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Upgrading from:

Algebra`RootIsolation`

New functions CountRoots, IsolatingInterval, and RootIntervals have been added to the built-in Mathematica kernel.
IsolatingInterval includes the functionality of ContractInterval from Version 5.2.
RootIntervals incorporates the functionality of RealRootIntervals and ComplexRootIntervals from Version 5.2.

CountRoots now counts roots in closed intervals; in Version 5.2, it used open intervals:

Version 5.2 $<< Algebra`RootIsolation`; CountRoots[(x^2 - 2) (x^2 - 3) (x^2 - 4), {x, 1, 2}]$

RootIntervals gives real roots by default:

Version 5.2 $RealRootIntervals[(x^2 - 2) (x^2 - 3) (x^2 - 4), {x, 1, 2}]$

RootIntervals also gives complex roots:

Version 5.2

IsolatingInterval includes the functionality of ContractInterval from Version 5.2:

Version 5.2

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