A holonomic systems approach to special functions identities
Journal of Computational and Applied Mathematics
Non-commmutative elimination in ore algebras proves multivariate identities
Journal of Symbolic Computation
Groebner Bases for Non-Commutative Polynomial Rings
AAECC-3 Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes
Buchberger's Algorithm: A Constraint-Based Completion Procedure
CCL '94 Proceedings of the First International Conference on Constraints in Computational Logics
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 skew polynomial approach to integro-differential operators
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
A Symbolic Framework for Operations on Linear Boundary Problems
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
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
The Theorema environment for interactive proof development
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Transforming problems from analysis to algebra: A case study in linear boundary problems
Journal of Symbolic Computation
Mathematical and Computer Modelling: An International Journal
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 present a new method for solving regular boundary value problems for linear ordinary differential equations with constant coefficients (the case of variable coefficients can be adopted readily but is not treated here). Our approach works directly on the level of operators and does not transform the problem to a functional setting for determining the Green's function. We proceed by representing operators as noncommutative polynomials, using as indeterminates basic operators like differentiation, integration, and boundary evaluation. The crucial step for solving the boundary value problem is to understand the desired Green's operator as an oblique Moore-Penrose inverse. The resulting equations are then solved for that operator by using a suitable noncommutative Grobner basis that reflects the essential interactions between basic operators. We have implemented our method as a Mathematica(TM) package, embedded in the TH@?OREM@? system developed in the group of Prof. Bruno Buchberger. We show some computations performed by this package.