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The software package [http://www.math.tamu.edu/~sottile/research/stories/alphaCertified/ alphaCertified] provides an implementation of the alpha test for polynomials by estimating <math>\beta</math> and <math>\gamma</math>.<ref name="alphacertified">{{cite journal |last1=Hauenstein |first1=Jonathan |last2=Sottile |first2=Frank |title=Algorithm 921: alphaCertified: certifying solutions to polynomial systems |journal=ACM Transactions on Mathematical Software (TOMS) |date=2012 |volume=38 |issue=4 |page=28 |doi=10.1145/2331130.2331136}}</ref>
=== The Interval Newton and Krawczyck Methods ===
Suppose <math>G:\mathbb{C}^n\rightarrow\mathbb{C}^n</math> is a function whose fixed points correspond to the roots of <math>F</math>. For example, the Newton operator has this property. Suppose that <math>I</math> is a region, then,
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