Multipoint polynomial evaluation and interpolation are fundamental for modern numerical and symbolic computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to quadratic for numerical solution. We decrease this cost dramatically and for a large class of inputs yield nearly linear time as well. We first restate our task...

Cloud services have been widely employed in IT industry and scientific research. By using Cloud services users can move computing tasks and data away from local computers to remote datacenters. By accessing Internet-based services over lightweight and mobile devices, users deploy diversified Cloud applications on powerful machines. The key drivers towards this paradigm for the scientific comput...

By using several tools coming from Real Algebraic Geometry, Computer Algebra and Projective Geometry (Sturm–Habicht sequences and the classification of pencils of conics in P2(R)), a new approach for characterizing the ten relative positions of two ellipses is introduced. Each relative position is exclusively characterized by a set of equalities and inequalities depending only on the matrices d...

A set of Maple V R.3/4 computer algebra routines for the analytical solving of 1 order ODEs, using Lie group symmetry methods, is presented. The set of commands includes a 1 order ODEsolver and routines for, among other things: the explicit determination of the coefficients of the infinitesimal symmetry generator; the construction of the most general invariant 1 order ODE under given symmetries...

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There exist many applications where both symbolic and floating-point computations are required at the same time. Image recognition, for example, requires huge amounts of numeric calculation to extract features from raw image data before the actual recognition is performed according to those features. Systems for symbolic computation should perform type-checking on numeric calculations. Although...

This paper is a review based on recent published articles by the author (Vulcanov, 2001; 2003; 2004; 2008), and is dedicated to the use of algebraic computing in general relativity (GR) and cosmology.

An alternative example of the method of multiple scales is presented. This example arises in the study of the classical heat equation with a slowly varying flux imposed at one end. The module presents introductory ideas about dimensionless variables, multiple-scale expansions, and scaling of the dependent variable. The necessarily obfuscating algebraic computation is less than that for more fam...