For a given polynomial system and a list of numerical roots, this function certifies roots using a software "alphaCertified".
In order to use alphaCertified, users need to let the package knows a directory for alphaCertified when it is loaded.
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The function can be used as alphaCertified(f,p). It generates output files via the software alphaCertified. The output can be found in the user's directory of alphaCertified.
Users can also apply options for alphaCertified (e.g. alphaCertified(f, P, PRECISION => 4096)). For possible options for alphaCertified, see "alphaCertified manual".
The object alphaCertified is a method function with options.