An introduction to commutative and noncommutative Gro¨bner bases
Selected papers of the second international colloquium on Words, languages and combinatorics
Term rewriting and all that
Non-commmutative elimination in ore algebras proves multivariate identities
Journal of Symbolic Computation
Journal of Symbolic Computation
Integro-differential polynomials and operators
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
ACM Communications in Computer Algebra
A new symbolic method for solving linear two-point boundary value problems on the level of operators
Journal of Symbolic Computation
A Symbolic Framework for Operations on Linear Boundary Problems
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
A maple package for integro-differential operators and boundary problems
ACM Communications in Computer Algebra
Regular and singular boundary problems in maple
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
A computational view on normal forms of matrices of Ore polynomials
ACM Communications in Computer Algebra
Transforming problems from analysis to algebra: A case study in linear boundary problems
Journal of Symbolic Computation
ISSAC 2012 software demonstrations: Symbolic computation for ordinary boundary problems in maple
ACM Communications in Computer Algebra
Annihilating monomials with the integro-differential Weyl algebra
ACM Communications in Computer Algebra
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We construct the algebra of integro-differential operators over an ordinary integro-differential algebra directly in terms of normal forms. In the case of polynomial coefficients, we use skew polynomials for defining the integro-differential Weyl algebra as a natural extension of the classical Weyl algebra in one variable. Its normal forms, algebraic properties and its relation to the localization of differential operators are studied. Fixing the integration constant, we regain the integro-differential operators with polynomial coefficients.