It is important to distinguish two different forms of the quartic.

Thus the intersection curve, which theory says must be a quartic, contains four double points.

Explicitly, the four points are for the four roots of the quartic.

In other words, a quartic graph is a 4-regular graph.

It can also easily be generalized to cubic, quartic and higher power residues.

Another example is ray-tracing against quartic surfaces such as tori.

It requires the appropriate solution of a quartic equation.

The integral of a cubic function is a quartic function.

This potential is explored in detail in the article on the quartic interaction.

For a different parametrization and resulting quartic, see Lawrence.

He also acknowledges that it was Ferrari who found a way of solving quartic equations.

He proposed ways to solve cubic and quartic equations.

The fact that this is a quartic invariant, rather than quadratic, has an important consequence.

One can solve a quartic by factoring it into a product of two quadratics.

The simplest interaction is the quartic self-interaction, with an action:

Some curves have higher order twists such as cubic and quartic twists.

If on the other hand the base field is finite, then it is said to be an arithmetic quartic surface.

Solving a quartic (solution too large to include here):

Quartic integrals of the non-functional kind are easier to solve so there is hope for the future.

It is known that quartic graphs have an even number of Hamiltonian decompositions.

The bifolium is a quartic plane curve of the equation:

There is a more complicated solution for the general cubic equation and quartic equation.

The Higgs mechanism is based on a symmetry-breaking scalar field potential, such as the quartic.

More specifically there are two closely related types of quartic surface: affine and projective.

It can be defined by a quartic equation: