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NCAlgebra or Non Commutative Algebra Packages run under Mathematica and give it the capability of manipulating noncommuting algebraic expressions.
NCGBX and NCGB computes Non Commutative Groebner Bases and has extensive sorting and display features as well as algorithms for automatically discarding redundant polynomials.
NCSDP solves Semidefinite Programs.
Follow the instructions on the main repository page:
https://github.com/NCAlgebra/NC
Follow the links for more details on working with NCAlgebra:
Please report any bug or your extraordinarily pleasant experience with NCAlgebra by email:
Thanks,
Bill Helton and Mauricio de Oliveira
NCAlgebra - A Mathematica Package for Noncommutative Calculations
J. William Helton, Mauricio de Oliveira, Mark Stankus