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Abstract:

The first step in the generalization of the classical theory of homogeneous equations to the case of arbitrary support is to consider algebraic systems with multihomogeneous structure. We propose constructive methods for resultant matrices in the entire spectrum of resultant formulae, ranging from pure Sylvester to pure Bézout types, and including matrices of hybrid type of these two. Our approach makes heavy use of the combinatorics of multihomogeneous systems, inspired by and generalizing certain joint results by Zelevinsky, and Sturmfels or Weyman (J. Algebra, 163 (1994) 115; J. Algebraic Geom., 3 (1994) 569). One contribution is to provide conditions and algorithmic tools so as to classify and construct the smallest possible determinantal formulae for multihomogeneous resultants. Whenever such formulae exist, we specify the underlying complexes so as to make the resultant matrix explicit. We also examine the smallest Sylvester-type matrices, generically of full rank, which yield a multiple of the resultant. The last contribution is to characterize the systems that admit a purely Bézout-type matrix and show a bijection of such matrices with the permutations of the variable groups. Interestingly, it is the same class of systems admitting an optimal Sylvester-type formula. We conclude with examples showing the kinds of matrices that may be encountered, and illustrations of our Maple implementation. © 2003 Elsevier Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:Multihomogeneous resultant formulae by means of complexes
Autor:Dickenstein, A.; Emiris, I.Z.
Filiación:Departamento de Matemática, Univ. de Buenos Aires F.C.E. y N., Pabellón I, 1428 Buenos Aires, Argentina
Dept. of Informatics/Telecomm., University of Athens, 15771 Athens, Greece
Palabras clave:Degree vector; Determinantal formula; Multihomogeneous system; Sparse resultant; Sylvester and Beźout type matrix
Año:2003
Volumen:36
Número:3-4
Página de inicio:317
Página de fin:342
DOI: http://dx.doi.org/10.1016/S0747-7171(03)00086-5
Título revista:Journal of Symbolic Computation
Título revista abreviado:J. Symb. Comput.
ISSN:07477171
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v36_n3-4_p317_Dickenstein

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Citas:

---------- APA ----------
Dickenstein, A. & Emiris, I.Z. (2003) . Multihomogeneous resultant formulae by means of complexes. Journal of Symbolic Computation, 36(3-4), 317-342.
http://dx.doi.org/10.1016/S0747-7171(03)00086-5
---------- CHICAGO ----------
Dickenstein, A., Emiris, I.Z. "Multihomogeneous resultant formulae by means of complexes" . Journal of Symbolic Computation 36, no. 3-4 (2003) : 317-342.
http://dx.doi.org/10.1016/S0747-7171(03)00086-5
---------- MLA ----------
Dickenstein, A., Emiris, I.Z. "Multihomogeneous resultant formulae by means of complexes" . Journal of Symbolic Computation, vol. 36, no. 3-4, 2003, pp. 317-342.
http://dx.doi.org/10.1016/S0747-7171(03)00086-5
---------- VANCOUVER ----------
Dickenstein, A., Emiris, I.Z. Multihomogeneous resultant formulae by means of complexes. J. Symb. Comput. 2003;36(3-4):317-342.
http://dx.doi.org/10.1016/S0747-7171(03)00086-5