A curve is algebraic
when its defining Cartesian equation is algebraic, that is a polynomial in x and y. The
order or degree of the curve is the maximum degree of each of its terms xi yj.
There are several examples of bicircular quartics.
And so on, a tricircular algebraic curve passes three times through the points (1, i) and (1, -i). In this case the highest degree of the Cartesian equation is divisible by (x2 + y2)3.
An example of a tricircular algebraic curve is the sextic Watt's curve.
When a curve is not algebraic, we call the curve (and its function) transcendental.
In the case a function is sufficiently sophisticated it is said to be a special function.