SturmHabichtPackage(R, UP)ΒΆ

sturm.spad line 1

This package provides functions for counting real roots of univariate polynomials over an OrderedIntegralDomain.

countRealRoots: UP -> Integer
countRealRoots(p) says how many real roots p has
countRealRootsMultiple: UP -> Integer if R has GcdDomain
countRealRootsMultiple(p) says how many real roots p has, counted with multiplicity
SturmHabicht: (UP, UP) -> Integer
SturmHabicht(p1, p2) computes c_{+}-c_{-} where c_{+} is the number of real roots of p1 with p2>0 and c_{-} is the number of real roots of p1 with p2<0. If p2=1 what you get is the number of real roots of p1.
SturmHabichtCoefficients: (UP, UP) -> List R
SturmHabichtCoefficients(p1, p2) computes the principal Sturm-Habicht coefficients of p1 and p2
SturmHabichtMultiple: (UP, UP) -> Integer if R has GcdDomain
SturmHabichtMultiple(p1, p2) computes c_{+}-c_{-} where c_{+} is the number of real roots of p1 with p2>0 and c_{-} is the number of real roots of p1 with p2<0. If p2=1 what you get is the number of real roots of p1.
SturmHabichtSequence: (UP, UP) -> List UP
SturmHabichtSequence(p1, p2) computes the Sturm-Habicht sequence of p1 and p2