Variables NCvars  constructs symbolic noncommuting variables
Toolbox for symbolic computation with polynomials in noncommuting variables Sum of hermitian squares (SOHS) related
NCsos  checks whether a polynomial is a SOHS
Cyclic equivalence and SOHSNCmin  computes the maximal epsilon such that the polynomial fepsilon is a SOHS NCdiff  computes the maximal epsilon such that the polynomial fepsilon*g is a SOHS NC2d  computes the second derivative of a polynomial NCisConvex0  checks if a polynomial is convex, i.e., if its second directional derivative is a SOHS NCisConvex  checks if a polynomial is convex (algorithm without SDP solvers) NCopt  computes minimizers and the minimum of a polynomial GNS  prepares a matrix X for the AWbd function by doing GelfandNaimarkSegal construction AWbd  numerical algorithm for the ArtinWedderburn blockdiagonal decomposition of matrix *algebras NCminBall  computes the minimum opt of a polynomial on an nc ball NCoptBall  computes minimizers and the minimum of a polynomial on an nc ball NCminCube  computes the minimum opt of a polynomial on an nc polydisc NCoptCube  computes minimizers and the minimum of a polynomial on an nc polydisc NCeigMin  computes the lower bound for the minimum eigenvalue of a polynomial subject to constraints S NCeigOpt  computes minimizers and the minimum eigenvalue of a polynomial subject to constraints S NCeigOptRand  computes minimizers and the minimum eigenvalue of a polynomial subject to constraints S using randomization NCisCycEq  checks whether two polynomials are cyclically equivalent
(i.e., whether their difference is a sum of commutators)
NCcycEqRep  constructs a canonical cyclically equivalent representative of a polynomial NCcycSos  checks whether a polynomial is cyclically equivalent to a SOHS NCcycMin  computes the maximal epsilon such that fepsilon is cyclically equivalent to a SOHS NCisCycConvex  checks if the second directional derivative of a polynomial is cyclically equivalent to a SOHS NCcycOpt  computes trace minimizers and trace minimum of a polynomial whenever the corresponding tracial moment matrix is flat NCFlatExt  checks whether the extension of dual moment matrices is flat GNS  prepares a matrix X for the AWbd function by doing GelfandNaimarkSegal construction AWbd  numerical algorithm for the ArtinWedderburn blockdiagonal decomposition of matrix *algebras NCtraceMin  computes the lower bound for the minimum of the trace of a polynomial subject to constraints S NCtraceOptRand  computes minimizers and the minimum of the trace of a polynomial subject to constraints S using randomization
Rationalization RprojRldlt  tries to find an exact rational positive semidefinite
solution of the SDP: X PsD, A*X=b from a floating point solution
fac_reduct  an interactive routine for finding a rational Gram matrix (feasible point) in case of singular feasible point with the aid of facial reduction BMV conjecture BMV  constructs the (m,k) BMV polynomial with x and y
as arguments
BMVq  constructs the (m,k) BMV polynomial with x^2 and y^2 as arguments (for modelling psd matrices) BMVsets  constructs the reduced monomial basis needed for the Gram matrix of (m,k) BMV polynomial with x^2 and y^2 as arguments Settings NCsetPrecision  sets the precision to be used in some numerical calculations
NCresetPrecision  resets the precision to the value set in NCparam.m NCsetSolver  sets the solver to be used for SDP (SeDuMi, SDPAM, SDPT3) NCresetSolver  resets the choice of SDP solver to the value set in NCparam.m See also
NCSOStoolsdemo  demonstration (brief tutorial and examples)

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