Observatorio de I+D+i UPM

Memorias de investigación
Communications at congresses:
Implicitization of linear DPPEs by perturbed differential resultants
Year:2011
Research Areas
  • Mathematics,
  • Determinants and matrices,
  • Ordinary differential equations,
  • Differential operators
Information
Abstract
The development of differential elimination techniques similar to the algebraic existing ones (Groebner basis and multivariate resultants) is an active field of research. Given a system $\mathcal{P}$ of $n$ linear ordinary differential polynomial parametric equations (linear DPPEs) in $n-1$ differential parameters, we proved that, if nonzero a differential resultant gives the implicit equation of $\mathcal{P}$. Unfortunately, differential resultants often vanish under specialization. Motivated by Canny's method and its generalizations, we consider now a linear perturbation of $\mathcal{P}$ and use it to give an algorithm to decide if the dimension of the implicit ideal of $\mathcal{P}$ is $n-1$ and, in the affirmative case, obtain the implicit equation of $\mathcal{P}$.
International
Si
Congress
DEAM 2, Differential Equations with Algebraic Methods
960
Place
Linz, Austria
Reviewers
Si
ISBN/ISSN
No
No
Start Date
11/02/2011
End Date
13/02/2011
From page
1
To page
4
No
Participants
  • Autor: Sonia Luisa Rueda Perez (UPM)
Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Modelos Matemáticos no Lineales
  • Departamento: Matemática Aplicada a la Edificación, al Medio Ambiente y al Urbanismo
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