Bezoutian and quotient ring structure

Journal of Symbolic Computation

Volumn 39, Issue 3-4 SPEC. ISS., 2005, Pages 397-415

  Mourrain, B ^a  

^a INRIA   (France)

Author keywords

Bezoutian; Linear algebra; Multiplication matrix; Normal form; Polynomial system solving; Quotient ring structure; Residu; Resultant

Indexed keywords

EID: 14944367312     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2004.11.010     Document Type: Article

References (43)

1. L.A. Aizenberg A.M. Kytmanov Multdimensional analogues of newtons formulas for systems of nonlinear algebraic equations and some of their applications Trans. Sib. Mat. Zhurnal 22 2 1981 19-39
2. W. Auzinger H.J. Stetter An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations In: Proc. Intern. Conf. on Numerical Math In: Int. Series of Numerical Math vol. 86 1988 Birkhäuser Verlag 12-30
3. E. Becker J.P. Cardinal M.F. Roy Z. Szafraniec Multivariate bezoutians, Kronecker symbol and Eisenbud-Levin formula In: L. González-Vega T. Recio (Eds.) Algorithms in Algebraic Geometry and Applications In: Prog. in Math. vol. 143 1996 Birkhäuser Basel 79-104
4. n] Acta Math. 166 1991 69-120
5. C.A. Berenstein R. Gay A. Vidras A. Yger Residue Currents and Bezout Identities In: Prog. in Math. vol. 114 1993 Birkhaäuser
6. Busé, L., 2001. Étude du résultant sur une variété algébrique. Ph.D. Thesis, Université de Nice Sophia-Antipolis
7. L. Busé M. Elkadi B. Mourrain Generalized resultant over unirational algebraic varieties J. Symbolic Comput. 29 2000 515-526
8. L. Busé M. Elkadi B. Mourrain Resultant over the residual of a complete intersection J. Pure Appl. Algebra 164 2001 35-57
9. Cardinal, J.-P., 1993. Dualité et algorithmes itératifs pour la résolution de syst̀mes polynomiaux. Ph.D. Thesis, Univ. de Rennes
10. J.P. Cardinal B. Mourrain Algebraic approach of residues and applications In: J. Renegar M. Shub S. Smale (Eds.) In: Proc. AMS-SIAM Summer Seminar on Math. of Numerical Analysis, 1995, Park City, Utah Lectures in Applied Math. vol. 32 1996 American Mathematical Society Press Providence 189-210
11. E. Cattani A. Dickenstein B. Sturmfels Computing multidimensional residues In: L. González-Vega T. Recio (Eds.) In: Algorithms in Algebraic Geometry and Applications In: Prog. in Math. vol. 143 1996 Birkhäuser Basel
12. A. Cayley On the theory of elimination Dublin Math. J. II 1848 116-120
13. D. Cox J. Little D. O'Shea Using Algebraic Geometry 1997 Springer-Verlag New York
14. C. D'Andrea A. Dickenstein Explicit formulas for the multivariate resultant J. Pure Appl. Algebra 162 2001 59-86
15. A.L. Dixon The eliminant of three quantics in two independent variables Proc. London Math. Soc. 6 1908 49-69, 473-492
16. M. Elkadi Bornes pour les Degrés et les Hauteurs dans le Problème de Division Michigan Math. J. 40 1993 609-618
17. Elkadi, M., Mourrain, B., 1996. Approche effective des résidus algébriques. Rapport de Recherche 2884, INRIA, Sophia Antipolis
18. Elkadi, M., Mourrain, B., 1998. Some applications of bezoutians in effective algebraic geometry. Rapport de Recherche 3572, INRIA, Sophia Antipolis
19. M. Elkadi B. Mourrain A new algorithm for the geometric decomposition of a variety In: S. Dooley (Ed.) Proc. Intern. Symp. on Symbolic and Algebraic Computation 1999 ACM Press New York 9-16
20. M. Elkadi B. Mourrain Algorithms for residues and Lojasiewicz exponents J. Pure Appl. Algebra 153 2000 27-44
21. Elkadi, M., Mourrain, B., 2003. Introduction à la résolution des systèmes d'équations algébriques, Notes de cours, Univ. de Nice. Soumis pour publication dans la série mathématiques appliquées (SMAI). p. 310
22. N. Fitchas M. Giusti M. Smietanski Sur la complexité du théorème des zéros In: J. Gudatt (Ed.) In: Proc. of the Second. Int. Conf. on Approximation and Optimization 1993 Peter Lang Verlag La Habana 274-329
23. M. Giusti J. Heintz J.E Morais J. Morgenstern L.M. Pardo Straight-line programs in geometric elimination theory J. Pure Appl. Algebra 124 1-3 1998 101-146
24. M. Giusti J. Heintz K. Hägele J.E. Morais L.M. Pardo S.L. Montaña Lower bounds for diophantine approximations J. Pure Appl. Algebra 117-118 1996 119-144
25. L. Gonzalez-Vega Implicitization of parametric curves and surfaces by using multidimensional Newton formulae J. Symbolic Comput. 23 2-3 1997 137-151
26. L. Gonzalez-Vega F. Rouillier M.F. Roy Symbolic Recipes for Polynomial System Solving In: Some Tapas of Computer Algebra 1997 Springer
27. Ph. Griffiths J. Harris Principles of Algebraic Geometry 1978 Wiley Interscience New York
28. J.P. Jouanolou Le formalisme du résultant Adv. Math. 90 2 1991 117-263
29. J.P. Jouanolou Formes d'inertie et résultant: Un formulaire Adv. Math. 126 2 1997 119-250
30. D. Kapur T. Saxena Comparison of various multivariate resultant formulations In: A.H.M. Levelt (Ed.) Proc. ISSAC 1995 ACM Press Montreal, Canada 187-194
31. D. Kapur T. Saxena Extraneous factors in the Dixon resultant formulation In: W.W. Küchlin (Ed.) Proc. ISSAC 1997 ACM Press 141-148
32. D. Kapur T. Saxena L. Yang Algebraic and geometric reasoning using Dixon resultants In: J. von zur Gathen (Ed.) Proc. ISSAC'94 1994 Oxford England 99-107
33. D. Kapur T. Saxena L. Yang Sparsity considerations in Dixon resultants In: Proc. STOC 1996 ACM Press 184-191
34. A. Khetan Determinantal formula for the chow form of a toric surface In: T. Mora (Ed.) Proc. Intern. Symp. on Symbolic and Algebraic Computation 2002 ACM Press New-York 231-238
35. T. Krick L.M. Pardo A computational method for diophantine approximation In: L. González-Vega T. Recio (Eds.) In: Algorithms in Algebraic Geometry and Applications In: Prog. in Math. vol. 143 1996 Birkhäuser Basel 193-254
36. T. Krick L.M. Pardo M. Sombra Sharp estimates for the arithmetic nullstellensatz Duke Math. J. 109 3 2001 521-598
37. E. Kunz Kähler Differentials In: Advanced Lectures in Mathematics 1986 Friedr. Vieweg and Sohn
38. B. Mourrain Isolated points, duality and residues In: Proc. of the 4th Int. Symp. on Effective Methods in Algebraic Geometry (MEGA) In: J. Pure Appl. Algebra 117-118 1996 469-493 (special issue)
39. B. Mourrain Computing isolated polynomial roots by matrix methods Symbolic-Numeric Algebra for Polynomials J. Symbolic Comput. 26 6 1998 715-738 (special issue)
40. B. Mourrain A new criterion for normal form algorithms In: M. Fossorier H. Imai S. Lin A. Poli (Eds.) Proc. AAECC In: LNCS vol. 1719 1999 Springer Berlin 430-443
41. Mourrain, B., Trébuchet, Ph., 2002. Algebraic methods for numerical solving. In: Proc. of the 3rd International Workshop on Symbolic and Numeric Algorithms for Scientific Computing'01. Timisoara, Romania, pp. 42-57
42. J. Sabia P. Solerno Bounds for traces in complete intersections and degrees in the Nullstellenstaz AAECC-6 948 1995 353-376
43. G. Scheja U. Storch Über Spurfunktionen bei vollständigen Durschnitten J. Reine Angew. Math. 278 1975 174-190