Algebraic programming: Methods and tools

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

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


2012 ◽  
Vol 56 (1) ◽  
pp. 139-144
Author(s):  
Dumitru N. Vulcanov ◽  
Remus-Ştefan Ş. Boată

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.



1997 ◽  
Vol 08 (02) ◽  
pp. 273-286 ◽  
Author(s):  
Ion I. Cotăescu ◽  
Dumitru N. Vulcanov

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.



Author(s):  
Anatoly E. Doroshenko ◽  
Alexander B. Godlevsky






1994 ◽  
Vol 4 (2) ◽  
pp. 185-238 ◽  
Author(s):  
Dominique Duval ◽  
Jean-Claude Reynaud

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.



1997 ◽  
Vol 08 (02) ◽  
pp. 345-359 ◽  
Author(s):  
Dumitru N. Vulcanov ◽  
Ion I. Cotăescu

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.



2018 ◽  
pp. 109-114
Author(s):  
V.S. Peschanenko ◽  
◽  
M. Poltoratskiy ◽  


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