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  1. MHB Journeyman
    MHB Math Helper
    mathbalarka's Avatar
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    Mar 2013
    West Bengal, India
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    This is a graph containing the main Tschirnhausen transformations of a general quintic and the algorithms to solve them. The methods would be explicitly described most probably elsewhere in this forum

    • The lower-most nodes are the elementariest functions to which the root of a general quintic can be extracted.
    • In any sub-graph of the above, the lowermost elements are the form reduced from the topmost elements via Tschirnhausen transformations.
    • Deeper colors indicates the effectiveness of the algorithm in computational research, as well as popularity.
    • Dotted lines indicates a reduction that is non-obvious although not a part of the interest, in most cases.
    • Black lines indicates a transformation that is not part of the algorithm.
    • The red arrows indicate the Kiepert algorithm, which I like to call Kiepert-Perron algorithm.
    • The green arrows indicate Glasser's derivation.
    • The magenta-like colors indicate Hasner's method and Kronecker-Brioschi derivation respectively.

    Any comment/question regarding this thread should be posted in
    Last edited by mathbalarka; December 19th, 2013 at 15:45.

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