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RealRootsApprox --
approximations to the real roots of a univariate poly
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RealRootsApprox(F: RINGELEM): LIST
RealRootsApprox(F: RINGELEM, Precision: RAT): LIST
RealRootsApprox(F: RINGELEM, Precision: RAT, Interval:[RAT, RAT]): LIST |
This function computes rational approximations to the real roots of a
univariate polyomial (with rational coefficients).
An optional second argument specifies the maximum separation between
the approximations produced and the corresponding exact root. An
optional third argument specifies a closed interval in which to search
for roots.
NOTE: the value of
F at an approximate root may not be small;
see also
ApproxSolve
which uses a heuristic to produce approximate
roots such that the evaluation is also "small".
/**/ use QQ[x];
/**/ RealRootsApprox(x^2-2);
[-3037000499/2147483648, 3037000499/2147483648]
/**/ RR := RealRootsApprox(x^2-2, 10^(-15), [0, 2]);
/**/ FloatStr(RR[1], 15); --> print as a decimal, easier to read
1.41421356237310*10^0
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