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RootBound 
bound on roots of a polynomial over QQ

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 
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 tradeoff 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.
/**/ use P ::= QQ[x];
/**/ RootBound(x^22);
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