RealRoots(F:POLY):LIST
RealRoots(F:POLY, Precision:RAT):LIST
RealRoots(F:POLY, Precision:RAT, Interval:[RAT,RAT]):LIST
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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.
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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
-------------------------------
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