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Posted on: Thursday, February 04, 2010 7:00 PM
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Subject: Math_Iteration Solve to Quintic
| Solving the quintic by iteration Peter Doyle and Curt McMullen Last revised 1989 Version 1.0A1 dated 15 September 1994 Abstract Equations that can be solved using iterated rational maps are characterized: an equation is ‘computable’ if and only if its Galois group is within A5 of solvable. We give 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; we show all rational maps with given symmetr |
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