In this paper we present a new strategy for PVS that implements a square root and division elimination in order to use automatic arithmetic strategies that were not able to deal with these operations in a rst place. This strategy relies on a PVS formalization of the square root and division elimination and deep embedding of PVS expressions inside PVS. Therefore using computational re ection and...

One approach for computations with special functions in computer algebra is the systematic use of analytic functions whenever possible. This naturally leads to problems of how to answer questions about analytic functions in a fully eeective way. Such questions comprise the determination of the radius of convergence or the evaluation of the analytic continuation of the function at the endpoint o...

We present a practical application of parallel symbolic computation in General Relativity: the calculation of curvature invariants for large dimension. We discuss the structure of the calculations, an implementation of the technique and scaling of the computation with spacetime dimension for various invariants. Electronic address: [email protected]

Two examples of a particular kind of form-finding problems are studied; given a set of fixed points, we ask for the position of an extra point such that a given framework admits a self-stress and hence a tensegrity structure can be built from it. We present two different approaches to solve these problems: The first method is geometric and hence more visual. A symbolic method is proposed as a s...

A method of computing a basis for the second Yang-Baxter cohomology of a finite biquandle with coefficients in Q and Zp from a matrix presentation of the finite biquandle is described. We also describe a method for computing the Yang-Baxter cocycle invariants of an oriented knot or link represented as a signed Gauss code. We provide a URL for our Maple implementations of these algorithms.

Algorithms are described and Maple implementations are provided for finding all quandles of order n, as well as computing all homomorphisms between two finite quandles or from a finitely presented quandle (e.g., a knot quandle) to a finite quandle, computing the automorphism group of a finite quandle, etc. Several of these programs work for arbitrary binary operation tables and hence algebraic ...

The use of computer algebra software has many applications in diverse fields like epidemiology. This work pretends to show how computer algebra software applications for symbolic computation have a very promissory future in mathematical epidemiology with a concrete problem of this kind. In this case; the basic reproductive rate, corresponding to the propagation of a certain disease inside a cir...

Three different approaches for the determination of conservation laws of differential equations are presented. For three corresponding REDUCE computer algebra programs CONLAW1/2/3 the necessary subroutines are described. One of them simplifies general solutions of overdetermined PDE systems so that all remaining free functions and constants correspond to independent conservation laws. It determ...

Constrictions on a surface are defined as simple closed curves whose length is locally minimal. In particular, constrictions are periodic geodesics. We use constrictions in order to segment objects. In [4], we proposed an approach based on progressive surface simplification and local geodesic computation. The drawback of this approach is that constrictions are approximated by closed piecewise g...

I was invited by Olivier Danvy and Carolyn Talcott to contribute to this special issue of Higher Order and Symbolic Computation in honour of Peter Landin. They were keen to include some technical contributions, and I recalled my very first piece of theoretical work, which had only appeared as a 1981 Queen Mary College technical report, and which seemed as if it might be appropriate for several ...