Related papers: Computer Algebra in Particle Physics
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
This paper offers what seems at first to be a minor technical correction to the current practice of computing indefinite integrals, and introduces the idea of a "Kahanian constant of integration". However, the total impact of this minor…
In recent years, computing has become an important part of the way we teach and learn physics. Teachers, both at high school and college levels, now use computational activities in many of their courses. Physics departments are offering…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing…
Linear programming is now included in algorithm undergraduate and postgraduate courses for computer science majors. We give a self-contained treatment of an interior-point method which is particularly tailored to the typical mathematical…
Numerical simulations have become an important tool to understand and predict non-perturbative phenomena in particle physics. In this article we attempt to present a general overview over the field. First, the basic concepts of lattice…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
This is a short introduction to quantum computers, quantum algorithms and quantum error correcting codes. Familiarity with the principles of quantum theory is assumed. Emphasis is put on a concise presentation of the principles avoiding…
Future quantum computers are anticipated to be able to perform simulations of quantum many-body systems and quantum field theories that lie beyond the capabilities of classical computation. This will lead to new insights and predictions for…
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 present here algorithms for efficient computation of linear algebra problems over finite fields.
In this contribution we discuss how to develop a physics curriculum for undergraduate students that includes computing as a central element. Our contribution starts with a definition of computing and pertinent learning outcomes and…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
Clifford algebras are important structures in Geometric Algebra and Quantum Mechanics. They have allowed a formalization of the primitive operators in Quantum Theory. The algebras are built over vector spaces with dimension a power of 2…
Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is required to create a user extension for an existing computer…
This is a short introduction to Quantum Computing intended for physicists. The basic idea of a quantum computer is introduced. Then we concentrate on Shor's integer factoring algorithm.
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…
Lecture notes to a one-term course on operator algebras and their application in physics. Very brief and basic introduction to the subject of Banach- and C-star algebras complemented with their appearance in physics. The course is intended…
We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded…