Deformation techniques to solve generalised Pham systems

  • Authors:

  • Luis Miguel Pardo;Jorge San Martín

  • Affiliations:

  • Departamento de Matemáticas, Estadistica y Computación, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander, Spain;Departemento de Informática Estadistica y Telemática, Escuela Superior de Ciencias Experimentales y Technológicas, Universidad Rey Juan Carlos, c/Tulipán s/n. 28933 Móstol ...

  • Venue:
  • Theoretical Computer Science - Algebraic and numerical algorithm
  • Year:
  • 2004

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Abstract

In Heintz et al. (Electron. J. SADIO 1(1) (1998) 37), Castro et al. (Found., Comput. Math. (2003) to appear) and Pardo (Proceedings EACA'2000, 2000, pp. 25-51), the authors have shown that universal solving procedures require exponential running time. Roughly speaking, a universal solving procedure takes as input a system of multivariate polynomial equations and outputs complete symbolic information on the solution variety. Here, we introduce a nonuniversal solving procedure adapted to Generalised Pham Systems. The aim is to compute partial information of the variety defined by the input system. The Algorithm is based on an homotopic deformation and on a non-Archimedean lifting procedure from a non-singular zero of the homotopy curve. The complexity of the procedure is also stated and it depends on some intrinsic quantity called the deformation degree of the given input system.