The Experts below are selected from a list of 11136 Experts worldwide ranked by ideXlab platform
Kasper Peeters - One of the best experts on this subject based on the ideXlab platform.
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introducing cadabra a symbolic Computer Algebra System for field theory problems arxiv hep th 0701238v3 updated
2018Co-Authors: Kasper PeetersAbstract:Cadabra is a new Computer Algebra System designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification taking care of Bianchi and Schouten identities, for fermions and anti-commuting variables, Clifford Algebras and Fierz transformations, implicit coordinate dependence, multiple index types and many other field theory related concepts. The input format is a subset of TeX and thus easy to learn. Both a command-line and a graphical interface are available. The present paper is an introduction to the program using several concrete problems from gravity, supergravity and quantum field theory.
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cadabra a field theory motivated symbolic Computer Algebra System
Computer Physics Communications, 2007Co-Authors: Kasper PeetersAbstract:Field theory is an area in physics with a deceptively compact notation. Although general purpose Computer Algebra Systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions, this often leads to cumbersome input formats, unexpected side-effects, or the need for a lot of special-purpose code. This makes a direct translation of problems from paper to Computer and back needlessly time-consuming and error-prone. A prototype Computer Algebra System is presented which features TEX-like input, graph data structures, lists with Young-tableaux symmetries and a multiple-inheritance property System. The usefulness of this approach is illustrated with a number of explicit field-theory problems. 1. Field theory versus general-purpose Computer Algebra
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introducing cadabra a symbolic Computer Algebra System for field theory problems
arXiv: High Energy Physics - Theory, 2007Co-Authors: Kasper PeetersAbstract:Cadabra is a new Computer Algebra System designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification taking care of Bianchi and Schouten identities, for fermions and anti-commuting variables, Clifford Algebras and Fierz transformations, implicit coordinate dependence, multiple index types and many other field theory related concepts. The input format is a subset of TeX and thus easy to learn. Both a command-line and a graphical interface are available. The present paper is an introduction to the program using several concrete problems from gravity, supergravity and quantum field theory.
E. D. Kuznetsov - One of the best experts on this subject based on the ideXlab platform.
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The Implementation of Hori–Deprit Method to the Construction Averaged Planetary Motion Theory by Means of Computer Algebra System Piranha
Mathematics in Computer Science, 2019Co-Authors: A. S. Perminov, E. D. KuznetsovAbstract:This article is related to the problem of the construction of planetary motion theory. We have expanded the Hamiltonian of the four-planetary problem into the Poisson series in osculating elements of the second Poincare System. The series expansion is constructed up to the third degree of the small parameter. The averaging procedure of the Hamiltonian is performed by the Hori–Deprit method. It allows to eliminate short-periodic perturbations and sufficiently increase time step of the integration of the equations of motion. This method is based on Lie transformation theory. The equations of motion in averaged elements are constructed as the Poisson brackets of the averaged Hamiltonian and corresponding orbital element. The transformation between averaged and osculating elements is given by the change-variable functions, which are obtained in the second approximation of the Hori–Deprit method. We used Computer Algebra System Piranha for the implementation of the Hori–Deprit method. Piranha is an echeloned Poisson series processor authored by F. Biscani. The properties of the obtained series are discussed. The numerical integration of the equations of motion is performed by Everhart method for the Solar System’s giant planets.
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the construction of averaged planetary motion theory by means of Computer Algebra System piranha
arXiv: Instrumentation and Methods for Astrophysics, 2018Co-Authors: A. S. Perminov, E. D. KuznetsovAbstract:The application of Computer Algebra System Piranha to the investigation of the planetary problem is described in this work. Piranha is an echeloned Poisson series processor authored by F. Biscani from Max Planck Institute for Astronomy in Heidelberg. Using Piranha the averaged semi-analytical motion theory of four-planetary System is constructed up to the second degree of planetary masses. In this work we use the algorithm of the Hamiltonian expansion into the Poisson series in only orbital elements without other variables. The motion equations are obtained analytically in time-averaged elements by Hori-Deprit method. Piranha showed high-performance of analytical manipulations. Different properties of obtained series are discussed. The numerical integration of the motion equations is performed by Everhart method for the Solar System's giant-planets and some exoplanetary Systems.
Hiromi Ishii - One of the best experts on this subject based on the ideXlab platform.
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a purely functional Computer Algebra System embedded in haskell
Computer Algebra in Scientific Computing, 2018Co-Authors: Hiromi IshiiAbstract: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 domain-specific language in Haskell, a purely functional programming language. Utilising methods in functional programming and prominent features of Haskell, this library achieves safety, composability, and correctness at the same time. To demonstrate the advantages of our approach, we have implemented advanced Grobner basis algorithms, such as Faugere’s \(F_4\) and \(F_5\), in a composable way.
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CASC - A Purely Functional Computer Algebra System Embedded in Haskell
Developments in Language Theory, 2018Co-Authors: Hiromi IshiiAbstract: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 domain-specific language in Haskell, a purely functional programming language. Utilising methods in functional programming and prominent features of Haskell, this library achieves safety, composability, and correctness at the same time. To demonstrate the advantages of our approach, we have implemented advanced Grobner basis algorithms, such as Faugere’s \(F_4\) and \(F_5\), in a composable way.
Laurent Thery - One of the best experts on this subject based on the ideXlab platform.
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HUG - Extending the HOL Theorem Prover with a Computer Algebra System to Reason about the Reals
Higher Order Logic Theorem Proving and Its Applications, 1994Co-Authors: John Harrison, Laurent TheryAbstract:In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a Computer Algebra System.
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extending the hol theorem prover with a Computer Algebra System to reason about the reals
HUG '93 Proceedings of the 6th International Workshop on Higher Order Logic Theorem Proving and its Applications, 1993Co-Authors: John Harrison, Laurent TheryAbstract:In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a Computer Algebra System.
S. Tertychniy - One of the best experts on this subject based on the ideXlab platform.
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Specialized Computer Algebra System for application in general relativity
arXiv: General Relativity and Quantum Cosmology, 2007Co-Authors: S. TertychniyAbstract:A brief characteristic of the specialized Computer Algebra System GRG_EC intended for symbolic computations in the field of general relativity is given.
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GRG EC : Computer Algebra System for applications to gravity theory
ACM Sigsam Bulletin, 1997Co-Authors: S. Tertychniy, I. G. ObukhovaAbstract:We present a general outline of the specialized Computer Algebra System GRC EC intended for symbolic calculations in the field of the gravitation theory, the classical field theory on a curved background, and the adjacent methods belonging to the differential geometry. The distinctive features of the GRC EC input language are exhibited and the noteworthy elements of the System design are discussed.
