RealRootCharacterizationCategory(TheField, ThePols)ΒΆ

reclos.spad line 170 [edit on github]

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

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

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

BasicType

CoercibleTo OutputForm

SetCategory