The concept behind Symbolic Tools is to augment the numeric and graphical capabilities of the GAUSS Mathematical & Statistical System (TM)
and GAUSS Engine (TM)
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 access to the full functionality of Maple, including all the mathematical functions and matrix forms, from within GAUSS, thus effectively extending the GAUSS language.
- Precision. Numerical evaluation of functions can occur at any specified level of accuracy.
The computational work is carried out by the Maple kernel using the Open Maple API. Maple is a symbolic mathematics package developed at the University of Waterloo. Symbolic Tools provides for an interface between GAUSS
and the Maple Kernel. This interface permits code to be evaluated symbolically in Maple, and the results returned to GAUSS,
or to create a GAUSS
proc based on Maple's symbolic results.
One of the main uses of Symbolic Tools is to enable GAUSS
to undertake Automatic Differentiation. Optimization packages, such as Aptech's Maximum Likelihood, Constrained Maximum Likelihood, Optimization, and Nonlinear Equations GAUSS Applications, can use procedures that return the gradient and/or Hessian, instead of doing forward differencing. Thus, as a trivial example, if the function being optimized were Ln(b), then the analytic gradient would be 1/b, and the analytic Hessian -1/b. Symbolic Tools can create compiled procs for the analytic gradient or Hessian of a likelihood, on the fly. The time savings are impressive. Using Monte Carlo simulation of a Tobit model with 2000 observations and 11 parameters, the AD gradient took 10% of the time required for forward differences using gradp - ie. approximately a 10 fold speed improvement. Similar results were also obtained for the Hessian, with the additional advantage that the AD methodology generated much more precise estimates of the gradients and Hessian.
- Language extension
- Analytical differentiation
- Analytical integration
- Automatic differentiation
- Symbolic arithmetic
- Variable precision
Symbolic Tools manual
is in a PDF format. Includes table of contents, examples, reference, and index. (470 kb)
symbolic.chm A compiled HTML help file provides the Symbolic Tools command reference.
GAUSS Mathematical & Statistical System v4.0+ for Windows or GAUSS Engine v4.0+ for Windows
Maple 9 or higher
447 Grosvenor Ave.
Westmount, PQ H3Y-2S5 Canada
Download Trial Version
This is a fully functional version of Symbolic Tools, and includes on-line help, as well as the manual in pdf format. The trial version is for evaluation purposes only, and your license to use it will expire after 30 days. The current version of Symbolic Tools is 2.0.
Download Symbolic Tools (1.1 Mb)
You can also download an evaluation version of Maple
Download Maple 9
Price and Ordering Information
If you already own Maple 9
Symbolic Tools is distributed by Aptech Systems, Inc. Please contact Aptech Systems for current prices.
Aptech Systems, Inc.
2350 East Germann Road, Suite 21
Chandler, AZ 85286
If you do not already own Maple 9
A Symbolic Tools/Maple 9 package is distributed by Waterloo Maplesoft, Inc. Please contact WMI for current prices.
57 Erb Street W.
N2L 6C2, Canada
Phone: (519) 747-2373
Toll Free: 1-800-267-6583
Fax: (519) 747-5284
- The current version of Symbolic Tools is 2.0
is a registered trademark of Econotron Software, Inc.
and GAUSS Engine
are trademarks of Aptech Systems, Inc.
Copyright 1983-2011. All Rights Reserved Worldwide.
is a registered trademark of Waterloo Maple, Inc.