Math.RootLoci.Dual.Localization

Localization formula for the dual class from:

L. M. Feher, A. Nemethi, R. Rimanyi: Coincident root loci of binary forms; Michigan Math. J. Volume 54, Issue 2 (2006), 375--392.

Note: This formula is in the form of rational function (as opposed to a polynomial). Since we don't have polynomial factorization implemented here, instead we evaluate it substituting different rational numbers into alpha and beta, and then use Lagrange interpolation to figure out the result (we know a priori that it is a homogenenous polynomial in alpha and beta).

Documentation

type X = U "x"

mkX :: Int -> X

localizeMathematica :: Partition -> String

The localization formula as a string which Mathematica can parse

localizeEval :: Fractional q => Partition -> q -> q -> q

The localization formula evaluated at given values of a and b

localizeDual :: Partition -> ZMod AB

The dual class, recovered via from the localization formula via Lagrange interpolation

localizeInterpolatedQ :: Partition -> QMod X

We can use Lagrange interpolation to express the dual class from the localization formula (since we know a priori that the result is a homogeneous polynomial in a and b)

localizeInterpolatedZ :: Partition -> ZMod X