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.