Abstract
Computer Algebra systems could be considered as software systems/packages that support interactive (and batch) processing of symbolic /mathematical nature, i.e. computerized “Buchstabenrechnung” {Cal.Com.Fit 1–2,Loo,Pav, Mac.Red.} That is, algebraic calculations (and numeric) with the speed and accuracy of a computer. In fact a fair part of it could be considered as “modern software technology”.
We give a broad overview of this “new” mathematical software, that so far has not found so many applications in chemistry. This even though the first application in chemistry goes back to 1956! [Boy]*.
We sketch the background and describe applications in physics — the main field for applications of computer algebra.
Some of the applications in chemistry are surveyed, and we try to describe how the field of computer algebra is related to the superfield of symbol/symbolic manipulation/computation — a more structural kind of computation. Some potential applications/application areas in chemistry are indicated.
We give an example of a session in the computer algebra language REDUCE and describe the essentials of such a system, we describe a fundamental difficulty with algebraic computing and finally we sketch some future trends.
In the bibliography {Was} there is a lot of material for those who want to investigate these matters more in detail. This could pay off since with the new situation old mathematical tools, previously considered as unpractical because of the extensive and complicated algebraic manipulations involved, can now develop to very practical methods. There are discoveries to be made!
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Armbruster, D. and Rand, R. H.: Perturbation Methods, Bifurcation Theory and Computer Algebra (Applied Mathematical Sciences, Vol. 65), Springer-Verlag, Berlin, 1987. [This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods]
Artificial Intelligence Applications in Chemistry, Pierce, Thomas H. and Hohne, Bruce A., eds., American Chemical Society, ACS Symp. Ser., Vol. 306, Washington, 1986.
Balaban, A. T.: Symbolic computation and chemistry, from [Eur 4] A survey of symbolic computation in chemistry is presented, emphasizing the impact on chemical information systems (storage and retrieval of chemical constitutional graphs), the enumeration and structural representation of chemical isomers.
Boys, S. F., Cook, G. B., Reeves, C. M. and Shavitt, I.: Automatic Fundamental Calculations of Molecular Structure. Nature, Dec. 1, 1956
Calmet, J. and van Hulzen, J. A.: Computer Algebra Systems, and Computer Algebra Applications at pages 221 respectively 245 in [Com].
Computer Algebra-Symbolic and Algebraic Computation, Buchberger, B., Collins, G. E. and Loos, R. eds. in cooperation with Albrecht, R., 2nd edition, Springer-Verlag, Wien, 1982 and 1983.
EUROCAL ‘85. European Conference on Computer Algebra, Linz, Austria, 1–3 April 1985, ed. Buchberger, B, 2 volumes. Published: Springer-Verlag, Berlin, Germany, 1985. The following topics were dealt with: computer algebra, MACSY-MA, current developments in LISP, symbolic computation and chemistry, computational geometry, digital signal processing, coding, cryptography, practical analysis, scientific computation, algorithmic methods in automatic programming, proof theory and synthesis of programs and mechanizing mathematics. Abstracts of individual papers can be found under the relevant classification codes in this or other issues.
Felsch, V.: A Bibliography on the Use of Computers in Group Theory and related Topics: Algorithms, Implementations, and Applications. Kept current and obtainable from Lehrstuhl D für Mathematik, RWTH Aachen, D-5100 Aachen, Federal Republic of Germany.
Fitch, John: Solving Algebraic Problems with REDUCE. J Symb Comput V.1, N. 2 Jun 1985 p 211–227.
Fitch, John: The Application of Symbolic Algebra in Physics-a Case of Creeping Flow, EUROSAM 1979, 30–41.
Johnson, Charles S., JR: Computer Algebra in Chemistry, J. Chem. Inf. Comput. Sci. 1983, 23, 151–157.
Khuen, Albrecht: Use of Symbolic Algebra Program in NMR. Mikrochim. Acta (Wien) 1986 II, 303–312
Loos, R.: Introduction, in [Com] 1–10.
MacCallum, Malcolm: Computer algebra — tomorrow’s calculator, New Scientist, October 23, 1986.
Ogilvie, J. F.: Applications of computer algebra in physical chemistry. Comput-Chem (GB), vol.6, no.4, p.169–172, 1982. 21 refs.
Pavelle, Richard, Rothstein, Michael and John Fitch, John: Computer Algebra, Scientific American, December 1981.
REDUCE USER’S MANUAL (3.3), Anthony C. Hearn ed., The Rand Corporation, Santa Monica, CA, 1987.
Wasén, Rolf: Bibliography on Algebraic and Relational Modelling, Algebraic Computing and Computer Algebra in Chemistry and Related Fields of Knowledge, forthcoming Internal Report at Dept. Comp. Science, Linköping University, Sweden (on request to the author).
Wigner, Eugene P.:The unreasonable effectiveness of mathematics in the natural sciences, Comm. Pure Appl. Math. 13 (1960), 1–14.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wasén, R. (1988). Computer Algebra — Software for Symbolic Mathematics — also a Possibility for Chemistry?. In: Gasteiger, J. (eds) Software-Entwicklung in der Chemie 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73283-6_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-73283-6_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18696-0
Online ISBN: 978-3-642-73283-6
eBook Packages: Springer Book Archive