# AlgebraicFunction(R, F)ΒΆ

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 `n`th 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 `n`th 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)`