Abstract
We describe an algorithm for the computation of the τ-radicals of ideals in polynomial rings over rational function fields k(T 1,…,T m) where (k, τ) is a preordered field satisfying certain computational conditions.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alonso, M. E., Mora, T., Raimondo, M. (1990). Local Decomposition Algorithms. Proceedings of the 8th International Conference AAECC-8, Tokyo, Japan, August 1990. Lecture Notes in Computer Science 508, 208–221.
Becker, E. (1981). Valuations and Real Places in the Theory of Formally Real Fields. In: ”Géométrie Algébrique Réelle et Formes Quadratiques”, Proceedings Rennes 1981, Lecture Notes in Math. 959, 1–40.
Bochnak, J., Coste, M., Roy, M. F. (1987). Géométrie algébrique réelle. Ergebnisse der Mathematik und ihrer Grenzgebiete, Folge 3, Band 12. Springer-Verlag.
Coste, M., Roy, M. F. (1988). Thorn’s Lemma, the Coding of Real Algebraic Numbers and the Computation of the Topology of Semi-algebraic Sets. Journal of Symbolic Computation (1988) 5, 121–129.
Dubois, D. W. (1969). A nullstellensatz for ordered fields. Arkiv for Mat. 8, 111–114.
Dubois, D. W., Recio, T. (1982). Order Extensions and Real Algebraic Geometry. Contemporary Mathematics, Vol. 8, 265–288.
Eisenbud, D., Huneke, C. (1989). A Jacobian method for finding the radical of an ideal. preprint.
Elman, R., Lam, T. Y., Wadsworth, A. R. (1979). Orderings under field extensions. J. Reine Angewandte Mathematik 306, 6–27.
Gianni, P., Mora, T. (1987). Algebraic Solution of Systems of Polynomial Equations using Gröbner Bases. Proceedings of the 5th International Conference AAECC-5, June 1987. Lecture Notes in Computer Science 356, 247–257.
Gianni, P., Trager, B., Zacharias, G. (1989). Gröbner Bases and Primary Decomposition of Polynomial Ideals. In: (Robbiano, L., ed.) Computational Aspects of Commutative Algebra, Academic Press, 15–33.
Krivine, J. L. (1964). Anneaux préordonnés. Journal d’analyse mathématique 12, 307–326.
Krick, T., Logar, A. (1991). An Algorithm for the Computation of the Radical of an Ideal in the Ring of Polynomials. Proceedings of the 9th International Symposium AAECC-9, New Orleans, LA, USA, October 1991. Lecture Notes in Computer Science 539, 195–205.
Kobayashi, H., Moritsugu, S., Hogan, R. W. (1989). On Radical Zero-dimensional Ideals. Journal of Symbolic Computation (1989) 8, 545–552.
Kredel, H., Weispfenning, V. (1989). Computing Dimension and Independent Sets for Polynomial Ideals. In: (Robbiano, L. ed.) Computational Asepects of Commutative Algebra, Academic Press, 97–113.
Lakshman, Y. N. (1990). On the Complexity of Computing a Gröbner Basis for the Radical of a Zero Dimensional Ideal. In: “Proc. of 22nd ACM Symposium on Theory of Computing”, May 1990.
Matsumura, H. (1970). Commutative Algebra. W. A. Benjamin, Inc.
Prestel, A. (1984). Lectures on Formally Real Fields. Lecture Notes in Math. 1093. Springer-Verlag.
Risler, J.-J. (1970). Une caractérisation des idéaux des variétés algébriques réelles. C.R.A.S. Paris, série A 271, 1171–1173.
Seidenberg, A. (1974). Constructions in Algebra. Trans. Amer. Math. Soc. 197, 273–313.
Vasconcelos W. V. (1991). Jacobian Matrices and Constructions in Algebra. Proceedings of the 9th International Symposium AAECC-9, New Orleans, LA, USA, October 1991. Lecture Notes in Computer Science 539, 48–64.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Birkhäuser Boston
About this paper
Cite this paper
Becker, E., Neuhaus, R. (1993). Computation of Real Radicals of Polynomial Ideals. In: Eyssette, F., Galligo, A. (eds) Computational Algebraic Geometry. Progress in Mathematics, vol 109. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2752-6_1
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2752-6_1
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7652-4
Online ISBN: 978-1-4612-2752-6
eBook Packages: Springer Book Archive