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
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"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
>
>
>