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21 NCALGEBRA Version 4.0 (Compatible with Mathematica version 5 to 7) J. William Helton, Maurı́cio C. de Oliveira and Mark Stankus Math Dept., UCSD Robert L. Miller General Atomic Corp. La Jolla, California 92093 Copyright by Helton and Miller on June 1991, Feb 1994 Copyright by Helton, Miller and Stankus on March 1996 Copyright by Helton, Miller and Stankus on September 2001 Copyright by Helton, Miller, Stankus and de Oliveira on January 2010 All Rights Reserved. If you would like to try the NCAlgebra package or want updates go to the NCAlgebra web site http://math.ucsd.edu/∼ncalg or contact [email protected] or [email protected]. The basic NCAlgebra program was written by the authors and David Hurst, Daniel Lamm, Orlando Merino, Robert Obarr, Henry Pfister, Stan Yoshinobu, Phillipe Bergman, Dell Kronewitter, and Eric Rowell. Various additions include contributions by Dave Glickstein, Juan Camino, Jeff Ovall, Tony Mendes, and Tony Shaheen. The Mathematica C++ hybrid was developed with Kurt Schneider, Victor Shih and Mike Moore. Control demos are coauthored with Mike Walker. Simplification commands are based on theory developed by Bill Helton, John Wavrik and Mark Stankus. The beginnings of the program come from eran@slac. This program was written with support from the AFOSR, the NSF, the Lab for Mathematics and Statistics at UCSD, the UCSD Faculty Mentor Program and the US Department of Education.