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Solving the Quintic with Mathematica
Authors

Michael Trott
Organization: Wolfram Research, Inc.
Department: Scientific Information Group
Victor Adamchik
Organization: Carnegie-Mellon University
Department: Computer Science
Description

These notebooks provide the complete code used to generate the results on the poster "Solving the Quintic with Mathematica."
Subjects

*Mathematics > Algebra > Group Theory
*Mathematics > Algebra > Polynomials
Keywords

quintic equation, polynomials, small degree polynomials, solving polynomials, Tschirnhaus's transformation, Klein's approach to the quintic, quadratic, cubic, quartic, history of the quintic
URL

http://library.wolfram.com/examples/quintic/
http://store.wolfram.com/catalog/posters/

Downloads Download Wolfram CDF Player

Download
Bibliography.nb (133.9 KB) - a bibliography on solutions of polynomial equations
Download
DiffResolvent.nb (13.8 KB) - Cockle and Harley's reduction of the solution of a polynomial equation to the solution of a differential equation
Download
Galois.nb (11.6 KB) - finds the galois group of a given quintic
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Hermite.nb (8.7 KB) - Hermite's solution of the quintic in terms of elliptic modular functions
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Isograph.nb (99 KB) - a simulation of the Isograph
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KleinsApproach.nb (10.3 KB) - Klein's solution of the quintic in terms of hypergeometric functions
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Pictures.nb (8.1 MB) - the source code for producing the pictures shown on the poster
Download
Radical.nb (12.1 KB) - solving quintics in radicals
Download
Series.nb (9.4 KB) - solving quintics using series
Download
TschirnhausTransformation.nb (22.2 KB) - an implementation of Tschirnhaus' transformation for eliminating terms from a polynomial

Files specific to Mathematica 2.2 version:
Download
Bibliography.ma (76.8 KB) - a bibliography on solutions of polynomial equations
Download
DiffResolvent.ma (10.5 KB) - Cockle and Harley's reduction of the solution of a polynomial equation to the solution of a differential equation
Download
Galois.ma (9.7 KB) - finds the galois group of a given quintic
Download
Hermite.ma (8.2 KB) - Hermite's solution of the quintic in terms of elliptic modular functions
Download
Isograph.ma (70 KB) - a simulation of the Isograph
Download
KleinsApproach.ma (9.1 KB) - Klein's solution of the quintic in terms of hypergeometric functions
Download
Pictures.ma (7.7 MB) - the source code for producing the pictures shown on the poster
Download
Radical.ma (10.9 KB) - solving quintics in radicals
Download
Series.ma (7.6 KB) - solving quintics using series
Download
TschirnhausTransformation.ma (17.2 KB) - an implementation of Tschirnhaus' transformation for eliminating terms from a polynomial