## Applications of Computer AlgebraToday, certain computer software systems exist which surpass the computational ability of researchers when their mathematical techniques are applied to many areas of science and engineering. These computer systems can perform a large portion of the calculations seen in mathematical analysis. Despite this massive power, thousands of people use these systems as a routine resource for everyday calculations. These software programs are commonly called "Computer Algebra" systems. They have names such as MACSYMA, MAPLE, muMATH, REDUCE and SMP. They are receiving credit as a computational aid with in creasing regularity in articles in the scientific and engineering literature. When most people think about computers and scientific research these days, they imagine a machine grinding away, processing numbers arithmetically. It is not generally realized that, for a number of years, computers have been performing non-numeric computations. This means, for example, that one inputs an equa tion and obtains a closed form analytic answer. It is these Computer Algebra systems, their capabilities, and applications which are the subject of the papers in this volume. |

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### Contents

MODERN SYMBOLIC MATHEMATICAL | 62 |

USING VAXIMA TO WRITE FORTRAN CODE | 77 |

Stanly Steinberg and Patrick Roache | 95 |

Copyright | |

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### Common terms and phrases

algorithm analysis applications approximation calculation center manifold chemistry CHR2 CHR2 coefficients complex Computer Algebra systems coordinate defined derivatives described DIFF differential equations dimensional dynamical eigenvalues engine evaluation example expanded expression factors Figure finite difference finite elements foreground kernels formulas FORTRAN FORTRAN code function given integral intermediate inverse involves irreducible irreducible representations Kernel Value linear LISP LTAB MACSYMA MACSYMA program matrix method nonlinear numerical obtain operations optimal parameters partial differential equations perform permutation Phys physical polynomial problem quantum rational simplification reduction procedure representation result rotation Semidirect Products simplify solution solve SQRT stabllity steady state polnt subroutine substitute symbol manipulation programs symbolic computation symbolic manipulation symbolic mathematical symmetry Taylor series techniques tensor theoretical theory THRU transformation Value F variables VAXIMA vector zero zout ia