Abstract.
The Brioschi resolvent y 5−10Zy 3+45Z 2 y−Z 2 is a key component of an algorithm for calculating the roots of a general quintic polynomial. It is obtained from the general quintic polynomial by applying two Tschirnhausen transformations. In this paper it is shown that if the quintic polynomial is a solvable polynomial, then its associated parameter Z in the Brioschi resolvent satisfies Z=g(t) where g(t) is a rational function in ℚ(t) and t is chosen from an appropriate field.
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Received: July 23, 2001; revised version: October 14, 2002
Keywords: Solvable quintic, Brioschi quintic, resolvent sextic, parametrization.
The author was supported by a research grant from the Natural Sciences and Engineering Research Council of Canada
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Spearman, B. Solvable Brioschi Resolvents. AAECC 13, 447–452 (2003). https://doi.org/10.1007/s00200-002-0108-y
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DOI: https://doi.org/10.1007/s00200-002-0108-y