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Chapter 0 Introduction

DOI: 10.1016/s0924-6509(00)80016-1
  • Computer Science
  • Mathematics


Publisher Summary This chapter presents the concepts of power geometry. The equations may be algebraic, ordinary differential or partial differential and systems may comprise the equations of one type, but may include equations of different types. The solutions to these equations and systems subdivide into regular and singular ones. The main concept of Power Geometry is to study the properties of solutions to an equation through the power exponents of its monomials. Power Geometry is based upon the three concepts—that is, Newton polyhedron, power transformation, and logarithmic transformation. The theory and algorithms presented considered only as the first steps on the way of using the concepts of Power Geometry. Algorithms of solution of systems of linear inequalities are set forth, as well as their modifications for the purposes of Power Geometry, and the corresponding computer programs are also presented in the chapter.

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