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RootBound --
bound on roots of a polynomial over QQ
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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 trade-off between speed and
tightness of the bound (more precisely: it says how many iterations of
Graeffe 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^2-2);
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