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Abstract:

We give a multivariate version of Descartes' rule of signs to bound the number of positive real roots of a system of polynomial equations in n variables with n+2 monomials, in terms of the sign variation of a sequence associated both to the exponent vectors and the given coefficients. We show that our bound is sharp and is related to the signature of the circuit. © The Author(s) 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

Registro:

Documento: Artículo
Título:Descartes' rule of signs for polynomial systems supported on circuits
Autor:Bihan, F.; Dickenstein, A.
Filiación:Laboratoire de Mathématiques, Université de Savoie, Le Bourget-du-Lac Cedex, 73376, France
Dto. de Matemática, FCEN, Universidad de Buenos Aires, IMAS (UBA-CONICET), Ciudad Universitaria, Pab. i, Buenos Aires, C1428EGA, Argentina
Año:2017
Volumen:2017
Número:22
Página de inicio:6867
Página de fin:6893
DOI: http://dx.doi.org/10.1093/imrn/rnw199
Título revista:International Mathematics Research Notices
Título revista abreviado:Int. Math. Res. Not.
ISSN:10737928
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10737928_v2017_n22_p6867_Bihan

Referencias:

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  • Bihan, F., Polynomial systems supported on circuits and dessins d'enfant (2007) Journal of the London Mathematical Society. Second Series, 75 (1), pp. 116-132
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Citas:

---------- APA ----------
Bihan, F. & Dickenstein, A. (2017) . Descartes' rule of signs for polynomial systems supported on circuits. International Mathematics Research Notices, 2017(22), 6867-6893.
http://dx.doi.org/10.1093/imrn/rnw199
---------- CHICAGO ----------
Bihan, F., Dickenstein, A. "Descartes' rule of signs for polynomial systems supported on circuits" . International Mathematics Research Notices 2017, no. 22 (2017) : 6867-6893.
http://dx.doi.org/10.1093/imrn/rnw199
---------- MLA ----------
Bihan, F., Dickenstein, A. "Descartes' rule of signs for polynomial systems supported on circuits" . International Mathematics Research Notices, vol. 2017, no. 22, 2017, pp. 6867-6893.
http://dx.doi.org/10.1093/imrn/rnw199
---------- VANCOUVER ----------
Bihan, F., Dickenstein, A. Descartes' rule of signs for polynomial systems supported on circuits. Int. Math. Res. Not. 2017;2017(22):6867-6893.
http://dx.doi.org/10.1093/imrn/rnw199