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}]](Files/RootIsolation.en/legacy_1.gif)
RootIntervals gives real roots by default:
Version 5.2
![RealRootIntervals[(x^2 - 2) (x^2 - 3) (x^2 - 4), {x, 1, 2}]](Files/RootIsolation.en/legacy_2.gif)
RootIntervals also gives complex roots:
Version 5.2
![ComplexRootIntervals[f + 3]](Files/RootIsolation.en/legacy_3.gif)
IsolatingInterval includes the functionality of ContractInterval from Version 5.2:
Version 5.2
![ContractInterval[Root[x^10 - 1, 5], 10]](Files/RootIsolation.en/legacy_4.gif)