From: mtrott@wri.com (Michael Trott) Newsgroups: sci.math Subject: Re: polynomials and elliptical functions Date: 24 Sep 1996 14:21:34 GMT In article <32471A67.41C8@student.utwente.nl> Wilbert Dijkhof writes: > I've read somewhere that fifth-degree polynomials are > solvable in terms of elliptical functions [Charles Hermite]. > Does anyone know how to do this? How is this in the general > case (n-degree polynomials)? > > Wilbert Dijkhof see http://www.wolfram.com/posters/quintic/ -- Michael Trott Wolfram Research, Inc. ============================================================================== From: mtrott@wri.com (Michael Trott) Newsgroups: sci.math Subject: Re: Solution of the Quintic Date: 25 Nov 1996 13:28:08 GMT In article <329A77A2.5EFB@hkstar.com> "Kenneth H. L. Chiu" writes: > I have heard of something like the solution of the > quintic (polynomial of degree 5) equation by > Hermite's Elliptic Function. > > Could someone please tell me how it works? > > Thanks in advance. Have a look at: http://www.wolfram.com/MathSource/Applications/Mathematics/0207-122/Hermite.ma -- Michael Trott Wolfram Research, Inc. ============================================================================== Also of possible interest: at http://math.ucsd.edu/~doyle/docs/icos/icos/icos.html we find the paper "Solving the quintic by iteration", Peter Doyle and Curt McMullen 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 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 symmetries can be described using the classical theory of invariant polynomials.