Efficient Algorithms in Zero-Characteristic for a New Model of Representation of Algebraic Varieties

1. Chistov, A.L.: Polynomial–Time Computation of the Dimension of Algebraic Varieties in Zero–Characteristic. Journal of Symbolic Computation 22(1), 1–25 (1996)

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2. Chistov, A.L.: Polynomial–time computation of the dimensions of components of algebraic varieties in zero–characteristic. Journal of Pure and Applied Algebra 117 & 118, 145–175 (1997)

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3. Chistov, A.L.: Polynomial–time computation of the degrees of algebraic varieties in zero–characteristic and its applications. Zap. Nauchn. Semin. St-Petersburg. Otdel. Mat. Inst. Steklov (POMI) 258, 7–59 (1999) (in Russian); English transl.: Journal of Mathematical Sciences 108(6), 897–933 (2002) (Preliminary versions of [3], [4], [5] and [6] in English can be found as Preprints (1999), http://www.MathSoc.spb.ru )

4. Chistov, A.L.: Strong version of the basic deciding algorithm for the existential theory of real fields. Zap. Nauchn. Semin. St-Petersburg. Otdel. Mat. Inst. Steklov (POMI) 256, 168–211 (1999) (in Russian); English transl.: J. of Mathematical Sciences 107(5), 4265–4295 (Preliminary versions of [3], [4], [5] and [6] in English can be found as Preprints (1999), http://www.MathSoc.spb.ru )

5. Chistov, A.L.: Efficient Construction of Local Parameters of Irreducible Components of an Algebraic Variety. In: Proc. of the St.–Petersburg Mathematical Society, vol. 7, pp. 230–266 (1999) (in Russian); English transl. In: Proceedings of the St.Petersburg Mathematical Society, vol. VII. American Math. Soc. Publisher (2001) (Preliminary versions of [3], [4], [5] and [6] in English can be found as Preprints (1999), http://www.MathSoc.spb.ru )

6. Chistov, A.L.: Efficient Smooth Stratification of an Algebraic Variety in Zero–Characteristic and its Applications. Zap. Nauchn. Semin. St-Petersburg. Otdel. Mat. Inst. Steklov (POMI) 266, 254–311 (2000) (in Russian); English transl.: Journal of Mathematical Sciences 113(5), 689–717 (2003) (Preliminary versions of [3], [4], [5] and [6] in English can be found as Preprints (1999), http://www.MathSoc.spb.ru )

7. Chistov, A.L.: Monodromy and irreducibility criteria with algorithmic applications in zero–characteristic. Zap. Nauchn. Semin. St-Petersburg. Otdel. Mat. Inst. Steklov (POMI) 292, 130–152 (2002) (in Russian); see Preprint of St.Petersburg Mathematical Society (2004) (in English)

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8. Chistov, A.L.: Polynomial–time computation of the degree of a dominant morphism in zero–characteristic I. Zap. Nauchn. Semin. St-Petersburg. Otdel. Mat. Inst. Steklov (POMI) 307, 189–235 (2004) (in Russian); see Preprint of St.Petersburg Mathematical Society (2004) (in English)

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9. Chistov, A.L.: Polynomial–time computation of the degree of a dominant morphism in zero–characteristic II, Preprint of St.Petersburg Mathematical Society (2004), http://www.MathSoc.spb.ru

10. Chistov, A.L.: A deterministic polynomial–time algorithm for the first Bertini theorem, Preprint of St.Petersburg Mathematical Society (2004), http://www.MathSoc.spb.ru

11. Chistov, A.L.: A correction in the statement of my theorem on the efficient smooth cover and smooth stratification of an algebraic variety. Preprint of the St.–Petersburg Mathematical Society, 13 (2004), http://www.mathsoc.spb.ru/preprint/2004/index.html

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