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 RealRoots

computes the real roots of a univariate polynomial
 Syntax
 ``` RealRoots(F:POLY):LIST RealRoots(F:POLY, Precision:RAT):LIST RealRoots(F:POLY, Precision:RAT, Interval:[RAT, RAT]):LIST ```

 Description
This function computes isolating intervals for the real roots of a univariate polyomial over Q. It returns the list of the real roots, where a root is represented as a record containing either the exact root (if the fields Inf and Sup are equal), or an open interval (Inf, Sup) containing the root. A third field (called CoeffList) has an obscure meaning.

An optional second argument specifies the maximum width an isolating interval may have. An optional third argument specifies a closed interval in which to search for roots.

The interval represented by a root record may be refined by using the function RealRootRefine . The function RealRootsApprox may be more useful to you: it produces rational approximations to the real roots (but these cannot later be refined).

 Example
 ``` RealRoots(x^2-2); [Record[CoeffList = [8, -16, 7], Inf = -4, Sup = 0], Record[CoeffList = [8, 0, -1], Inf = 0, Sup = 4]] ------------------------------- RR := RealRoots((x^2-2)*(x-1), 10^(-5)); FloatStr(RR.Inf); -- left end of interval -1.414213657*10^0 ------------------------------- FloatStr(RR.Sup); -- right end of interval -1.414213419*10^0 ------------------------------- RR := RealRoots(x^2-2, 10^(-20), [0, 2]); RR.Inf; -- incomprehensible 3339217363285192246361/2361183241434822606848 ------------------------------- FloatStr(RR.Inf, 20); -- comprehensible 1.4142135623730950488*10^0 ------------------------------- ```

 See Also