On intrinsic bounds in the Nullstellensatz
Let k be a field and f1 , . . . , fs be non constant polynomials in k[X1 , . . . , Xn] which generate the trivial ideal. In this paper we define an invariant associated to the sequence f1 , . . . , fs: the geometric degree of the system. With this notion we can show the following effective Nullstell...
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Springer Verlag
1997
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| LEADER | 06867caa a22007577a 4500 | ||
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| 001 | PAPER-3323 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518203247.0 | ||
| 008 | 190411s1997 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-0030734174 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a AAECE | ||
| 100 | 1 | |a Krick, T. | |
| 245 | 1 | 3 | |a On intrinsic bounds in the Nullstellensatz |
| 260 | |b Springer Verlag |c 1997 | ||
| 270 | 1 | 0 | |m Krick, T.; Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428- Buenos Aires, Argentina; email: krick@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
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| 504 | |a Berenstein, C., Struppa, D., Recent improvements in the Complexity of the Effective Nullstellensatz (1991) Linear Algebra and Its Appl., 157, pp. 203-215 | ||
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| 504 | |a Caniglia, E., Guccione, J.A., Guccione, J.J., Local membership problems for polynomial ideals. Effective Methods in Algebraic Geometry MEGA 90 (1991) Progress in Mathematics, 94, pp. 31-45. , Mora, T., Traverso, C. (eds). Birkhäuser | ||
| 504 | |a Cardinal, J.-P., (1993) Dualité et Algorithmes Itératifs pour la Résolution de Systèmes Polynomiaux, , Thesis. Université de Rennes | ||
| 504 | |a Dickenstein, A., Sessa, C., An effective residual criterion for the membership problem in ℂ[z1 , . . . , zn] (1991) J. Pure and Appl. Algebra, 74, pp. 149-158. , Amsterdam: North-Holland | ||
| 504 | |a Fitchas, N., Galligo, A., Nullstellensatz effectif et conjecture de Serre (théorème de Quillen-Suslin) pour le Calcul Formel (1990) Math. Nachr., 149, pp. 231-253 | ||
| 504 | |a Fitchas, N., Giusti, M., Smietanski, F., Sur la complexité du théorème des zéros (1995) Approximation and Optimization, 8, pp. 274-329. , Verlag Peter Lang | ||
| 504 | |a Giusti, M., Heintz, J., Sabia, J., On the efficiency of effective Nullstellensätze (1993) Comput. Complexity, 3, pp. 56-95. , Basel: Birkhäuser | ||
| 504 | |a Giusti, M., Heintz, J., Morais, J., Morgenstern, J., Pardo, L., Straight-line Programs in Geometric Elimination Theory J. Pure and Appl. Algebra, , to appear | ||
| 504 | |a Heintz, J., Definability and fast quantifier elimination in algebraically closed fields (1983) Theoret. Comput. Sci., 24, pp. 239-277 | ||
| 504 | |a Hermann, G., Die Frage der endlich vielen Schritte in der Theorie der Polynomideale (1926) Math. Ann., 95, pp. 736-788 | ||
| 504 | |a Kollár, J., Sharp effective Nullstellensatz (1988) J. AMS, 1, pp. 963-975 | ||
| 504 | |a Krick, T., Pardo, L., A computational Method for Diophantine Approximation Proc. MEGA '94, , Birkhäuser Progress in Math (to appear) | ||
| 504 | |a Kunz, E., Kähler Differentials (1986) Adv. Lect. in Math, , Vieweg Verlag | ||
| 504 | |a Philippon, P., Dénominateurs dans le théorème des zéros de Hilbert (1991) Acta. Arith., 58, pp. 1-25 | ||
| 504 | |a Sabia, J., Solernó, P., Bounds for Traces in Complete Intersections and Degrees in the Nullstellensatz (1995) AAECC, 6 (6), pp. 353-376 | ||
| 504 | |a Shiffman, B., Degree bounds for the division problem in polynomial ideals (1989) Michigan Math. J., 36, pp. 163-171 | ||
| 504 | |a Sombra, M., (1996) Bounds for the Hilbert Function of Polynomial Ideals, , Preprint, Universidad de Buenos Aires | ||
| 504 | |a Teissier, B., Résultats récents d'algèbre commutative effective. Séminaire Bourbaki 1989-1990 (1991) Astérisque, 189-190, pp. 107-131 | ||
| 504 | |a Vasconcelos, W., Jacobian Matrices and Constructions in Algebra (1992) Lecture Notes Comput. Sci., 539, pp. 48-64. , Proc. 9th Int. Conf. Applied Algebra. Algebraic Algorithms and Error Correcting Codes AAECC-9, New Orleans, 1991, Berlin, Heidelberg, New York: Springer | ||
| 520 | 3 | |a Let k be a field and f1 , . . . , fs be non constant polynomials in k[X1 , . . . , Xn] which generate the trivial ideal. In this paper we define an invariant associated to the sequence f1 , . . . , fs: the geometric degree of the system. With this notion we can show the following effective Nullstellensatz: if δ denotes the geometric degree of the trivial system f1 , . . .. , fs and d:= maxjdeg(fj), then there exist polynomials p1 , . . . , ps ∈ k[X1 , . . . , Xn] such that 1 = ∑jpjfjand deg pjfj ≦ 3n2δd. Since the number δ is always bounded by (d + 1)n-1, one deduces a classical single exponential upper bound in terms of d and n, but in some cases our new bound improves the known ones. |l eng | |
| 593 | |a Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428- Buenos Aires, Argentina | ||
| 593 | |a Depto. de Economía y Matemat., Universidad de San Andrés, Vito Dumas 284, 1644- Victoria, Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a COMPLETE INTERSECTION POLYNOMIAL IDEALS |
| 690 | 1 | 0 | |a EFFECTIVE NULLSTELLENSATZ |
| 690 | 1 | 0 | |a GEOMETRIC DEGREE |
| 690 | 1 | 0 | |a TRACE THEORY |
| 690 | 1 | 0 | |a FUNCTIONS |
| 690 | 1 | 0 | |a GEOMETRY |
| 690 | 1 | 0 | |a NUMBER THEORY |
| 690 | 1 | 0 | |a SET THEORY |
| 690 | 1 | 0 | |a GEOMETRIC DEGREE |
| 690 | 1 | 0 | |a HILBERT NULLSTELLENSATZ |
| 690 | 1 | 0 | |a TRACE THEORY |
| 690 | 1 | 0 | |a POLYNOMIALS |
| 700 | 1 | |a Sabia, J. | |
| 700 | 1 | |a Solernó, P. | |
| 773 | 0 | |d Springer Verlag, 1997 |g v. 8 |h pp. 125-134 |k n. 2 |p Appl Algebra Eng Commun Comput |x 09381279 |t Applicable Algebra in Engineering, Communications and Computing | |
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| 856 | 4 | 0 | |u https://doi.org/10.1007/s002000050057 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_09381279_v8_n2_p125_Krick |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09381279_v8_n2_p125_Krick |y Registro en la Biblioteca Digital |
| 961 | |a paper_09381279_v8_n2_p125_Krick |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 64276 | ||