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# realRootIsolation -- a list that isolates the real roots of a univariate polynomial with rational coefficients

- Usage:
    `realRootIsolation(f,r)`
- Inputs:
  - f, a ring element, a univariate polynomial with rational coefficients
  - r, a rational number, a positive rational number
- Outputs:
  - a list, of disjoint intervals

## Description

This computes disjoint intervals of length at most r, each containing exactly one real root of f.

    i1 : R = QQ[t]

    o1 = R

    o1 : PolynomialRing

    i2 : f = 45 - 39*t - 34*t^2 + 38*t^3 - 11*t^4 + t^5

          5      4      3      2
    o2 = t  - 11t  + 38t  - 34t  - 39t + 45

    o2 : R

    i3 : realRootIsolation(f,1/2)

             3        1       5       9
    o3 = {{- -, -1}, {-, 1}, {-, 3}, {-, 5}}
             2        2       2       2

    o3 : List

## See also

- sturmSequence -- the Sturm sequence of a univariate polynomial with rational coefficients

## Ways to use realRootIsolation:

- `realRootIsolation(RingElement,QQ)`

## For the programmer

The object realRootIsolation is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RealRoots.m2:901:0.