AlgebraicFunction(R, F)

algfunc.spad line 257 [edit on github]

• R : Join(Comparable, IntegralDomain)
• F : FunctionSpace(R)

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)