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numerical roots of a polynomial

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1163] numerical roots of a polynomial
• From: Sigurd.Schelstraete at rug.ac.be (Sigurd Schelstraete)
• Date: Sat, 20 May 1995 02:23:23 -0400
• Organization: University of Ghent, Belgium

hello,

does anyone know if there exists a package/function that allows one to find 
(numerically) all n roots of a polynomial of degree n, whether they are 
real or not? Since NSolve seems to be equivalent to N[Solve], it can not 
be used for generic polynomials of fifth degree or higher. Also the 
function FindRoot only allows one to find a single root near a given 
starting value (which can be complex though).

What I would like, is a function that returns the numerical values of all 
n roots as a list of substitution rules, as does Solve or NSolve. 

I guess it could be done by successively dividing out a single root found 
with FindRoot, but I'd rather first hear if anyone out there already has 
a clear-cut solution to this problem. 

All answers are appreciated.

Greetings,

Sigurd Schelstraete
University of Gent
Belgium