Toolbox for symbolic computation with polynomials in noncommuting variables

plus, f+g (symbolic addition)

minus, f-g (symbolic subtraction)

uminus, -f (symbolic negation)

times, f.*g (symbolic element-by-element multiplication)

power, f.^n (element-by-element powers)

prod (product of the elements)

sum (sum of the elements)

mtimes, f*g (symbolic matrix multiplication)

mpower, f^n (symbolic matrix power)

transpose, f.' (symbolic matrix transpose)

ctranspose, f' (involution)

diag (diagonal matrices and diagonals of a matrix)

tril (lower triangular part)

triu (upper triangular part)

horzcat, [ , ] (horizontal concatenation of matrices)

vertcat, [ ; ] (vertical concatenation of matrices)

eq, f==g (element by element symbolic equality test)

ne, f~=g (element by element symbolic inequality test)

isequal (symbolic equality test)

NCsimplify (writing monomials shortly using exponents)

NCexpand (writing monomials in expanded form without using exponents)

NCeval (symbolic evaluation and substitution)

char (converting to its string representation)