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Our Non Commutative Algebra Packages run under Mathematica© and give it the capability of manipulating noncommuting algebraic expressions.   NCGB Computes Non Commutative Groebner Bases and has extensive sorting and display features as well as algorithms for automatically discarding "redundant" polynomials ...

Table of Contents

Introduction

Our NonCommutative Algebra Packages run under Mathematica© and give it the capability of manipulating noncommuting expressions. To get them click NCAlgebra and NCGB download. If you have any trouble getting our software, then send us email at ncalg@ucsd.edu.

NCAlgebra  For an introduction to NCAlgebra see the short tutorial of some of the most basic commands in HTML or a Mma notebook; or a brief Demo of NCAlgebra Mathematica Notebook (you need Mma to read it and you must load NCAlgebra to run it). Also the palette NCPalette for NCAlgebra contains the main NCAlgebra and NCGB commands, so is informative. The rather extensive NCDOCUMENT is available in Pdf

NCGB    Computes NonCommutative Groebner Bases and has extensive sorting and display features as well as algorithms for automatically discarding "redundant" polynomials, as well as "kludgy" methods for suggesting changes of variables (which work better than one would expect). NCGB runs in conjunction with NCAlgebra. A very brief TEMPLATE/DEMO is given here. The whole story appears in the rather long NCGBDOCUMENT obtainable as Dvi or Postscript.

SIMPLE DEMOS (You NEED Mma too view all but (1a) ): NONCOMMUTATIVE INEQUATITIES Is a given noncommutative function "convex"? You type in a function of noncommutative variables; the command NCConvexityRegion[Func, ListOfVariables] tells you where the (symbolic) Function is convex in the Variables. NCConvexityRegion download software and papers on Convexity and on representing Polys as Sums of Squares

GROUPS You can compute a complete list of rewrite rules for Groups using NCGB. See demos below.

AS OF DEC 2001 TO RUN NCGB YOU NEED

Mathematica running under the Solaris operating system and GNU C++ (free)

OR Windows on a PC

Linux (Mandrake) Also you need one of the above to run (all but the first of) these DEMOS, downloaded. We use Mathematica 3.0+ and 4.0
WE REPEAT TO RUN NCAlgebra you only need Mathematica.


SOME ACCOMPLISHMENTS OF NON COMMUTATIVE COMPUTER ALGEBRA

This part of the site contains examples of problems which have been investigated with the aid of the features in NCAlgebra for DISCOVERING FORMULAS. Exactly what can be done for engineering systems theory and operator theory with NonCommuting GB's (Mora's algorithm) and techniques we are developing is thoroughly unexplored. Our goal is to test these methods on a variety of problems, most of which are classic theorems in some field. Classifying existing mathematics according to what is required to discover it is an extremely valuable gauge of these symbolic techniques. However, some of the results described here are new, and a few contain open questions.

SYSTEMS ENGINEERING

OPERATOR THEORY

PROBLEMS ORDERED ACCORDING TO METHODOLOGY REQUIRED TO SOLVE


 
 

USE OF NCGB ON GROUPS-- to generate a complete list of rewrite rules

 Some of these examples along with more about ``strategies'' is in the paper Computer assistance for ``discovering'' formulas in system engineering and operator theory by J. William Helton and Mark Stankus, Journal of Functional Analysis 1999. It is available via anonymous ftp in either Dvi or PostScript formats. It is also on the World Wide Web in HTML


Click here for complete documentation for NCAlgebra and NCGB in HTML. format(Mar 1999). 

NonCommuters


 
 

Misc. References

Add on package to NCAlgbera

Symbolic calculations of unitary transfomations in quantum dynamics. N.-A. Nguyen, T.T. Nguyen-Dang.

Partially supported by the AFOSR and the NSF.

The BIG DOCUMENT

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