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

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

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

CoercibleTo(OutputForm)