CoCoA:RealRoots

RealRoots

computes the real roots of a univariate polynomial

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 <ttref>RealRootRefine</ttref>. The

function <ttref>RealRootsApprox</ttref> 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[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
-------------------------------

Syntax

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

RealRootRefine

RealRootsApprox

RootBound

   <type>polynomial</type>