In this paper, we present a truncated version of the classical Fast Fourier Transform. When applied to polynomial multiplication, this algorithm has the nice property of eliminating the "jumps" inâ€¦ (More)

A holonomic finction is an analytic function, which satisfies a linear differential equation with polynomial coefficients. In particular, the elementary functions exp, log, sin, etc. and many specialâ€¦ (More)

There is a common belief that wysiwyg technical editors are not suited for editing structured texts and generating documents with a high typographical quality. In this paper, we analyze the reasonsâ€¦ (More)

Current implementations of p-adic numbers usually rely on so called zealous algorithms, which compute with truncated p-adic expansions at a precision that can be specified by the user. In combinationâ€¦ (More)

Let C[[z]] be the ring of power series over an effective ring C. In Brent and Kung (1978), it was first shown that differential equations over C[[z]] may be solved in an asymptotically efficient wayâ€¦ (More)

Let LâˆˆK(z)[âˆ‚] be a linear differential operator, where K is an effective algebraically closed subfield of C. It can be shown that the differential Galois group of L is generated (as a closedâ€¦ (More)

In this paper, we present a new zero-test for expressions which are constructed from formal power solutions to algebraic differential equations using the ring operations and differentiation. We alsoâ€¦ (More)

In this paper, we present a truncated version of the classical Fast Fourier Transform. When applied to polynomial multiplication, this algorithm has the nice property of eliminating the jumpss in theâ€¦ (More)