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RealRoots

computes a root of a univariate polynomial over Q

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.

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


See Also