Some Applications of Generalized Char-Sets of Ordinary Differential Polynomial Sets

Farkhanda Afzal

doi:10.1051/matecconf/20167702007

Abstract

The notion of characteristic sets, which are a special kind of triangular sets, is introduced by J. F Ritt and W.T. Wu. Wu extended Ritt’s work and developed the characteristic set method not only in theory but in algorithms, efficiency and its numerous applications. Triangular sets are widely considered as a good representation for the solution of polynomial systems. After the introduction of characteristic sets by Ritt, triangular sets have become an alternative tool for representing the ideal besides the Grobner bases. This paper is about implementation and applications of generalized characteristic sets of ordinary differential polynomial sets defined by author.

Highlights

The key inclination in the information era is the mechanization of mental labor with the assistance of computers
Ritt [11] introduced the concept of a characteristic set of a finite or infinite set of differential polynomials
We have two types of triangular decompositions that are basically different. Those systems for which output triangular system can encode all the points of the zero set of input polynomial system. The second are those for which triangular system represents only the generic zeros of the irreducible components of the input polynomial system

Summary

Introduction

The key inclination in the information era is the mechanization of mental labor with the assistance of computers. Ritt [11] introduced the concept of a characteristic set of a finite or infinite set of differential polynomials One of his objective was to provide a method to solve systems of differential equations. Wu Wen-tsun used Ritt’s work to provide an algorithm for solving systems of algebraic equations by means of triangular sets which only requires pseudoremainder computations. Characteristic Set Method of Wu has released Ritt’s decomposition from polynomial factorization, opening access to a variety of discoveries in polynomial system solving. This method and the methods for geometry reasoning and computation have various applications. Based on d-pseudo division in efficiency and simplicity of outcome

Preliminaries

Generalized differential characteristic sets

Applications of generalized differential characteristic sets

Conclusion and future work