Related papers: Computer Algebra for Microhydrodynamics
We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.
This paper develops techniques for producing presentations of upper cluster algebras. These techniques are suited to computer implementation, and will always succeed when the upper cluster algebra is totally coprime and finitely generated.…
Thermodynamic computing has emerged as a promising paradigm for accelerating computation by harnessing the thermalization properties of physical systems. This work introduces a novel approach to solving quadratic programming problems using…
We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
In this paper, by way of three examples - a fourth order low pass active RC filter, a rudimentary BJT amplifier, and an LC ladder - we show, how the algebraic capabilities of modern computer algebra systems can, or in the last example,…
We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting…
We extend a machine learning (ML) framework presented previously to model galaxy formation and evolution in a hierarchical universe using N-body + hydrodynamical simulations. In this work, we show that ML is a promising technique to study…
This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave)…
Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of…
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical…
Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the…
Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considered. Processes of this kind can be described using an…
This paper describes a numerical scheme for multi-fluid hydrodynamics in the limit of small mass densities of the charged particles. The inertia of the charged particles can then be neglected, which makes it possible to write an evolution…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere. It is known to have doubly exponential complexity in the number of…
The chemistry of an astrophysical environment is closely coupled to its dynamics, the latter often found to be complex. Hence, to properly model these environments a 3D context is necessary. However, solving chemical kinetics within a 3D…
In this paper we introduce Redberry --- an open source computer algebra system with native support of tensorial expressions. It provides basic computer algebra tools (algebraic manipulations, substitutions, basic simplifications etc.) which…
In perturbative calculations, e.g., in the setting of Quantum Chromodynamics (QCD) one aims at the evaluation of Feynman integrals. Here one is often faced with the problem to simplify multiple nested integrals or sums to expressions in…