A characteristic set method for ordinary difference polynomial systems

DOI10.1016/j.jsc.2007.05.005zbMath1164.39008OpenAlexW1974479962MaRDI QIDQ1006653

Yong Luo, Xiao-Shan Gao, Chun-Ming Yuan

Publication date: 25 March 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2007.05.005

zbMATH Keywords

difference polynomialcharacteristic set methoddifference ascending chainzero decomposition

Mathematics Subject Classification ID

Discrete version of topics in analysis (39A12) Numerical algorithms for specific classes of architectures (65Y10)

Related Items

Algorithms yield upper bounds in differential algebra, A triangular decomposition algorithm for differential polynomial systems with elementary computation complexity, Toric difference variety, Characteristic set algorithms for equation solving in finite fields, Thomas Decomposition and Nonlinear Control Systems, Binomial difference ideals, Sparse difference resultant, A criterion for testing whether a difference ideal is prime, Ritt-Wu characteristic set method for Laurent partial differential polynomial systems, Elimination theory in differential and difference algebra, SOLVING DIFFERENCE EQUATIONS IN SEQUENCES: UNIVERSALITY AND UNDECIDABILITY, Difference Chow form, New bounds and an efficient algorithm for sparse difference resultants, Characteristic set method for differential-difference polynomial systems, Dimension polynomials and the Einstein's strength of some systems of quasi-linear algebraic difference equations, Effective difference elimination and nullstellensatz

Uses Software

• GeneratingFunctions

Cites Work

• A holonomic systems approach to special functions identities
• A new method for solving algebraic systems of positive dimension
• A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
• Non-commutative elimination in Ore algebras proves multivariate identities
• Automated reasoning in differential geometry and mechanics using the characteristic set method. I: An improved version of Ritt-Wu's decomposition algorithm
• Factorization-free decomposition algorithms in differential algebra
• On the theories of triangular sets
• Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution
• Sharp estimates for triangular sets
• Systems of Algebraic Difference Equations
• Specializations in Differential Algebra
• Manifolds of Difference Polynomials
• Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
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