles. 
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A. L. Chistov. Polynomial-time algorithms for a new model of representation of algebraic varieties (in characteristic zero). Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Tome 378 (2010), pp. 133-170. http://geodesic.mathdoc.fr/item/ZNSL_2010_378_a9/

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[2] A. L. Chistov, “Algoritm polinomialnoi slozhnosti dlya razlozheniya mnogochlenov na neprivodimye mnozhiteli i nakhozhdenie komponent mnogoobraziya v subeksponentsialnoe vremya”, Zap. nauchn. semin. LOMI, 137, 1984, 124–188 | MR | Zbl

[3] A. L. Chistov, “Vychislenie stepenei algebraicheskikh mnogoobrazii nad polem nulevoi kharakteristiki za polinomialnoe vremya i ego prilozheniya”, Zap. nauchn. seminarov POMI, 258, 1999, 7–59 | MR | Zbl

[4] A. L. Chistov, “Silnaya versiya osnovnogo razreshayuschego algoritma dlya ekzistentsionalnoi teorii pervogo poryadka veschestvenno zamknutykh polei”, Zap. nauchn. semin. POMI, 256, 1999, 168–211 | MR | Zbl

[5] A. L. Chistov, “Effektivnaya konstruktsiya lokalnykh parametrov neprivodimykh komponent algebraicheskogo mnogoobraziya”, Trudy S.-Peterburgskogo mat. obschestva, 7, 1999, 230–266 | MR

[6] A. L. Chistov, “Effektivnaya gladkaya stratifikatsiya algebraicheskogo mnogoobraziya v nulevoi kharakteristike i eë prilozheniya”, Zap. nauchn. semin. POMI, 266, 2000, 254–311 | MR | Zbl

[7] A. L. Chistov, “Monodromiya i kriterii neprivodimosti s algoritmicheskimi prilozheniyami v nulevoi kharakteristicheske”, Zap. nauchn. semin. POMI, 292, 2002, 130–152 | MR | Zbl

[8] A. L. Chistov, “Vychislenie stepeni dominantnogo morfizma v nulevoi kharakteristike za polinomialnoe vremya. I”, Zap. nauchn. semin. POMI, 307, 2004, 189–235 | MR | Zbl

[9] A. L. Chistov, “Vychislenie stepeni dominantnogo morfizma v nulevoi kharakteristike za polinomialnoe vremya. II”, Zap. nauchn. semin. POMI, 325, 2005, 181–224 | MR | Zbl

[10] A. L. Chistov, “Vychislenie stepeni dominantnogo morfizma v nulevoi kharakteristike za polinomialnoe vremya. III”, Zap. nauchn. semin. POMI, 344, 2007, 203–239 | MR

[11] A. L. Chistov, “Vychislenie stepeni dominantnogo morfizma v nulevoi kharakteristike za polinomialnoe vremya. IV”, Zap. nauchn. semin. POMI, 360, 2008, 260–294 | Zbl

[12] A. L. Chistov, A deterministic polynomial-time algorithm for the first Bertini theorem, Preprint, St. Petersburg Mathematical Society 2004-09, 2004

[13] A. L. Chistov, “Polynomial–time computation of the dimension of algebraic varieties in zero–characteristic”, J. Symbolic Comput., 22:1 (1996), 1–25 | DOI | MR | Zbl

[14] A. L. Chistov, “Polynomial–time computation of the dimensions of components of algebraic varieties in zero–characteristic”, J. Pure Appl. Algebra, 117/118 (1997), 145–175 | DOI | MR | Zbl

[15] A. L. Chistov, “Efficient algorithms in zero-characteristic for a new model of representation of algebraic varieties”, Computer Science – Theory and Applications, Lecture Notes Comput. Sci., 3967, 2006, 137–146 | DOI | MR | Zbl

[16] A. L. Chistov, A correction in the statement of my theorem on the efficient smooth cover and smooth stratification of an algebraic variety, Preprint, St. Petersburg Math. Soc., #13, 2004