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This is an English translation of Anders Wiman's classical paper "\"{U}berdie Anwendung der Tschirnhausen Transformation auf die Reduktion algebraischerGleichungen" from 1927. The original work first appeared in the 1927extraordinary edition of Nova Acta Regiae Societatis Scientiarum Upsaliensis.In this paper, Wiman gives an argument that the general polynomial of degreenine can be solved using one algebraic function of four variables and accessoryirrationalities of degree at most five. However, his argument assumes certainintersections in affine space are generic without proof.

Anders Wiman's "On the Application of Tschirnhaus Transformations to the Reduction of Algebraic Equations''