PolynomialRoots(E, V, R, P, F)

manip.spad line 39 [edit on github]

• E : OrderedAbelianMonoidSup
• V : OrderedSet
• R : IntegralDomain
• P : PolynomialCategory(R, E, V)
• F : Field with

  numer : % -> P

  denom : % -> P

  coerce : P -> %

computes n-th roots of quotients of multivariate polynomials

froot : (F, NonNegativeInteger) -> Record(exponent : NonNegativeInteger, coef : F, radicand : F) if R has GcdDomain

froot(f, n) returns [m, c, r] such that f^(1/n) = c * r^(1/m).

nthr : (P, NonNegativeInteger) -> Record(exponent : NonNegativeInteger, coef : P, radicand : List(P))

nthr(p, n) should be local but conditional

qroot : (Fraction(Integer), NonNegativeInteger) -> Record(exponent : NonNegativeInteger, coef : F, radicand : F)

qroot(f, n) returns [m, c, r] such that f^(1/n) = c * r^(1/m).

rroot : (R, NonNegativeInteger) -> Record(exponent : NonNegativeInteger, coef : F, radicand : F)

rroot(f, n) returns [m, c, r] such that f^(1/n) = c * r^(1/m).