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Programming via rewriting is a part of the declarative programming which is illustrated by the languages: OBJ, Maude, CafeOBJ, CASL and so on. Programming via rewriting is very close to the equational logic. In the equational logic a set Γ of axioms is given. Axioms are Horn clauses, called also conditional equations. We are looking for all universal quantified equalities which are consequences...
We consider the problem of deciding whether two given points in a semialgebraic set can be connected, that is, whether the two points lie in a same connected component. In particular, we consider a semialgebraic set consisting of points where a given polynomial is non-zero. We will describe a method based on gradient fields, eigenvectors and interval analysis.
Mistakes are generally considered a negative phenomenon. There is however a positive face of mistakes, essential in learning, in teaching, in scientific research and in any creative work. We discuss the reason of this fact, we give several such examples and we show how various historical failures in some respect became important successes in another respect. In a second part of this paper, three types...
The mathematical backbone of this article is formed by three classical formulas of Wallis: his product formula for π, an inequality implying the product formula in the limit, and a related definite integral involving powers of the sine function. For the latter we present various evaluations to illustrate recent algorithmic developments. In the main part of the article we automatically refine...
Accurate computer recognition of handwritten mathematics offers to provide a natural interface for mathematical computing, document creation and collaboration. Mathematical handwriting, however, provides a number of challenges beyond what is required for the recognition of handwritten natural languages. For example, it is usual to use symbols from a range of different alphabets and there are many...
We report on a symbolic-numeric algorithm for computing the Alexander polynomial of each singularity of a plane complex algebraic curve defined by a polynomial with coefficients of limited accuracy, i.e. the coefficients are both exact and inexact data. We base the algorithm on combinatorial methods from knot theory which we combine with computational geometry algorithms in order to compute efficient...
We discuss computation of approximate Gröbner bases at finite precision. We show how this can be used to deduce exact results for polynomial greatest common divisors and factorization. In particular we indicate an algorithm for factoring multivariate polynomials over the closure algebraic of the rationals.
This paper presents an overview of the initiative based on non-commercial software, which is being carried out in the University of La Rioja, to develop an e-Science and e-Learning Web-Site with the aim to encourage open science and e-Collaboration. This infrastructure is focused on supplying free access to a variety of symbolic and numeric applications related to Dynamics Systems, in general, and...
Recently, we have proposed a recursive partitioning based layout for multi-core computations on sparse matrices. Based on positive results of our initial experiments with matrix-vector multiplication, we discuss how this storage format can be utilized across a range of BLAS-style matrix operations.
In our earlier work, we have investigated the feasibility of utilization of recursive partitioning in basic (BLAS oriented) sparse matrix computations, on multi-core cache-based computers. Following encouraging experimental results obtained for SpMV and SpSV operations, here we proceed to tune the storage format. To limit the memory bandwidth overhead we introduce usage of shorter (16 bit) indices...
In this paper we propose an x-coordinate point compression method for elliptic curves over Fp, where p >; 3 is prime, as an alternative to the classical y-coordinate point compression method. A point P̃ = (x̃, y) will be compressed as P = (x, y) where x has only two bits and, thus, our method allows more compact representations when [log2 x] >; [log2 y]+1. Both...
In Constraint Programming (CP), the central notion of consistency can be defined as a fix point of some contracting operators. These operators always deal with cartesian products of domains of the same nature (real intervals, integer sets, etc), due to the cartesian nature of the CSP format. However, \textit{inside} the solving process, there is no particular reason why the domains should be cartesian...
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