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A Tschirnhausen transformation can be used to algebraically transform a general quintic equation to the form z^5+c_1z+c_0=0. (1) In practice, the general quintic is first ...

Using a Tschirnhausen transformation, the principal quintic form can be transformed to the one-parameter form w^5-10cw^3+45c^2w-c^2=0 (1) named after Francesco Brioschi ...

A catastrophe which can occur for four control factors and one behavior axis. The butterfly catastrophe is the universal unfolding of the singularity f(x)=x^6 of codimension ...

The maximum number of regions that can be created by n cuts using space division by planes, cube division by planes, cylinder cutting, etc., is given by N_(max)=1/6(n^3+5n+6) ...

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...

Let phi(t) be the characteristic function, defined as the Fourier transform of the probability density function P(x) using Fourier transform parameters a=b=1, phi(t) = ...

A surface of constant negative curvature obtained by twisting a pseudosphere and given by the parametric equations x = acosusinv (1) y = asinusinv (2) z = ...

The discrete uniform distribution is also known as the "equally likely outcomes" distribution. Letting a set S have N elements, each of them having the same probability, then ...

The E_n(x) function is defined by the integral E_n(x)=int_1^infty(e^(-xt)dt)/(t^n) (1) and is given by the Wolfram Language function ExpIntegralE[n, x]. Defining t=eta^(-1) ...

Fractran is an algorithm applied to a given list f_1, f_2, ..., f_k of fractions. Given a starting integer N, the FRACTRAN algorithm proceeds by repeatedly multiplying the ...