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Computer Algebra and Symbolic Processing in Modern Telecommunication Applications:A New Kind of Survey

Vlastimir D. Pavlovic
Vladimir Mladenovic
Miroslav D. Lutovac
Organization: University of Belgrade
Department: School of Electrical Engineering
Journal / Anthology

Telecommunications: Applications, Modern Technologies and Economic Impact
Year: 2014
Page range: 29-116

The task of the theory domain is to develop methods to solve practical problems, organizes and makes intelligible field of knowledge on which it is based. In order to solve them, it is needed to be considered as part of a logical structure, and they need to understand the structures which solve it.

The main tools, used in telecommunications for calculating, designing and analyzing, are based on the numerical-only algorithms. So, many computer-based numerical algorithms are developed as consequence of development of hardware and computer techniques in numerical mathematic, adapted to computer calculations, and the main drawback is generating of the tremendous amount of numerical data, and the user might easily lose insight into the phenomenon being investigated, and numerical computation manipulates with numerical values, so, very often it is important to take care about final results: accuracy, execution time of numerical algorithm, efficiency-based reasoning, etc.

Computer algebra system belongs to the comtemporary trends that use very sophisticated algorithms combine expertise in many areas, such as dynamic system design, control engineering, and signal processing, and the user makes a better and more advanced troubleshooting. It is based on well-defined semantics and algebraic algorithms, it is used to simplify rational functions, find the solutions to a system of equations, and give general formulas as answers, model industrial mathematical problems, automated-proven properties and various other manipulations.

Symbolic processing is the special feature of these systems. This is the excitation signals may represent not only numbers, even the symbols, and it is analyzed what happens to them during processing. The parameters of the system can be analyzed subsequently appointing of additional requirements on the desired response, so, on this way the analysis is used in system design. Symbolic processing is concerned with alternative forms, partially-specified domains, and symbolic derivations in general and it can be treated as a transformation of expression trees, such as symbols for operations, variables, constants, and simplification, and plenty expressions, functions and equations can be derived in closed form using symbolic processing, as well as the error-free derived simulation code can be obtained.

*Mathematics > Algebra