Re: Real roots of polynomials

*To*: mathgroup at smc.vnet.net*Subject*: [mg24724] Re: Real roots of polynomials*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Wed, 9 Aug 2000 02:31:23 -0400 (EDT)*References*: <8mdl69$5hc@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Jack, How abour using InequalitySolve? <<Algebra`InequalitySolve` poly = Expand[x (x^2 - 2) (x^2 - 3)(x^8 - 3.)]//N 3 5 9 11 13 -18. x + 15. x - 3. x + 6. x - 5. x + x InequalitySolve[poly == 0, x] x == -1.73205 || x == -1.41421 || x == -1.1472 || x == 0. || x == 1.1472 || x == 1.41421 || x == 1.73205 Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Jack Goldberg" <jackgold at math.lsa.umich.edu> wrote in message news:8mdl69$5hc at smc.vnet.net... > Hi, > > Suppose Pn[x] is a polynomial of degree n in x. Its coefficients > are real. > > Question: What is a good way of determining the real roots of Pn > and their multiplicities? > > Use NSolve and "cast out" the complex roots and Chop any > roots with a "too" small imaginary part (in case NSolve > inserts spurious imaginary parts). > In cases where n is large and the number of real roots is small > compared to n, one can imagine that better methods exist. I have > searched MathSource with no real (pun intended) progress. Possibly > this is more a math question than a Mathematica question. > > Help is appreciated. > > Jack > > >