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.
