References

1

Aldaz M., Heintz J., Matera G., Montaña J. L. & Pardo L. M.: Time-space trade-offs in algebraic complexity theory.- Enviado a Computational Complexity (1996).

2

Armendáriz I. & Solernó P.: On the computation of the radical of polynomial complete intersection ideals.- Applied Algebra, Algebraic Algorithms and Error Correcting Codes, L.N.Comp.Sci. 948, Springer Verlag (1995) 106-119.

3

Bank B., Giusti M., Heintz J. & Mbakop G.: Polar Varieties, Real Equation Solving and Data-Structures: The Hypersurface Case.- Aparecerá en J. of Complexity (1996).

4

Brownawell D.: Bounds for the degrees in the Nullstellensatz.- Ann. of Math. Second Series 126 No.3 (1987) 577-591.

5

Caniglia L., Galligo A., Heintz J.: Some new effectivity bounds in computational geometry.- Applied Algebra, Algebraic Algorithms and Error Correcting Codes, L.N.Comp.Sci. 357, Springer Verlag, (1989), 131-152.

6

Canny J.: Some algebraic and geometric computations in PSPACE.- Proc. 20th Ann. ACM STOC'88 (1988) 46-467.

7

Chistov A. & Grigor'ev D.: Subexponential-time solving systems of algebraic equations.- LOMI Pre- prints E-g-83, E-10-83, Leningrad (1983).

8

Fitchas N. & Galligo A.: Nullstellensatz effective et conjecture de Serre (théorème de Quillen-Suslin) pour le calcul Formel.- Math. Nachrichten 149 (1990) 231-253.

9

Fitchas N., Giusti M., Smietanski G.: Sur la complexité du théoreme des zéros.- Approximation and Optimization 8, ed. J. Guddat et al., Peter Lange Verlag, Frankfurt am Main (1995) 274-329.

10

Giusti M. & Heintz J.: La détermination de la dimension et des points isolés d'une variété algébrique peut se faire en temps polynomial.- Computational Algebraic Geometry and Commutative Algebra Symposia Mathematica, vol. 34, Instituto de Alta Matematica Francesco Severi and Cambridge University Press, Cambridge (1993) 216-256

11

Giusti M., Heintz J., Sabia J.: On the efficiency of effective Nullstellensätze.- Computational Complexity 3, (1993) 56-95.

12

Giusti M., Heintz J., Morais J., Pardo L.: When polynomial equation systems can be `solved' fast?.- Applied Algebra, Algebraic Algorithms and Error Correcting Codes, L.N.Comp.Sci. 948, Springer Verlag (1995) 205-231.

13

Giusti M., Hägele K., Heintz J., Morais J., Pardo L.: Lower Bounds for Diophantine Approximation.- Aparecerá en J. of Pure and Appl. Algebra (1996).

14

Giusti M., Heintz J., Morais J., Morgenstern J., Pardo L.: Straight-line programs in geometric elimination theory.- Aparecerá en J. of Pure and Appl. Algebra (1996).

15

Grigor'ev D. & Vorobjov N.: Solving Systems of Polynomial Inequalities in Subexponential Time.- J. of Symb. Comp. 5 (1988) 37-64.

16

Grosso A., Herrera N., Matera G., Stefanoni M.E., Turull J. M.: A PSPACE implementation of the effective Nullstellensatz.- Proc. JAIIO, Buenos Aires, (1996).

17

Heintz J. & Morgenstern J.: On the intrinsic complexity of elimination theory.- J. of Complexity 9 (1993) 471-498.

18

Heintz J. & Schnorr C.: Testing Polynomials wich are easy to compute.- Logic and Algorithmic (an International Symposium in honour of Ernst Specker), Monographie n. 30 de l'Enseignement Mathématique (1982) 237-254.

19

Heintz J.: The project TERA: the Comeback of Oblomov in Computer Science.- Informe (1996).

20

Hermann G.: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale.- Math. Ann. 95 (1926) 736-788.

21

Kollár J.: Sharp effective Nullstellensatz.- J. AMS 1 (1988) 963-975.

22

Krick T. & Pardo L.M.: A Computational Method for Diophantine Approximation.- Algorithms in Algebraic Geometry and Applications, Progress in Mathematics 143, Birkhäuser Verlag (1996) 193-254.

23

Krick T., Sabia J. & Solernó P.: On intrinsic Bounds in the Nullstellesatz.- Aparecerá en AAECC Journal, 1997.

24

Matera G.: Integration of multivariate rational functions given by straight-line programs.- Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, L.N.Comp.Sci. 948, Springer Verlag (1995) 347-364.

25

Matera G. & Turull J.: The space complexity of elimination theory.- Aparecerá en Proc. Foundations of Computational Mathematics FOCM'97, 1997.

26

Pardo L. M.: How Lower and Upper Complexity Bounds meet in Elimination Theory.- Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, L.N.Comp.Sci. 948, Springer Verlag (1995) 33-69.

27

Puddu S. & Sabia J.: An effective algorithm for quantifier elimination over algebraically closed fields using straight-line programs.- Aparecerá en J. of Pure and Appl. Algebra, 1997.

28

Renegar J.: On the computational Complexity and Geometry of the First-order Theory of the Reals. (Part I: Introduction. Preliminaries. The Geometry of Semi-algebraic sets.- The Decision Problem for the Existencial Theory of the Reals.).- J. of Symb. Computation 13 (1992) 255-301.

29

Sabia J. & Solernó P.: Bounds for Traces in Complete Intersections and Degrees in the Nullstellensatz.- AAECC Journal 6, No.6, Springer-Verlag (1995) 353-376.

30

Shub M. & Smale S.: Complexity of Bezout's theorem V: Polynomial time.- Theoretical Comp. Sci. 133 (1994)

31

Sombra M.: Bounds for the Hilbert function of polynomial ideals and for the degrees in the Nulstellen- satz.- Aparecerá en J. Pure and Appl. Algebra, 1997.

32

TERA '96.- M. Giusti, J. Heintz & L.M. Pardo, (Eds.) Preprint Depto. de Matemáticas, Est. y Comp. 7, Univ. de Cantabria (1996).