RealPolynomialUtilitiesPackage(TheField, ThePols)

reclos.spad line 60 [edit on github]

• TheField : Field
• ThePols : UnivariatePolynomialCategory(TheField)

RealPolynomialUtilitiesPackage provides common functions used by interval coding.

boundOfCauchy : ThePols -> TheField if TheField has OrderedRing

boundOfCauchy(p) bounds the roots of p

lazyVariations : (List(TheField), Integer, Integer) -> NonNegativeInteger if TheField has OrderedRing

lazyVariations(l, s1, sn) is the number of sign variations in the list of non null numbers [s1::l]@sn,

sturmSequence : ThePols -> List(ThePols)

sturmSequence(p) = sylvesterSequence(p, p')

sturmVariationsOf : List(TheField) -> NonNegativeInteger if TheField has OrderedRing

sturmVariationsOf(l) is the number of sign variations in the list of numbers l, note that the first term counts as a sign

sylvesterSequence : (ThePols, ThePols) -> List(ThePols)

sylvesterSequence(p, q) is the negated remainder sequence of p and q divided by the last computed term