# RealPolynomialUtilitiesPackage(TheField, ThePols)¶

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