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...
Get the February 2015 Version of NCAlgebra, NCGBX (alpha) and NCGB Releases for Windows, Mac OSX, Linux, Solaris
NCGBX (new in February 2015 versions) is 100% Mathematica code that does NC Groebner Basis calculations and does not require C/C++ code compilation.
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.
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.
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.
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.
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.
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
(You NEED Mma too view all but (1a)):
You can compute a complete list of rewrite rules for Groups using NCGB. See demos below.
NCGB is a 100% Mathematica version of NC Groebner Basis Algorithm and does not require C/C++ code compilation
Look for demos in the NC/NCPoly/DEMOS subdirectory of the most current distributions.
Do not load NCGB and NCGBX simultaneously.
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.
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
Symbolic calculations of unitary transfomations in quantum dynamics. N.-A. Nguyen, T.T. Nguyen-Dang.
Partially supported by the NSF Division of Mathematical Sciences.