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Abstract:

We propose a new algorithm for the computation of the radical of an ideal in a polynomial ring. In recent years many algorithms have been proposed. A common technique used is to reduce the problem to the zero dimensional case. In the algorithm we present here, we use this reduction, but we avoid the redundant components that appeared in other algorithms . As a result, our algorithm is in some cases more efficient. Copyright 2006 ACM.

Registro:

Documento: Conferencia
Título:An algorithm for the computation of the radical of an ideal
Autor:Laplagne, S.
Ciudad:Genova
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Algorithms; Complexity; Polynomial ideal; Primary decomposition; Radical; Computational complexity; Computational methods; Polynomial approximation; Problem solving; Polynomial ideal; Primary decomposition; Radical; Algorithms
Año:2006
Volumen:2006
Página de inicio:191
Página de fin:195
Título revista:International Symposium on Symbolic and Algebraic Computation, ISSAC 2006
Título revista abreviado:Proc Int Symp Symbol Algebraic Comput ISSAC
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15959327_v2006_n_p191_Laplagne

Referencias:

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  • Cox, D., Little, J., O'Shea, D., Using Algebraic Geometry., , Springer, 1998
  • Decker, W., Gruel, G.-M., Pfister, G., Primary decomposition: Algorithms and comparisons (1998) Algorithmic Algebra and Number Theory, Springer Verlag, Heidelberg, pp. 187-220
  • Decker, W., Pfister, G., Schoenemann, H., (2005) A SINGULAR 3.0 Library for Computing Primary Decomposition and Radical of Ideals, , primdec.lib
  • Dickenstein, A., Fitchas, N., Giusti, M., Sessa, C., The membership problem for unmixed polynomial ideals is solvable in single exponential time (1991) Discrete Applied Mathematics, (33), pp. 73-94
  • Dube, T.W., The structure of polynomial ideals and grobner bases (1990) SIAM J. Comput., (19), pp. 750-773
  • Eisenbud, D., Huneke, C., Vasconcelos, W., Direct methods for primary decomposition (1992) Invent. Math., (110), pp. 207-235
  • Gianni, P., Trager, B., Zacharias, G., Bases and primary decomposition of ideals (1988) J. Symbolic Computation, (6), pp. 149-167
  • Giusti, M., Some effective problems in polynomial ideal theory (1984) EUROSAM 84, Lecture Notes in Computer Science, (174), pp. 159-171
  • Greuel, G.-M., Pfister, G., (2002) A Singular Introduction to Commutative Algebra, , Springer
  • Greuel, G.-M., Pfister, G., Schonemann, H., (2005) SINGULAR 3.0.1. A Computer Algebra System for Polynomial Computations, , http://www.singular.uni-kl.de, Centre for Computer Algebra, University of Kaiserslautern
  • Heintz, J., Definability and fast quantifier elimination over algebraically closed fields (1983) Theor. Comp. Science, (24), pp. 239-278
  • Kemper, G., The calculation of radical ideals in positive characteristic (2002) J. Symbolic Computation, (34), pp. 229-238
  • Krick, T., Logar, A., An algorithm for the computation of the radical of an ideal in the ring of polynomials (1991) AAECC9, Springer LNCS, (539), pp. 195-205
  • Krick, T., Logar, A., Membership problem, representation problem and the computation of the radical for one-dimensional ideals (1991) Progress in Mathematics, (94), pp. 203-216
  • Krick, T., Pardo, L.M., Sombra, M., Sharp estimates for the arithmetic nullstellensatz (2001) Duke Math J., (109), pp. 521-598
  • Matsumoto, R., Computing the radical of an ideal in positive characteristic (2001) J. Symbolic Computation, (32), pp. 263-271
  • Seidenberg, A., Constructions in algebra (1974) Trans. Amer. Math. Soc., 197, pp. 273-313
  • Vasconcelos, W., (1998) Computational Methods in Commutative Algebra and Algebraic Geometry, , Springer-VerlagA4 - ACM SIGSAM

Citas:

---------- APA ----------
(2006) . An algorithm for the computation of the radical of an ideal. International Symposium on Symbolic and Algebraic Computation, ISSAC 2006, 2006, 191-195.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15959327_v2006_n_p191_Laplagne [ ]
---------- CHICAGO ----------
Laplagne, S. "An algorithm for the computation of the radical of an ideal" . International Symposium on Symbolic and Algebraic Computation, ISSAC 2006 2006 (2006) : 191-195.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15959327_v2006_n_p191_Laplagne [ ]
---------- MLA ----------
Laplagne, S. "An algorithm for the computation of the radical of an ideal" . International Symposium on Symbolic and Algebraic Computation, ISSAC 2006, vol. 2006, 2006, pp. 191-195.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15959327_v2006_n_p191_Laplagne [ ]
---------- VANCOUVER ----------
Laplagne, S. An algorithm for the computation of the radical of an ideal. Proc Int Symp Symbol Algebraic Comput ISSAC. 2006;2006:191-195.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15959327_v2006_n_p191_Laplagne [ ]