The moving line ideal basis of planar rational curves Original Research Article

This paper shows that the ideal of any degree n planar rational curve can be generated by two polynomials that are each linear in x, y and degree n1 and n2 (⩾ n1) in t, n1 + n2 = n. The value of n1 is fixed for a given rational curve, and serves to split all degree n curves into [n2] + 1 equivalence classes. These classes bear on the determinantal form of the implicit equation of the rational curve.