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- Tschirnhaus_transformation abstract "In mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried Walther von Tschirnhaus in 1683. 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, thenK[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(α)where α is t modulo (P). That is, α is a primitive element of L. There will be other choices β of primitive element in L: for any such choice of β we will haveβ = F(α), α = G(β),with polynomials F and G over K. In fact this follows from the quotient representation above. Now if Q is the minimal polynomial for β over K, we can call Q a Tschirnhaus transformation of P.Therefore the set of all Tschirnhaus transformations of an irreducible polynomial is to be described as running over all ways of changing P, but leaving L the same. This concept is used in reducing quintics to Bring–Jerrard form, for example. There is a connection with Galois theory, when L is a Galois extension of K. The Galois group is then described (in one way) as all the Tschirnhaus transformations of P to itself.".
- Tschirnhaus_transformation wikiPageExternalLink tschirnhaus.pdf.
- Tschirnhaus_transformation wikiPageID "595824".
- Tschirnhaus_transformation wikiPageLength "2253".
- Tschirnhaus_transformation wikiPageOutDegree "19".
- Tschirnhaus_transformation wikiPageRevisionID "650002350".
- Tschirnhaus_transformation wikiPageWikiLink Bring_radical.
- Tschirnhaus_transformation wikiPageWikiLink Category:Field_theory.
- Tschirnhaus_transformation wikiPageWikiLink Category:Polynomials.
- Tschirnhaus_transformation wikiPageWikiLink Ehrenfried_Walther_von_Tschirnhaus.
- Tschirnhaus_transformation wikiPageWikiLink Field_(mathematics).
- Tschirnhaus_transformation wikiPageWikiLink Field_extension.
- Tschirnhaus_transformation wikiPageWikiLink Galois_extension.
- Tschirnhaus_transformation wikiPageWikiLink Galois_group.
- Tschirnhaus_transformation wikiPageWikiLink Galois_theory.
- Tschirnhaus_transformation wikiPageWikiLink Irreducible_polynomial.
- Tschirnhaus_transformation wikiPageWikiLink Mathematics.
- Tschirnhaus_transformation wikiPageWikiLink Minimal_polynomial_(field_theory).
- Tschirnhaus_transformation wikiPageWikiLink Polynomial.
- Tschirnhaus_transformation wikiPageWikiLink Polynomial_ring.
- Tschirnhaus_transformation wikiPageWikiLink Polynomial_transformations.
- Tschirnhaus_transformation wikiPageWikiLink Principal_ideal.
- Tschirnhaus_transformation wikiPageWikiLink Quotient_ring.
- Tschirnhaus_transformation wikiPageWikiLink Rational_function.
- Tschirnhaus_transformation wikiPageWikiLink Simple_extension.
- Tschirnhaus_transformation wikiPageWikiLinkText "Tschirnhaus transformation".
- Tschirnhaus_transformation title "Tschirnhausen Transformation".
- Tschirnhaus_transformation urlname "TschirnhausenTransformation".
- Tschirnhaus_transformation wikiPageUsesTemplate Template:Algebra-stub.
- Tschirnhaus_transformation wikiPageUsesTemplate Template:MathWorld.
- Tschirnhaus_transformation subject Category:Field_theory.
- Tschirnhaus_transformation subject Category:Polynomials.
- Tschirnhaus_transformation hypernym Mapping.
- Tschirnhaus_transformation type Software.
- Tschirnhaus_transformation type Type.
- Tschirnhaus_transformation type Function.
- Tschirnhaus_transformation type Polynomial.
- Tschirnhaus_transformation type Redirect.
- Tschirnhaus_transformation type Type.
- Tschirnhaus_transformation comment "In mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried Walther von Tschirnhaus in 1683. It may be defined conveniently by means of field theory, as the transformation on minimal polynomials implied by a different choice of primitive element.".
- Tschirnhaus_transformation label "Tschirnhaus transformation".
- Tschirnhaus_transformation sameAs Q2670133.
- Tschirnhaus_transformation sameAs Mètode_de_Tschirnhaus.
- Tschirnhaus_transformation sameAs Tschirnhaus-Transformation.
- Tschirnhaus_transformation sameAs Transformación_de_Tschirnhaus.
- Tschirnhaus_transformation sameAs Méthode_de_Tschirnhaus.
- Tschirnhaus_transformation sameAs Methode_van_Tschirnhaus.
- Tschirnhaus_transformation sameAs m.02tq57.
- Tschirnhaus_transformation sameAs Преобразование_Чирнгауза.
- Tschirnhaus_transformation sameAs Q2670133.
- Tschirnhaus_transformation wasDerivedFrom Tschirnhaus_transformation?oldid=650002350.
- Tschirnhaus_transformation isPrimaryTopicOf Tschirnhaus_transformation.