Tschirnhaus Transformation
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High Quality Content by WIKIPEDIA articles! In mathematics, a Tschirnhaus transformation, developed by Ehrenfried Walther von Tschirnhaus in 1683, is a type of mapping on polynomials. It may be defined conveniently by means of field theory, as the transformation on minimal polynomials implied by a different choice of primitive element. This is the most general transformation of an irreducible polynomial that takes a root to some rational function applied to that root. In detail, let K be a field, and P(t) a polynomial over K. If P is irreducible, then K[t]/(P(t)) = L, the quotient ring of the…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, a Tschirnhaus transformation, developed by Ehrenfried Walther von Tschirnhaus in 1683, is a type of mapping on polynomials. It may be defined conveniently by means of field theory, as the transformation on minimal polynomials implied by a different choice of primitive element. This is the most general transformation of an irreducible polynomial that takes a root to some rational function applied to that root. In detail, let K be a field, and P(t) a polynomial over K. If P is irreducible, then K[t]/(P(t)) = L, the quotient ring of the polynomial ring K[t] by the principal ideal generated by P, is a field extension of K. We haveL = K( ) where is t modulo (P).