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D. Bayer, M. Stillman: On the complexity of computing syzygies. Preprint 1985.
C.A. Berenstein, A. Yger: Effective Bezout Identities in Q[z1, ... zn]. Preprint University of Maryland 1987.
S.J. Berkowitz: On computing the determinant in small parallel time using a small number of processors. Information Processing Letters 18 (1984) 147–150.
J. Briançon: Sur le degré des relations entre polynômes. C.R. Acad.Sci. Paris 287, Série I (1982) 553–556.
D. Brownawell: Bounds for the degrees in the Nullstellensatz. Ann.math. Second Series, Vol. 126 No 3 (1987) 577–591.
W.D. Brownawell: Borne effective pour l'exponent dans le théorème des zéros. C.R. Acad.Sci. Paris 305, Série I (1987) 287–290.
W.D. Brownawell: Local Diophantine Nullstellen Inequalities. Preprint Penn State University 1987.
B. Buchberger: Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems. Aequat.math. 4 (1970) 374–383.
B. Buchberger: A criterion for detecting unnecessary reductions in the construction of Gröbner bases. Sym. and Alg.Comp., Springer LN Comput.Sci. 72 (1979) 3–21.
B. Buchberger: A note on the complexity of constructing Gröbner bases. Proc. Eurocal'83, Computer Algebra, ed. J.A. van Hulzen, Springer LN Comput.Sci. 162 (1983) 137–145.
L. Caniglia, A. Galligo, J. Heintz: Borne simple exponentielle pour les degrés dans le théorème des zéros sur un corps de caractéristique quelconque. to appear in: C.R. Acad.Sci. Paris 1988.
A.L. Chistov, D.Yu. Grigor'ev: Subexponential time solving systems of algebraic equations I,II. LOMI preprints E-9-83, E-10-83, Leningrad 1983.
A.L. Chistov, D.Yu. Grigor'ev: Complexity of quantifier elimination in the theory of algebraically closed fields. Proc. 11th Symp. MFCS 1984, Springer LN Comput.Sci. 176 (1984) 17–31.
A.L. Chistov: Fast parallel calculation of the rank of matrices over a field of arbitrary characteristic. Proc. Int.Conf. FCT 1985, Springer LN Comput.Sci. 199 (1985) 63–69.
N. Fitchas, A. Galligo, J. Morgenstern: Algorithmes rapides en séquentiel et en parallel pour l'élimination de quantificateurs en géométrie élémentaire. to appear in: Séminaire Structures Algébriques Ordonnées, UER de Math., Université de Paris VII (1987); final version to appear in: Same Seminary, Publ.Univ. Paris VII.
A. Galligo: Algorithmes de construction de bases standards. Preprint University of Nice 1985.
A. Galligo, J. Heintz, J. Morgenstern: Parallelism and fast quantifier elimination over algebraically (and real) closed fields. Invited lecture Int.Conf. FCT'87 Kazan 1987.
M. Giusti: Some effectivity problems in polynomial ideal theory. Proc. Eurosam 84, Springer LN Comput.Sci. 174 (1984) 159–171.
M. Giusti: Complexity of standard bases in projective dimension zero. Preprint Ecole Polytechnique Paris 1987.
M. Giusti: Combinatorial dimension theory of algebraic varieties. Preprint Ecole Polytechnique Paris 1988.
D.Yu. Grigor'ev: The complexity of the decision problem for the first order theory of algebraically closed fields. Math. USSR Izvestija, Vol. 29, No 2 (1987) 459–475.
J. Heintz: Definability and fast quantifier elimination in algebraically closed fields. Theoret.Comput.Sci. 24 (1983) 239–277; Russian transl. in: Kyberneticeskij Sbornik, Novaja Serija Vyp. 22, Mir Moscow (1985) 113–158.
J. Heintz, R. Wüthrich: An efficient quantifier elimination algorithm for algebraically closed fields. SIGSAM Bull. 9(4) (1975) 11.
J. Kollár: Sharp effective Nullstellensatz. Manuscript 1988.
B. Iversen: Generic Local Structure in Commutative Algebra. Springer LN Math. 310 (1973).
J.P. Jouanolou: Théorèmes de Bertini et applications. Birkhäuser PM 42 (1983).
C. Kollreider, B. Buchberger: An improved algorithmic construction of Gröbnerbases for polynomial ideals. Bericht Nr. 170 (1978), Technical Report, Universität Linz.
D. Lazard: Algèbre linéaire sur K[X1, ..., Xn] et élimination. Bull.Soc.Math. France 105 (1977) 165–190.
D. Lazard: Gröbner Bases, Gaussian Elimination and Resolution of Algebraic Equations. Proc. Eurocal'83, Computer Algebra, ed. J.A. van Hulzen, Springer LN Comput.Sci. 162 (1983) 146–156.
H. Matsumura: Commutative algebra. W.A. Benjamin 1980 (first edition).
E. Mayr, A. Meyer: The complexity of the word problem for commutative semigroups and polynomial ideals. Advances in Math. 46 (1982) 305–329.
H.M. Möller, F. Mora: New Constructive Methods in Classical Ideal Theory. J. of Algebra, Vol. 100, No 1 (1986) 138–178.
K. Mulmuley: A fast parallel algorithm to compute the rank of a matrix over an arbitrary field. Proc. 18th Ann. ACM Symp. Theory of Computing (1986) 338–339.
I.R. Shafarevich: Algebraic Geometry. Springer Berlin 1974.
B. Shiffman: New degree bounds for the Nullstellensatz in arbitrary characteristic. Manuscript 1988.
V. Weispfenning: The complexity of linear problems in fields. J. on symbolic Comput. Vol. 5, No. 1–2 (1988) 3–27.
R. Wüthrich: Ein schnelles Quantoreneliminationsverfahren für die Theorie der algebraisch abgeschlossenen Körper. Ph.D.-Thesis, Univ. Zurich 1977.
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Caniglia, L., Galligo, A., Heintz, J. (1989). Some new effectivity bounds in computational geometry. In: Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1988. Lecture Notes in Computer Science, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51083-4_54
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