# AlgebraicFunction(R, F)¶

This package provides algebraic functions over an integral domain.

^: (F, Fraction Integer) -> F if R has RetractableTo Integer
x ^ q is x raised to the rational power q.
belong?: BasicOperator -> Boolean
belong?(op) is true if op is an algebraic operator, that is, an nth root or implicit algebraic operator.
definingPolynomial: F -> F if R has RetractableTo Integer
definingPolynomial(f) returns the defining polynomial of f as an element of F. Error: if f is not a kernel.
droot: List F -> OutputForm
droot(l) should be a non-exported function.
inrootof: (SparseUnivariatePolynomial F, F) -> F
inrootof(p, x) should be a non-exported function.
iroot: (R, Integer) -> F if R has RetractableTo Integer
iroot(p, n) should be a non-exported function.
minPoly: Kernel F -> SparseUnivariatePolynomial F if R has RetractableTo Integer
minPoly(k) returns the defining polynomial of k.
operator: BasicOperator -> BasicOperator
operator(op) returns a copy of op with the domain-dependent properties appropriate for F. Error: if op is not an algebraic operator, that is, an nth root or implicit algebraic operator.
rootOf: (SparseUnivariatePolynomial F, Symbol) -> F
rootOf(p, y) returns y such that p(y) = 0. The object returned displays as 'y.
rootSum: (F, SparseUnivariatePolynomial F, Symbol) -> F
rootSum(expr, p, s)