Solving the Quintic by Iteration [PDF]
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|Peter Doyle, Curt McMullen|
|This paper, which appeared in Acta Mathematica, gives explicitly a new solution to the quintic polynomial, in which the transcendental inversion of the icosahedral map (due to Hermite and Kronecker) is replaced by a purely iterative algorithm. The algorithm requires a rational map with icosahedral symmetries; this paper shows that all rational maps with given symmetries can be described using the classical theory of invariant polynomials. With a historical illustration. A PostScript file and MACSYMA input and output are available from Doyle's site.|
|Math Topics:||Analysis, Algorithms, Differential Geometry, Symmetry/Tessellations, History and Biography|
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