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 f-epsilon is a SOHS NCdiff - computes the maximal epsilon such that the polynomial f-epsilon*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 Gelfand-Naimark-Segal construction AWbd - numerical algorithm for the Artin-Wedderburn block-diagonal 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 f-epsilon 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 Gelfand-Naimark-Segal construction AWbd - numerical algorithm for the Artin-Wedderburn block-diagonal 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, SDPA-M, 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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