RealPolynomialUtilitiesPackage(TheField, ThePols)ΒΆ

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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