A holonomic systems approach to special functions identities
Journal of Computational and Applied Mathematics
GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable
ACM Transactions on Mathematical Software (TOMS)
Some complexity results for polynomial ideals
Journal of Complexity
Non-commmutative elimination in ore algebras proves multivariate identities
Journal of Symbolic Computation
Journal of the ACM (JACM)
An extension of Zeilberger's fast algorithm to general holonomic functions
Discrete Mathematics
Concrete Math
Computer proofs for polynomial identities in arbitrary many variables
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Solving difference equations whose coefficients are not transcendental
Theoretical Computer Science
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We introduce the class of nested polynomially recurrent sequences which includes a large number of sequences that are of combinatorial interest. We present an algorithm for deciding zero equivalence of these sequences, thereby providing a new algorithm for proving identities among combinatorial sequences: In order to prove an identity, decide by the algorithm whether the difference of lefthand-side and righthand-side is identically zero. This algorithm is able to treat mathematical objects which are not covered by any other known symbolic method for proving combinatorial identities. Despite its theoretical flavor and high complexity, an implementation of the algorithm can be successfully applied to nontrivial examples.