Algebraic programming: Methods and tools

1993 ◽  
Vol 29 (3) ◽  
pp. 307-312 ◽  
Author(s):  
Yu. V. Kapitonova ◽  
A. A. Letichevskii
Keyword(s):  
Algebraic Programming

Using algebraic programming to teach general relativity

2001 ◽  
Vol 3 (2) ◽  
pp. 65-70 ◽  
Author(s):  
F.A. Ghergu ◽  
D.N. Vulcanov
Keyword(s):  
General Relativity ◽  
Algebraic Programming

scholarly journals Using Algebraic Computing To Teach General Relativity And Cosmology

2012 ◽  
Vol 56 (1) ◽  
pp. 139-144
Author(s):  
Dumitru N. Vulcanov ◽  
Remus-Ştefan Ş. Boată
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Undergraduate Students ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Einstein Equations ◽  
Algebraic Programming ◽  
Algebraic Computing

AbstractThe article presents some new aspects and experience on the use of computer in teaching general relativity and cosmology for undergraduate students (and not only) with some experience in computer manipulation. Some years ago certain results were reported [1] using old fashioned computer algebra platforms but the growing popularity of graphical platforms as Maple and Mathematica forced us to adapt and reconsider our methods and programs. We will describe some simple algebraic programming procedures (in Maple with GrTensorII package) for obtaining and the study of some exact solutions of the Einstein equations in order to convince a dedicated student in general relativity about the utility of a computer algebra system.

New Routines for Algebraic Programming of the Dirac Equation

1997 ◽  
Vol 08 (02) ◽  
pp. 273-286 ◽  
Author(s):  
Ion I. Cotăescu ◽  
Dumitru N. Vulcanov
Keyword(s):  
Dirac Equation ◽  
Main Part ◽  
Space Time ◽  
Curved Space ◽  
Algebraic Programming ◽  
Matrix Algebras ◽  
Dirac Matrix ◽  
New Procedures

We present new procedures in the REDUCE language for algebraic programming of the Dirac equation on curved space-time. The main part of the program is a package of routines defining the Pauli and Dirac matrix algebras. Then the Dirac equation is obtained using the facilities of the EXCALC package. Finally we present some results obtained after running our procedures for the Dirac equation on several curved space-times.

Parallelising programs with algebraic programming tools

1995 ◽  
pp. 685-690
Author(s):  
Anatoly E. Doroshenko ◽  
Alexander B. Godlevsky
Keyword(s):  
Algebraic Programming ◽  
Programming Tools

Algebraic programming of Hamiltonian formalism in general relativity: Application to inhomogeneous space-times

1983 ◽  
Vol 15 (3) ◽  
pp. 209-226 ◽  
Author(s):  
A. Moussiaux ◽  
P. Tombal ◽  
J. Demaret
Keyword(s):  
General Relativity ◽  
Hamiltonian Formalism ◽  
Algebraic Programming

A critique of algebraic programming languages

1969 ◽  
pp. 18-27
Author(s):  
John J. Cannon
Keyword(s):  
Programming Languages ◽  
Algebraic Programming

Sketches and computation – I: basic definitions and static evaluation

1994 ◽  
Vol 4 (2) ◽  
pp. 185-238 ◽  
Author(s):  
Dominique Duval ◽  
Jean-Claude Reynaud
Keyword(s):  
Initial Model ◽  
Algebraic Numbers ◽  
General Process ◽  
Algebraic Programming ◽  
Dynamic Evaluation ◽  
Algebraic Specifications ◽  
Categorical Framework ◽  
The Senses ◽  
Static Evaluation

We define a categorical framework, based on the notion of sketch, for specification and evaluation in the senses of algebraic specifications and algebraic programming. This framework goes far beyond our initial motivation, which was to specify computation with algebraic numbers. We begin by redefining sketches in order to deal explicitly with programs. Expressions and terms are carefully defined and studied, then quasi-projective sketches are introduced. We describe static evaluation in these sketches: we propose a rigorous basis for evalution in the corresponding structures. These structures admit an initial model, but are not necessarily equational. In Part II (Duval and Reynaud 1994), we study a more general process, called dynamic evaluation, for structures that may have no initial model.

Dirac Field, Gravity, Inertial Effects, and Computer Algebra

1997 ◽  
Vol 08 (02) ◽  
pp. 345-359 ◽  
Author(s):  
Dumitru N. Vulcanov ◽  
Ion I. Cotăescu
Keyword(s):  
Gravitational Field ◽  
Dirac Equation ◽  
Reference Frame ◽  
Computer Algebra ◽  
Dirac Field ◽  
Inertial Reference Frame ◽  
Inertial Effects ◽  
Algebraic Programming ◽  
Relativistic Approximation

The article presents some new results obtained for the non-relativistic approximation of the Dirac equation in a non-inertial reference frame — rotated and accelerated — and in Schwarzschild gravitational field. These results are obtained with new routines of algebraic programming in REDUCE + EXCALC language for the Dirac equation in a non-inertial reference frame and after three successive Foldy–Wouthuysen transformations.

scholarly journals Use of methods of algebraic programming for the formal verification of legal acts

2018 ◽  
pp. 109-114
Author(s):  
V.S. Peschanenko ◽  
◽  
M. Poltoratskiy ◽  
Keyword(s):  
Formal Verification ◽  
Algebraic Programming
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