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 RootBound    --    bound on roots of a polynomial over QQ

 Syntax
 ```RootBound(F: RINGELEM): RAT RootBound(F: RINGELEM, N: INT): RAT RootBound_Birkhoff(F: RINGELEM): RAT RootBound_Cauchy(F: RINGELEM): RAT RootBound_Lagrange(F: RINGELEM): RAT RootBound_LMS(F: RINGELEM): RAT```

 Description
The function RootBound computes a bound on the absolute values of the complex roots of a univariate polynomial with rational coefficients. In some cases you may get a better bound by applying first the transformation produced by the function LinearSimplify . The optional second argument specifies a trade-off between speed and tightness of the bound (more precisely: it says how many iterations of Graeffe's transformation to apply); higher numbers give better bounds but can take significantly more time. With just one argument, the number of iterations is determined heuristically.

The functions RootBound_Birkhoff , RootBound_Cauchy , RootBound_Lagrange and RootBound_LMS compute those bounds directly. You should normally use the function RootBound which computes all the bounds, and takes the smallest; it may also apply some Graeffe transformations.

 Example
 ```/**/ use P ::= QQ[x]; /**/ RootBound(x^2-2); 363/256 ```

 See Also