Implicit Curves

Axiom has facilities for graphing a non-singular algebraic curve in a rectangular region of the plane. An algebraic curve is a curve defined by a polynomial equation p(x,y)=0. Non-singular means that the curve is "smooth" in that it does not cross itself or come to a point (cusp). Algebraically, this means that for any point (a,b) on the curve (i.e. a point such that p(a,b)=0), the partial derivatives dp/dx(a,b) and dp/dy(a,b) are not both zero. We require that the polynomial have rational or integral coefficients. Here is a Cartesian ovals algebraic curve example:

A range must be declared for each variable specified in the algebraic curve equation.