last modified August 2012
NCAlgebra

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...

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Get the March 2013 Alpha Version of NCAlgebra and NCGB Releases for Windows, Mac OSX, Linux, Solaris

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;

The rather extensive NC DOCUMENT is available in html or pdf.

NONCOMMUTATIVE INEQUALITIES

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. This corresponds to papers of Camino Helton and Skelton.

LINEAR SYSTEMS AND CONTROL

NCAlgebra integrates with Mathematica's version 8.0 control toolbox to work on noncommutative block systems, just as a human would do...
Look for NCControl.nb in the NC/DEMOS subdirectory.

SEMIDEFINITE PROGRAMMING

NCAlgebra now comes with a numerical solver that can compute the solution to semidefinite programs, aka linear matrix inequalities.
Look for demos in the NC/NCSDP/DEMOS subdirectory.

You can find examples of systems and control linear matrix inequalities problems being manipulated and numerically solved by NCAlgebra on the UCSD course webpage.
Look for the .nb files, starting with the file sat5.nb at Lecture 8.

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 NC DOCUMENT obtainable as PDF

SIMPLE DEMOS

(You NEED Mma too view all but (1a)):

GROUPS

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


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
  • 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


    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 NSF Division of Mathematical Sciences.

    The BIG DOCUMENT in html
    in PDF

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