I recently wrote to Henrik Gudat of Bright Software, the author of GATE, requesting more information about his products, and in particular, GSmbolix.  Here's what he had to say:

        "...I am just readying the most complex and useful program Bright Software has ever written.  Its name is GSymbolix and it introduces a completely new genre of software on the Apple IIGS: symbolic math.
        "...this program has GSnumerics already integrated and goes even a giant step further.  Bright Software won't sell this program through a distributor, we will publish it ourselves.  This enables us to sell it at a very fair price (around US$90,-) and to keep in touch with our customers.
        "If you have any suggestions or remarks then please don't hesitate and write me.  It is sometimes extremely difficult for us to know what the end-users will need and what not, and any comments from outside would help us to develop programs that will stand the test."

This program sounds great (he included two screen dumps from it, and it looks great as well.)  A third sheet included in his reply listed the specifications and details about GSymbolix, which I reproduce here verbatim:
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GSymbolix 1.2
Numeric And Symbolic Math - And A Little Bit More.

GSymbolic is the first math program for the Apple IIGS that calculates with pure numbers as well as with complex algebraic expressions.  It combines both worlds in a single, easy-to-use package.  Concentrate on the math problem and not on the program.  Enjoy its simplicity, its capabilities, its power.  Enjoy your Apple IIGS!

GSymbolix:
.Completely written in pure, ultrafast and clean assembly language
.GS/OS application with desktop interface
.uses resources
.friendly user interface

Numeric Math:
.64 bit precision of mantissa
.uses the SANE(tm) tool set
.scientific RPN (reverse polish notation) calculator
.21 stack levels
.15 sophisticated stack commands
.define up to 200 variables
.access to built-in library of constants
.save/load stacks

Graphics:
.Graph one or two functions simultaneously
.Autoscaling
.Zoom function
.Relative coordinates
.Slope
.Save graphics in SHR format
.Print graphs
.Plot 3D graphs

Formulas:
.Size: up to 49,150 characters or 8870 objects
.Formulas may contain functions, variables, symbolic and numeric constants and  other formulas on disk
.Enter formulas in a word-processor environment
.Enter functions, variables and symbolic constants with simple mous clicks
.Nest formulas
.Find roots
.Let GSymbolix check and rewrite the formula
.Comprehensive error handling
.Undo function

Variables:
.Define up to 200 variables
.Names: up to 15 characters

Constants:
.40 built-in symbolic constants
.Use names instead of values
.Short description, value and unit for each constant

Values:
.Scientific or standard format
.Up to 715 numeric constants in a formula

Symbolic Math:
.Expand formulas automatically
.Sort formulas automatically
.Collect formulas automatically
.Simplify formulas automatically
.Convert trigonometric expressions automatically
.Evaluate formulas to numeric or to symbolic results
.Insert formulas from disk
.Mix list of variables
.Keep variables when changing files
.Move values from the formula to the calculator and vice versa
.Print formulas like documents in a word processor

Formularies:
.Math formulary
.Geometry formulary
.Table of all elements (boiling point, state...)
.Copy and paste from the formularies

c1991 Bright Software Switzerland
     Written by Henrik Gudat
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So if this sounds interesting to you... write to Henrik at the below address!  Like his letter said, he loves to hear suggestions, and he NEEDS to hear suggestions to make the program better... the letter he wrote and the sheets he included were very professionally done, and I'm sure he'll do the same when he hears from you.  'Nuff said - write to the guy.:)

Bright Software - Henrik Gudat
Pantelweg 2
CH-4153 Reinach
SWITZERLAND

Or telephone him at: 061-711 23 83.