Let be its homogeneous defining ideal. Suppose that are two homogeneous polynomials such that is a regular sequence. D is called the link of C via the complete intersection X .
Linkages are an important technique in the theory of curves.
This curve has degree five. After we find the equations of D , we then see whether the result is a nonsingular curve. The ideal defining the curve D is the ideal quotient This is accomplished in Macaulay using the quotient command. The following list of remarks refers to the Macaulay session below. In this example we use polynomial expressions using the generators for the ideal .