Abstract:
We give a rational expression for the subresultants of n + 1 generic polynomials f1, ..., fn + 1 in n variables as a function of the coordinates of the common roots of f1, ..., fn and their evaluation in fn + 1. We present a simple technique to prove our results, giving new proofs and generalizing the classical Poisson product formula for the projective resultant, as well as the expressions of Hong for univariate subresultants in roots. © 2005 Elsevier Inc. All rights reserved.
Registro:
Documento: |
Artículo
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Título: | Multivariate subresultants in roots |
Autor: | D'Andrea, C.; Krick, T.; Szanto, A. |
Filiación: | Department of Mathematics, University of California at Berkeley, CA 94720, United States Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States
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Palabras clave: | Poisson product formula; Subresultants; Vandermonde determinants |
Año: | 2006
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Volumen: | 302
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Número: | 1
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Página de inicio: | 16
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Página de fin: | 36
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DOI: |
http://dx.doi.org/10.1016/j.jalgebra.2005.08.016 |
Título revista: | Journal of Algebra
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Título revista abreviado: | J. Algebra
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ISSN: | 00218693
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CODEN: | JALGA
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PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00218693_v302_n1_p16_DAndrea.pdf |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v302_n1_p16_DAndrea |
Referencias:
- Brown, W.S., Traub, J.F., On Euclid's algorithm and the theory of subresultants (1971) J. ACM, 18, pp. 505-514
- Busé, L., D'Andrea, C., Inversion of parameterized hypersurfaces by means of subresultants (2004) Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation, pp. 65-71. , ACM Press
- Busé, L., D'Andrea, C., On the irreducibility of multivariate subresultants (2004) C. R. Math. Acad. Sci. Paris, 338 (4), pp. 287-290
- Chardin, M., Formules à la Macaulay pour les sous-résultants en plusieurs variables (1994) C. R. Acad. Sci. Paris Sér. I Math., 319 (5), pp. 433-436
- Chardin, M., Multivariate subresultants (1995) J. Pure Appl. Algebra, 101 (2), pp. 129-138
- Cox, D., Little, J., O'Shea, D., Using Algebraic Geometry (1998) Grad. Texts in Math., 185. , Springer-Verlag, New York xii+499 pp
- Collins, E.G., Subresultants and reduced polynomial remainder sequences (1967) J. ACM, 14, pp. 128-142
- D'Andrea, C., Jeronimo, G., Subresultants and generic monomial bases (2005) J. Symbolic Comput., 39 (3-4), pp. 259-277
- Diaz-Toca, G.M., González-Vega, L., Various new expressions for subresultants and their applications (2004) Appl. Algebra Engrg. Comm. Comput., 15 (3-4), pp. 233-266
- Ducos, L., Algorithme de Bareiss, algorithme des sous-résultants (1996) RAIRO Inform. Théor. Appl., 30 (4), pp. 319-347
- Emiris, I.Z., Galligo, A., Lombardi, H., Certified approximate univariate GCDs (1997) J. Pure Appl. Algebra, 117-118, pp. 229-251. , Algorithms for Algebra. Eindhoven, 1996
- von zur Gathen, J., Gerhard, J., (1999) Modern Computer Algebra, , Cambridge Univ. Press
- González-Vega, L., A subresultant theory for multivariate polynomials (1990) Extracta Math., 5 (3), pp. 150-152
- González-Vega, L., Determinantal formulae for the solution set of zero-dimensional ideals (1991) J. Pure Appl. Algebra, 76 (1), pp. 57-80
- González-Vega, L., Lombardi, H., Recio, T., Roy, M.-F., Spécialisation de la suite de Sturm et sous-résultants (1990) RAIRO Inform. Théor. Appl., 24 (6), pp. 561-588
- Habicht, W., Zur inhomogenen Eliminationstheorie (1948) Comment. Math. Helv., 21, pp. 79-98
- Hong, H., Ore subresultants coefficients in solutions (2001) J. Appl. Algebra, 12 (5), pp. 421-428
- Hou, X., Wang, D., Subresultants with the Bézout matrix (2000) Lecture Notes Ser. Comput., 8, pp. 19-28. , Computer Mathematics. Chiang Mai, 2000, World Scientific, River Edge, NJ
- Ho, C.-J., Yap, C.K., The Habicht approach to subresultants (1996) J. Symbolic Comput., 21 (1), pp. 1-14
- Jouanolou, J.-P., Le formalisme du résultant (1991) Adv. Math., 90 (2), pp. 117-263
- Kaltofen, E., May, J., On approximate irreducibility of polynomials in several variables (2003) Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, pp. 161-168. , ACM Press, New York
- Lascoux, A., Symmetric functions and combinatorial operators on polynomials (2003) CBMS Reg. Conf. Ser. Math., 99. , Amer. Math. Soc., Providence, RI published for the Conference Board of the Mathematical Sciences, Washington, DC
- Macaulay, F., Some formulae in elimination (1902) Proc. London Math. Soc., 33 (1), pp. 3-27
- Reischert, D., Asymptotically fast computation of subresultants (1997) Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation, pp. 233-240. , Kihei, HI, ACM Press, New York
- Sylvester, J., A theory of syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm's functions, and that of the greatest algebraic common measure (1853) Philos. Trans.
- Weber, H., (1912) Lehrbuch der Algebra, , Vieweg, Braunschweig
- Zeng, Z., Dayton, B., The approximate gcd of inexact polynomials (2004) Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation, pp. 320-327. , ACM Press
- Zeng, Z., A method computing multiple roots of inexact polynomials (2003) Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, pp. 266-272. , ACM Press, New York
Citas:
---------- APA ----------
D'Andrea, C., Krick, T. & Szanto, A.
(2006)
. Multivariate subresultants in roots. Journal of Algebra, 302(1), 16-36.
http://dx.doi.org/10.1016/j.jalgebra.2005.08.016---------- CHICAGO ----------
D'Andrea, C., Krick, T., Szanto, A.
"Multivariate subresultants in roots"
. Journal of Algebra 302, no. 1
(2006) : 16-36.
http://dx.doi.org/10.1016/j.jalgebra.2005.08.016---------- MLA ----------
D'Andrea, C., Krick, T., Szanto, A.
"Multivariate subresultants in roots"
. Journal of Algebra, vol. 302, no. 1, 2006, pp. 16-36.
http://dx.doi.org/10.1016/j.jalgebra.2005.08.016---------- VANCOUVER ----------
D'Andrea, C., Krick, T., Szanto, A. Multivariate subresultants in roots. J. Algebra. 2006;302(1):16-36.
http://dx.doi.org/10.1016/j.jalgebra.2005.08.016