RealRootCharacterizationCategory(TheField, ThePols)¶

reclos.spad line 170 [edit on github]

TheField: Join(OrderedRing, Field)
ThePols: UnivariatePolynomialCategory TheField

RealRootCharacterizationCategory provides common access functions for all real root codings.

=: (%, %) -> Boolean: from BasicType

~=: (%, %) -> Boolean: from BasicType

allRootsOf: ThePols -> List %: allRootsOf(pol) creates all the roots of pol in the Real Closure, assumed in order.

approximate: (ThePols, %, TheField) -> TheField: approximate(term, root, prec) gives an approximation of term over root with precision prec

coerce: % -> OutputForm: from CoercibleTo OutputForm

definingPolynomial: % -> ThePols: definingPolynomial(aRoot) gives a polynomial such that definingPolynomial(aRoot).aRoot = 0

latex: % -> String: from SetCategory

negative?: (ThePols, %) -> Boolean: negative?(pol, aRoot) answers if pol interpreted as aRoot is negative

positive?: (ThePols, %) -> Boolean: positive?(pol, aRoot) answers if pol interpreted as aRoot is positive

recip: (ThePols, %) -> Union(ThePols, failed): recip(pol, aRoot) tries to inverse pol interpreted as aRoot

relativeApprox: (ThePols, %, TheField) -> TheField: approximate(term, root, prec) gives an approximation of term over root with precision prec

rootOf: (ThePols, PositiveInteger) -> Union(%, failed): rootOf(pol, n) gives the nth root for the order of the Real Closure

sign: (ThePols, %) -> Integer: sign(pol, aRoot) gives the sign of pol interpreted as aRoot

zero?: (ThePols, %) -> Boolean: zero?(pol, aRoot) answers if pol interpreted as aRoot is 0

CoercibleTo OutputForm