Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from most quantum algorithms currently under discussion in that the output would presumably be obtained by classical superposition of the output of many identical...

This paper evaluates the suitability of Java as an implementation language for the foundations of a computer algebra library. The design of basic arithmetic and multivariate polynomial interfaces and classes have been presented in [1]. The library is type-safe due to its design with Java’s generic type parameters and thread-safe using Java’s concurrent programming facilities. We evaluate some k...

Spiking neural P system with chain structure (SNPC, for short) is a new membrane system, which combines spiking neural P system (SNP, for short) with discrete Morse theory, that is to say, neural membrane cells in spiking neural P system are set on chain by discrete gradient vector path, building a SNP system with chain structure. Membrane computing is a computational model, which simulates the...

Lattice basis reduction is an important problem in the areas of computer algebra and geometry of numbers There are several e cient sequential algorithms for lattice basis reduction e g the well known LLL algorithm and a variant of Schnorr and Euchner which uses fast oating point arithmetic Recently parallel algorithms were developed but they use slow exact integer arithmetic and until now a for...

The ability to control the transport of individual electrons in SET technology introduces a broad range of new possibilities and challenges for implementing computer arithmetic circuits. In this paper, we first briefly discuss the concept of electron counting based arithmetic. Second, we introduce the types of building blocks that are required in order to implement this concept in SET technolog...

We present a simple algorithm for computing the arithmetic weight of an integer with respect to a given radix r ≥ 2. The arithmetic weight of n is the minimum number of nonzero digits in any signed radix-r representation of n. This algorithm leads to a new family of minimal weight signed radix-r representations which can be constructed using a left-to-right on-line algorithm. These representati...

One of the main successes of the computer algebra community in the last 30 years has been the discovery of algorithms, called modular methods, that allow to keep the swell of the intermediate expressions under control. Without these methods, many applications of computer algebra would not be possible and the impact of computer algebra in scientific computing would be severely limited. Amongst t...

This paper is devoted to the software implementation of two mathematical methods which are often used in biological applications: interpolation and curve tting in the presence of uncertainties in the input data given in the form of intervals. The methods involve model functions linear in their parameters and are formulated by means of simple expressions in terms of interval arithmetic allowing ...

Data mining is an interesting focus in computer science field now. This paper deals with data mining techniques based on Grey system theories for time sequence data. Firstly, thoughts of data mining with embedded knowledge are expatiated, and the status quo of Data mining techniques is presented briefly. Then, based on the above thoughts and the Grey system theories, data mining techniques base...

We present a new approach to the robustness problem in computational geometry, called controlled linear perturbation, and demonstrate it on Minkowski sums of polyhedra. The robustness problem is how to implement real RAM algorithms accurately and efficiently using computer arithmetic. Approximate computation in floating point arithmetic is efficient but can assign incorrect signs to geometric p...