Despite the fact that the importance of Sylvester's determinant identity has been recognized in the past, we were able to find only one proof of it in English (Bareiss, 1968), with reference to some others. (Recall that Sylvester (1857) stated this theorem without proof.) Having used this...

A suite of computer algebra programs for tensor and spinor calculations in torsion theories of gravitation is presented. Modules for the algebraic classification of curvature tensors in Riemann-Cartan space-times are discussed. The basic theoretical results and an algorithm for the equivalence...

The use of n-tuple or weightless neural networks as pattern recognition devices is well known (Aleksander and Stonham, 1979). They have some significant advantages over the more common and biologically plausible networks, such as multi-layer perceptrons; for example, n-tuple networks have been...

Elsewhere we have reported our simulations of general hovering aerodynamics as practiced, for example, by hummingbirds and dragonflies. These studies explain rather satisfactorily from the point of view of partial differential equations (Navier-Stokes) how such high lift is generated in such...

In the neighbourhood of irregular singularities the formal power series solutions of complex analytic ordinary differential equations are generally divergent. The resummation theory developed by J. Ecalle and J.P. Ramis enables us to sum these series by multisummation effective algorithms. In...

Seidenberg's elimination algorithm computes a projection of the algebraic differential manifold associated with a system of differential polynomials (here with coefficients in an ordinary differential field of characteristic zero).

A symbolical computation approach to the preprocessing of distributed parameter systems for preparing a numerical solution by a method of lines technique is investigated. A first prototype of a toolbox for the semi-discretization of partial differential equation systems on simple spatial domains...

This paper is devoted to some last algorithmic progress in classical elimination theory from the complexity point of view. These results will be presented as a short survey (without proofs) treating essentially upper and lower bounds problems. The first aim of this paper is to show that the...

An involution approach to solving systems of polynomial equations is proposed. A notion of involutive polynomial system is introduced and an algorithm for its construction is presented. The relation between involutive systems and Gröbner bases is clarified, and some advantages of the involution...

The Faà di Bruno formula enables us to compute the derivatives of a function of several variables. We show here, in spite of the noncommutativity of causal computations, that the Faà di Bruno grammar makes it possible to compute the derivatives of any causal functional. Using this property and...