Differential elimination by differential specialization of Sylvester style matrices

Rueda Pérez, Sonia Luisa (2016). Differential elimination by differential specialization of Sylvester style matrices. "Advances in Applied Mathematics", v. 72 ; pp. 4-37. ISSN 0196-8858. https://doi.org/10.1016/j.aam.2015.07.002.

Description

Title: Differential elimination by differential specialization of Sylvester style matrices
Author/s:
  • Rueda Pérez, Sonia Luisa
Item Type: Article
Título de Revista/Publicación: Advances in Applied Mathematics
Date: January 2016
ISSN: 0196-8858
Volume: 72
Subjects:
Freetext Keywords: differential elimination, Laurent differential polynomial, sparse resultant, differential specialization, sparse differential resultant
Faculty: E.T.S. Arquitectura (UPM)
Department: Matemática Aplicada
UPM's Research Group: Modelos Matemáticos no Lineales
Creative Commons Licenses: None

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Abstract

Differential resultant formulas are defined, for a system $\cP$ of $n$ ordinary Laurent differential polynomials in $n-1$ differential variables. These are determinants of coefficient matrices of an extended system of polynomials obtained from $\cP$ through derivations and multiplications by Laurent monomials. To start, through derivations, a system $\ps(\cP)$ of $L$ polynomials in $L-1$ algebraic variables is obtained, which is non sparse in the order of derivation. This enables the use of existing formulas for the computation of algebraic resultants, of the multivariate sparse algebraic polynomials in $\ps(\cP)$, to obtain polynomials in the differential elimination ideal generated by $\cP$. The formulas obtained are multiples of the sparse differential resultant defined by Li, Yuan and Gao, and provide order and degree bounds in terms of mixed volumes in the generic case.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2011-25816-C02-01UnspecifiedJuan Rafael Sendra PonsAlgoritmos y aplicaciones en geometría de curvas y superficies

More information

Item ID: 38522
DC Identifier: http://oa.upm.es/38522/
OAI Identifier: oai:oa.upm.es:38522
DOI: 10.1016/j.aam.2015.07.002
Official URL: https://doi.org/10.1016/j.aam.2015.07.002
Deposited by: PhD Sonia Luisa Rueda Pérez
Deposited on: 24 Nov 2015 13:49
Last Modified: 13 Mar 2019 14:41
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