SturmHabichtPackage(R, UP)

sturm.spad line 1 [edit on github]

• R : OrderedIntegralDomain
• UP : UnivariatePolynomialCategory(R)

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

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

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