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

  coerce: P -> %

  denom: % -> P

  numer: % -> 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).