![[NC]](NC.png)
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IntroductionOur NonCommutative Algebra Packages run under Mathematica© and give it the capability to manipulate noncommuting expressions. To get these packages, select the appropriate link under "Downloads" in the list of options to your left. If you have any trouble getting our software, then send us email at ncalg@ucsd.edu. More detailed information about NCAlgebra (including tutorials, documentation and pallettes) can be obtained here. More detailed information about the different types of NonCommutative Groebner Basis Packages which are available (i.e., NCGB, NGB and NGBMma) can be found here. More detailed information about a specific NonCommutative Groebner Basis Packages can be found via one of the following links ( NCGB | NGB | NGBMma ).
NCAlgebra NCAlgebra is iimplemented using Mathematica© and allows for the basic manipulation of noncommutative expressions. TutorialsFor an introduction to NCAlgebra, use a tutorial:
PalletesThe palette NCPalette for NCAlgebra contains the main NCAlgebra and NCGB commands, so is informative and can be used to help remember and to input NCAlgebra and NCGB commands.Complete documentationThe rather extensive documentation is available in pdf and ps formats.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 Demo Which Does Not Require MathematicaSimple Demo Which Does Require Mathematica, NCAlgebra and NCGBIf you choose to execute the following notebooks, be sure to load NCGB first.
NONCOMMUTATIVE INEQUATITIESIs a given noncommutative function positive? "convex"? The papers ( fillin and fillin ) define what that means. The NCAlgebra code is implemented in NCConvexityRegion. Executing the command NCConvexityRegion[Func, ListOfVariables] tells you where the (symbolic) function is convex in the variables. See here for more information.GroupsNCGB can be used to compute complete sets of rewrite rules for groups. (Note: Computing a complete set of rewrite rules for groups is usually thought of in terms of string rewrite rules and not Grobner Basis. However, NCGB can handle string rewrite rules written as differences.)Current Status of NCAlgebraTo run NCAlgebra you only need Mathematica.Current Status of NCGBAs of December 2001, to run NCGB you need
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