# RealPolynomialUtilitiesPackage(TheField, ThePols)ΒΆ

- 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