Tschirnhaus transformation

Tschirnhaus transformation is a polynomial equation of degree (n≧2) with some nonzero intermediate coefficients.

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Ex.
n=3

a’1=0 and a’2=0

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K is a field, and P(t) is polynomial over K.

K(t)/P(t)=L

L=K(α)

α is t modulo P.

β=F(α), α=G(β)

F and G over K are polynomials. Moreover, Q is the minimal polynomial for β over K. This is the Tschirnhaus transformation of P.

L is a Galois extension of K.