The worksheet computes linear transformation matrix T and its characteristic polynomial that belongs to a given polynomial map F (at least degree 2 in z) that can depend on parameters. The fastest computations are for the Mandelbrot map z^2+alpha, but other polynomial can be used. Matrix T represents multiplication by derivative of the map in a certain cyclic polynomial basis, the vector space that it works in is a cyclic polynomial factor ring according to ideal that belongs to k-cycles. The basis is chosen in a proper way to structure the matrix T into blocks that belong to cycle branches of known period d, d|k. The d-cycle branches degenerate at izolated parameter values with lambda = 1, where branches cross, so we can compute Guckenheimer's bifurcation points of a known type at connections of Mandelbrot bulbs and roots of newborn bulbs. Minimal bifurcation polynomials of d-cycles can be computed by this method. The characteristic polynomial for the Mandelbrot map transforms to the logistic map characteristic polynomial by a parameter change, since the maps are topologically equivalent. Fold bifurcation points of the logistic map are roots of the characteristic polynomials (more precisely their proper factors) for lambda = 1 and flip bifurcation points for lambda = -1. For k = 8 and lambda = -1 the worksheet 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.) this method is relatively rapid (around 90 seconds, depending on the computer performance). The procedure matrixT with argument k (length of the cycle) is restricted to 150 polynomials in the cyclic basis to avoid time consuming operations, but you can change it. The same worksheet for the cubic Mandelbrot map z^3+alpha works analogously and computes the structure in the basis of dimension 130, but it takes more time to compute.