Observatorio de I+D+i UPM

Memorias de investigación
Courses, Seminars and tutorials:
Differential resultants, a differential elimination tool
Year:2011
Research Areas
  • Mathematics,
  • Algebra,
  • Ordinary differential equations,
  • Differential operators
Information
Abstract
Differential resultant problems were first studied for differential operators by Ore (1932), Berkovich and Tsirulik (1986), Chardin (1991), Carra'Ferro (1994) and Li (1995). The differential resultant of two differential polynomials in one variable was studied by Ritt (1932), under some hypothesis on the differential polynomials. It was G. Carra'Ferro, who gave the definition of a differential resultant for a set of $n$ ordinary differential polynomials in $n-1$ differential variables (1997). The differential resultant defined by Carra'Ferro is based on the algebraic resultant of Macaulay, and for generic differential polynomials it can be computed as a quotient of two determinants. Apparently forgotten for some years, Carra'Ferro's differential resultant of a set of partial differential operators (1994) was used by Kasman and Previato (2001,2010). The differential resultant for differential polynomials was used recently by Rueda and Sendra (2010) to approach the linear ordinary differential implicitization problem. We defined linear complete differential resultants and we used them to compute the implicit equation of a set of linear differential polynomial parametric equations (linear DPPEs). Also recently, Gao et al. gave a more complete definition of the (sparse) differential resultant of $n$ differential polynomials in $n-1$ variables (in terms of the generalized differential Chow form), suggesting a revival of the subject (of differential resultants in general). We may say that the theory of differential resultants is rather incomplete and offers a wide field of research, in many different directions regarding its definition and its computation.
International
Si
Congress
Algebra Seminar
Entity
Institute für Mathematik. Goethe Universität
Entity Nationality
ALEMANIA
Place
Frankfurt
Start Date
14/06/2011
End Date
14/06/2011
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
S2i 2020 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)