Applications of Computer Algebra
Applications of computer algebra range over the entire spectrum of research, development, production, and education. Computer algebra problems arise in industry, commerce, software engineering, and also in banking and insurance applications, although some
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Applications of Computer Algebra
Applications of computer algebra range over the entire spectrum of research, development, production, and education. Computer algebra problems arise in industry, commerce, software engineering, and also in banking and insurance applications, although sometimes hidden. We compiled several interesting applications which are exemplary for the most important areas. Classical areas of computer algebra applications are physics - see page 163 - and mathematics - see page 195. However, more and more methods and systems of computer algebra are also utilized in computer science, - see page 217 - in engineering, - see page 221 - and in other natural sciences - see page 242. A very important application area of computer algebra is education. More and more computer algebras are used for teaching - both in schools and universities - see page 244. 3.1
Physics
Physics is one of the classical and traditional areas of computer algebra application, most likely being the reason why physicists - given the need to deal with mathematical formulas and relations of highest complexity - always participated at the forefront in the practical development of computer algebra. Nowadays computer algebra is used in essentially all areas of physics. Therefore below we didn't try to cover the whole of physics, rather we picked some typical applications in physics in order to give the reader an idea of how to select the suitable computer algebra system which may solve his or her own problem in physics. Moreover, the merits and the limitation of computer algebra systems may also come into focus . • Elementary Particle Physics in 3.1.1.1: In this field, computer algebra tools are indispensable for generation, evaluation, and summing up of Feynman integrals. J. Fleischer gives a general overview, whereas M. Steinhauser concentrates on the strong interaction, i.e., on quantum chromodynamics (QCD), and G. Weiglein on the electroweak interaction. J. Vermaseren sketches the use of his Mincer Form-package for the evaluation of certain loop diagrams. - Fleischer - Steinhauser - Weiglein - Vermaseren • Gravity: In gravity and general relativity, computer algebra was used right from its beginnings. C. Heinicke and F.W. Hehl survey computer algebra applications in the whole field, whereas I. Kotsireas turns his attention to one important problem: The N-body problem of Newtonian mechanics with gravitational interaction. - Heinicke & Hehl J. Grabmeier et al (eds.), Computer Algebra Handbook © Springer-Verlag Berlin Heidelberg 2003
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Chapter 3 Applications of Computer Algebra
- Kotsireas • computer algebra-Systems for Differential Geometry and Applications: Differential geometry plays a fundamental role in physics such as in mechanics, in field and relativity theory, and, in particular, in gauge field theory, in string theory etc.. Therefore in this section computer algebra systems are discussed which support differential geometric applications in physics (and also in mathematics, of course). E. Schriifer describes how Exca
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