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2001 Solving the quintic by iteration in three dimensions
Scott Crass
Experiment. Math. 10(1): 1-24 (2001).


The requirement for solving a polynomial is a means of breaking its symmetry, which in the case of the quintic, is that of the symmetric group S5. Induced by its five-dimensional linear permutation representation is a three-dimensional projective action. A mapping of complex projective 3-space with this S5 symmetry can provide the requisite symmetry-breaking tool. The article describes some of the S5 geometry in CP3 as well as several maps with particularly elegant geometric and dynamical properties. Using a rational map in degree six, it culminates with an explicit algorithm for solving a general quintic. In contrast to the Doyle-McMullen procedure, which involves three 1-dimensional iterations, the present solution employs one 3-dimensional iteration.


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Scott Crass. "Solving the quintic by iteration in three dimensions." Experiment. Math. 10 (1) 1 - 24, 2001.


Published: 2001
First available in Project Euclid: 30 August 2001

zbMATH: 0992.37035
MathSciNet: MR1 821 568

Primary: 37Fxx
Secondary: 32Hxx , 65P40

Rights: Copyright © 2001 A K Peters, Ltd.


Vol.10 • No. 1 • 2001
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