Things

Things you can do with NCAlgebra and NCGB

In this page you will find some things that you can do with NCAlgebra and NCGB.

NCAlgebra

Noncommutative Inequalities

Is a given noncommutative function convex? You type in a function of noncommutative variables; the command NCConvexityRegion[Function, ListOfVariables] tells you where the (symbolic) Function is convex in the Variables. This corresponds to papers of Camino, Helton and Skelton.

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 DEMOS/NCSDP subdirectory.

You can also find examples of systems and control linear matrix inequalities problems being manipulated and numerically solved by NCAlgebra on the UCSD course webpage.

Groups

You can compute a complete list of rewrite rules for Groups using NCGB. See demos at http://math.ucsd.edu/~ncalg.

NCGBX

NCGBX is a 100% Mathematica version of our 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.

IMPORTANT: Do not load NCGB and NCGBX simultaneously.

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.