Algebraic Functions

Algebraic functions are functions defined by algebraic equations. There are
two ways of constructing them, either by using rational powers or implicitly.
For rational powers, use ** or the system
functions sqrt and
nthRoot for square and nth roots.
To define an algebraic function implicitly use
rootOf. The following line defines a function
y of x satisfying the equation
y^3 = x*y-y^2-x^3+1

You can manipulate, differentiate or integrate an implicitly defined
algebraic function like any other Axiom function.
Higher powers of algebraic functions are automatically reduced during
calculations.
But denominators are not automatically rationalized.
Use ratDenom to remove the algebraic
quantities from the denominator.