Efficient Rational Creative Telescoping

09/15/2019
by   Mark Giesbrecht, et al.
0

We present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. As with recent reduction-based approach, our algorithm has the nice feature that the computation of a telescoper is independent of its certificate. Moreover, our algorithm uses a sparse representation of the certificate, which allows it to be easily manipulated and analyzed without knowing the precise expanded form. This representation hides potential expression swell until the final (and optional) expansion, which can be accomplished in time polynomial in the size of the expanded certificate. A complexity analysis, along with a Maple implementation, suggests that our algorithm has better theoretical and practical performance than the reduction-based approach in the rational case.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/25/2019

Constructing minimal telescopers for rational functions in three discrete variables

We present a new algorithm for constructing minimal telescopers for rati...
research
08/07/2018

Minimal solutions of the rational interpolation problem

We compute minimal solutions of the rational interpolation problem in te...
research
01/12/2016

Existence Problem of Telescopers: Beyond the Bivariate Case

In this paper, we solve the existence problem of telescopers for rationa...
research
07/20/2017

FORM version 4.2

We introduce FORM 4.2, a new minor release of the symbolic manipulation ...
research
10/15/2015

Algebraic Diagonals and Walks: Algorithms, Bounds, Complexity

The diagonal of a multivariate power series F is the univariate power se...
research
03/18/2023

Computing a compact local Smith McMillan form

We define a compact local Smith-McMillan form of a rational matrix R(λ) ...
research
05/17/2016

Efficient Algorithms for Mixed Creative Telescoping

Creative telescoping is a powerful computer algebra paradigm -initiated ...

Please sign up or login with your details

Forgot password? Click here to reset