Eliminating monotonous mathematics with FORMAC

Abstract

The FORMAC (FORmula MAnipulation Compiler) programming system provides a powerful tool for performing mathematical analysis. It is an extension of FORTRAN IV which permits the use of the computer to perform the tedious algebraic computations that arise in many different fields. Among the areas in which it has been successfully used are: differentiation of complicated expressions, expansion of truncated power series, solution of simultaneous equations with literal coefficients, nonlinear maximum likelihood estimation, tensor analysis, and generation of the coefficients of equations in Keplerian motion. These types of analysis-which arose in the solution of specific practical problems in physics, engineering, astronomy, statistics and astronautics-are discussed in the paper.In addition to its usage for specific problem solutions, FORMAC can also be used to automate the analysis phase in certain production programming. Several such applications are presented.

On Monte Carlo algebra

“…The use of non-numerical or algebraic computations on computers for scientific purposes is just beginning (Brown (1963); Brown, Hyde and Tague (1964); Campbell(1966); Howard (1967); Howard and Tashjian (1968); Hyde (1964); Lapidus and Goldstein (1965); Rhoads and Pring (1968); Sammet (1969); Slagle (1963); Tobey (1966)). The approach of Monte Carlo algebra offers the advantage of eliminating the sometimes enormous intermediate results of such calculations (Brown (1963); Brown, Hyde and Tague (1964); Hyde (1964); Tobey (1966)) which "can exceed the memory of the largest computers and thus block solution, and gives algebraic solutions to otherwise "transcomputational" problems (Bremermann (1966); Ashby (1968».…”