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Computing Characteristic Sets of Ordinary Radical Differential Ideals

Published/Copyright: March 10, 2010
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Georgian Mathematical Journal
From the journal Volume 13 Issue 3

Abstract

We give upper bounds for the order of the elements in a characteristic set of a regular differential ideal or a radical of a finitely generated differential ideal with respect to some specific orderings. We then show how to compute characteristic sets of these ideals using algebraic methods.

Key words and phrases:: Differential algebra; characteristic sets; differential ideals; Gröbner bases
Received: 2005-05-17
Revised: 2006-05-18
Published Online: 2010-03-10
Published in Print: 2006-September

© Heldermann Verlag

Articles in the same Issue

  1. Global Existence and Energy Decay of Solutions to a Petrovsky Equation with General Nonlinear Dissipation and Source Term
  2. Curves with Two Pencils and Associated Maps to Projective Spaces
  3. The Second Obstruction Functor
  4. Ground State Solutions of Nonlinear Stationary Schrödinger Systems with Discontinuous Nonlinearity and Variable Potential
  5. Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–Fourier Series
  6. On the Convergence of Conjugate Trigonometric Polynomials
  7. Existence of Solutions for Fourth Order Nonlocal Boundary Value Problems
  8. New Proof of the 𝑇(1) Theorem for Triebel–Lizorkin Spaces
  9. Inversion of Ahlfors and Grunsky Inequalities
  10. On Non-Compact Operators in Weighted Ideal and Symmetric Function Spaces
  11. Computing Characteristic Sets of Ordinary Radical Differential Ideals
  12. Approximating Common Fixed Points of Nonexpansive Mappings in Banach Spaces
  13. On Systems of Linear Functional Differential Inequalities
  14. The Dirichlet Problem for a Second Order Elliptic Equation Degenerating on the Whole Boundary When the Boundary Condition Is Satisfied in the Presence of Some Weight
  15. Fourier Series with Small Gaps
  16. Oscillations of Higher Order Functional Differential Equations with Impulses
https://doi.org/10.1515/GMJ.2006.515
Keywords for this article
Differential algebra; characteristic sets; differential ideals; Gröbner bases

Articles in the same Issue

  1. Global Existence and Energy Decay of Solutions to a Petrovsky Equation with General Nonlinear Dissipation and Source Term
  2. Curves with Two Pencils and Associated Maps to Projective Spaces
  3. The Second Obstruction Functor
  4. Ground State Solutions of Nonlinear Stationary Schrödinger Systems with Discontinuous Nonlinearity and Variable Potential
  5. Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–Fourier Series
  6. On the Convergence of Conjugate Trigonometric Polynomials
  7. Existence of Solutions for Fourth Order Nonlocal Boundary Value Problems
  8. New Proof of the 𝑇(1) Theorem for Triebel–Lizorkin Spaces
  9. Inversion of Ahlfors and Grunsky Inequalities
  10. On Non-Compact Operators in Weighted Ideal and Symmetric Function Spaces
  11. Computing Characteristic Sets of Ordinary Radical Differential Ideals
  12. Approximating Common Fixed Points of Nonexpansive Mappings in Banach Spaces
  13. On Systems of Linear Functional Differential Inequalities
  14. The Dirichlet Problem for a Second Order Elliptic Equation Degenerating on the Whole Boundary When the Boundary Condition Is Satisfied in the Presence of Some Weight
  15. Fourier Series with Small Gaps
  16. Oscillations of Higher Order Functional Differential Equations with Impulses
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