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This book constitutes the proceedings of the 5th International Meeting on Algebraic and Algorithmic Aspects of Differential and Integral Operators, AADIOS 2012, held at the Applications of Computer Algebra Conference in Sofia, Bulgaria, on June 25-28, 2012. The total of 9 papers presented in this volume consists of 2 invited papers and 7 regular papers which were carefully reviewed and selected from 13 submissions. The topics of interest are: symbolic computation for operator algebras, factorization of differential/integral operators, linear boundary problems and green's operators, initial value problems for differential equations, symbolic integration and differential galois theory, symbolic operator calculi, algorithmic D-module theory, rota-baxter algebra, differential algebra, as well as discrete analogs and software aspects of the above.

Computer science. --- Computer software. --- Logic design. --- Computational complexity. --- Algebra --- Differential equations, partial. --- Computer Science. --- Logics and Meanings of Programs. --- Mathematical Logic and Formal Languages. --- Discrete Mathematics in Computer Science. --- Algorithm Analysis and Problem Complexity. --- Symbolic and Algebraic Manipulation. --- Partial Differential Equations. --- Differential equations --- Engineering & Applied Sciences --- Computer Science --- Data processing. --- Data processing --- Complexity, Computational --- Design, Logic --- Design of logic systems --- Software, Computer --- Partial differential equations --- Informatics --- 517.91 Differential equations --- Algorithms. --- Computer logic. --- Mathematical logic. --- Computer science --- Partial differential equations. --- Mathematics. --- Computer systems --- Electronic data processing --- Machine theory --- Science --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Computer science—Mathematics. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer science logic --- Logic, Symbolic and mathematical --- Algorism --- Arithmetic --- Foundations --- Machine theory. --- Discrete mathematics. --- Differential equations. --- Computer Science Logic and Foundations of Programming. --- Formal Languages and Automata Theory. --- Differential Equations. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Recursive functions --- Robotics

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This volume contains survey articles and original research papers, presenting the state of the art on applying the symbolic approach of Gröbner bases and related methods to differential and difference equations. The contributions are based on talks delivered at the Special Semester on Gröbner Bases and Related Methods hosted by the Johann Radon Institute of Computational and Applied Mathematics, Linz, Austria, in May 2006.

Gröbner bases --- Differential equations --- 517.91 Differential equations --- Gröbner basis theory --- Commutative algebra --- Kongress. --- Linz <2006> --- Algebras. --- base. --- ideal. --- polynomial. --- sybolic computation.

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Mathematical logic --- Molecular biology --- Computer science --- Programming --- Computer architecture. Operating systems --- Computer. Automation --- algebra --- informatica --- programmeren (informatica) --- wiskunde --- software engineering --- logica --- moleculaire biologie