The worksheet computes linear transformation matrix T and its characteristic polynomial that belongs to the Mandelbrot map and represents multiplication by derivative of the map in a certain cyclic polynomial basis. Eigenvalues of the characteristic polynomial for given k are eigenvalues of k-cycles (possibly degenerated cycles) of the Mandelbrot map. The characteristic polynomial transforms to the logistic map characteristic polynomial. Fold bifurcation points of the logistic map are roots of the polynomial for lambda = 1 and flip bifurcation points for lambda = -1. For k = 8 and lambda = -1 it computes the bifurcation polynomial for the B4 point of the logistic map. Since the basis have 36 cyclic polynomials, it computes determinant 36x36. Compared to the Groebner Basis method (see Kotsireas, Ilias S., and Kostas Karamanos. "Exact computation of the bifurcation point B4 of the logistic map and the Bailey-Broadhurst conjectures." International Journal of Bifurcation and Chaos 14.07 (2004): 2417-2423.) used method is relatively rapid (around a minute, depending on the computer performance). The procedure matrixT with argument k - length of the cycle - is restricted to 50 polynomials in the cyclic basis to avoid overflow, but you can change it...