In this period he published high-quality work on algebraic curves.

See also algebraic curve for more specific examples of curves.

In general, an algebraic curve that passes through these two points is called circular.

The astroid is therefore a real algebraic curve of degree six.

Her doctoral work was on the topology of algebraic curves.

The projective line is a fundamental example of an algebraic curve.

However, in the case of algebraic curves it is very common to consider number systems more general than the reals.

Now, are intersection points of with an algebraic curve.

Another viewpoint is to model moving objects as a locus of algebraic curves.

The concept of a focus can be generalized to arbitrary algebraic curves.

In either form, it is a plane algebraic curve of genus zero.

This is how the theory could be applied to the local zeta-function of an algebraic curve.

Neither are algebraic curves or surfaces defined over fields other than the complex numbers.

Algebraic curves were studied extensively since the 18th century.

This leads to the most general definition of an algebraic curve:

Historically, singularities were first noticed in the study of algebraic curves.

His early work studied singularities on algebraic curves and surfaces.

These definitions also apply to algebraic curves (see below).

However, in the case of algebraic curves it is very common not to restrict the curve to having points only defined over the real numbers.

Suppose that C is a smooth algebraic curve of genus g.

Korchmaros On algebraic curves over a finite field with many rational points.

He is an expert in number theory and cryptography, especially as they relate to algebraic curves.

A package which contains a number of algorithms for computing with algebraic curves.

For more general algebraic curves, lines could also be:

For example, a divisor on an algebraic curve is a formal sum of its closed points.