3 research outputs found
Bounds for D-finite closure properties
We provide bounds on the size of operators obtained by algorithms for
executing D-finite closure properties. For operators of small order, we give
bounds on the degree and on the height (bit-size). For higher order operators,
we give degree bounds that are parameterized with respect to the order and
reflect the phenomenon that higher order operators may have lower degrees
(order-degree curves)
Efficient Algorithms for Mixed Creative Telescoping
Creative telescoping is a powerful computer algebra paradigm -initiated by
Doron Zeilberger in the 90's- for dealing with definite integrals and sums with
parameters. We address the mixed continuous-discrete case, and focus on the
integration of bivariate hypergeometric-hyperexponential terms. We design a new
creative telescoping algorithm operating on this class of inputs, based on a
Hermite-like reduction procedure. The new algorithm has two nice features: it
is efficient and it delivers, for a suitable representation of the input, a
minimal-order telescoper. Its analysis reveals tight bounds on the sizes of the
telescoper it produces.Comment: To be published in the proceedings of ISSAC'1