Category:Tschirnhaus Transformations
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This category contains results about Tschirnhaus Transformations.
Let $\map f x$ be a polynomial over a field $k$:
- $\map f x = a_n x^n + a_{n - 1} x^{n - 1} + a_{n - 2} x^{n - 2} + \cdots + a_1 x + a_0$
Then the Tschirnhaus transformation is the linear substitution $x = y - \dfrac {a_{n - 1} } {n a_n}$.
The Tschirnhaus transformation produces a resulting polynomial $\map {f'} y$ which is depressed, as shown on Tschirnhaus Transformation yields Depressed Polynomial.
This technique is used in the derivation of Cardano's Formula for the roots of the general cubic.
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