Symbolic Tools™ augments the numeric and graphical capabilities of GAUSS™, the matrix programming system used by econometricians and financial analysts, with additional types of mathematical functionality based on symbolic computations. The computational work is carried out by the Maple™ kernel using the OpenMaple™ API. The interface permits code to be evaluated symbolically in Maple and the results returned to GAUSS, or to create a GAUSS procedure based on Maple's symbolic results. The principal application is the creation of analytically evaluated gradients and Hessians for optimization problems, resulting in speed increases in the order of 10 to 20 fold.
The concept behind Symbolic Tools is to augment the numeric and graphical capabilities of GAUSS with additional types of mathematical functionality based on symbolic computations. These include:
- Symbolic Algebra. This includes analytic differentiation and integration, automatic differentiation, as well as simplification.
- Linear Algebra. This capability allows for the exact (as opposed to the numeric) evaluation of matrix forms, including inverses, determinants and eigenvalues.
- Language Extension. This permits the evaluation of a wide range of mathematical functions and matrix forms, effectively extending the GAUSS language.
- Precision. Numerical evaluation of functions can occur at any specified level of accuracy.
