where f(x,y) is a polynomial in two variables1.
There are many familiar examples of plane curves:
for example, the circle
(x-3)2 + (y-2)2 = 4is a plane curve, as one sees by taking
f(x,y) to be
(x-3)2 + (y-2)2 - 4.
A plane curve is the set of the form
where f(x,y) is a polynomial in two variables1.
There are many familiar examples of plane curves:
for example, the circle
(x-3)2 + (y-2)2 = 4is a plane curve, as one sees by taking
f(x,y) to be
(x-3)2 + (y-2)2 - 4.
The degree of the curve is the total degree of f;
this is defined as the maximum of i+j such that
there is a monomial a xi yj occurring in f with 
.
For example, the plane curve