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Differential Equations from the Algebraic Standpoint

https://doi.org/10.1090/coll/014
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Baxter Algebras and Shuffle Products
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An Elimination Method for Polynomial Systems
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A Symbolic-Numerical Method for Finding a Real Solution of an Arbitrary System of Nonlinear Algebraic Equations
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Foreword of the Guest Editors
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A Systematic Framework for Solving Geometric Constraints Analytically
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A Symbolic Approach to Modeling Cellular Behavior
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Notes on Triangular Sets and Triangulation-Decomposition Algorithms I: Polynomial Systems
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Notes on Triangular Sets and Triangulation-Decomposition Algorithms II: Differential Systems
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Standard bases of differential ideals
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Differential resultants and subresultants
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Some constructions in rings of differential polynomials
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On the parallelization of characteristic-set-based algorithms
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A strategy for speeding-up the computation of characteristic sets
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Polynomial equations-solving and its applications
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A resultant theory for ordinary algebraic differential equations
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On “Good” Bases of Algebraico-Differential Ideals
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On the Construction of Groebner Basis of a Polynomial Ideal Based on Riquier—Janet Theory
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An Elimination Method Based on Seidenberg’s Theory and Its Applications
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Geometry Theorem Proving in Euclidean, Descartesian, Hilbertian and Computerwise Fashion
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Chordality Preserving Incremental Triangular Decomposition and Its Implementation
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Overview
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On the Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry
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Analyses and Implementations of Chordality-Preserving Top-Down Algorithms for Triangular Decomposition
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Advances in Elimination Theory for Algebraic Differential and Difference Equations
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Computing the Limit Points of the Quasi-component of a Regular Chain in Dimension One
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Simple Differential Field Extensions and Effective Bounds
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Differential Algebra in Control Theory
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The Differential Dimension Polynomial for Characterizable Differential Ideals
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On the Computation of Differential Resultants
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Constructions of Free Commutative Integro-Differential Algebras
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Differential (Monoid) Algebra and More
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Primary Decomposition: Algorithms and Comparisons
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Presentations and Representations of Groups
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Matrix Formulae of Differential Resultant for First Order Generic Ordinary Differential Polynomials
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An Implementation of the Characteristic Set Method in Maple
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Epilogue: Singularities of Differential Equations
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Espaces Vectoriels Differentiels
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Introduction
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A Resultant Theory for the Systems of Two Ordinary Algebraic Differential Equations
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Corners Always Scatter
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Sparse Differential Resultant for Laurent Differential Polynomials
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Extensions of Operators, Liftings of Monads, and Distributive Laws
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Bounded motion design in the Earth zonal problem using differential algebra based normal form methods
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Automated Reducible Geometric Theorem Proving and Discovery by Gröbner Basis Method
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Integral Operators on Lattices
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Elimination Theory in Differential and Difference Algebra
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Equality-constrained minimization of polynomial functions
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On the Connection Between Ritt Characteristic Sets and Buchberger–Gröbner Bases
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Generalized solutions of algebraic differential equations
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Multiplicity of the solutions of a differential polynomial
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BIBLIOGRAPHY
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New Operated Polynomial Identities and Gröbner-Shirshov Bases
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Sparse Differential Resultant for Laurent Differential Polynomials
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Groebner bases and gradings for partial difference ideals
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Matrix Formula of Differential Resultant for First Order Generic Ordinary Differential Polynomials
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Constructions of free commutative integro-differential algebras
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Free differential Lie Rota-Baxter algebras and Gröbner-Shirshov bases
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Cohomologies, extensions and deformations of differential algebras with any weights
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Fast finite field arithmetic
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