A direct approach to computing the mu-basis of planar rational curves

This paper presents an O(n(2)) algorithm, based on Grobner basis techniques , to compute the mu -basis of a degree n planar rational curve. The prior m ethod involved solving a set of linear equations whose complexity by standa rd numerical methods was O(n(3)). The mu -basis is useful in computing the implicit equation of a parametric curve and can express the implicit equati on in the form of a determinant that is smaller than that obtained by takin g the resultant of the parametric equations. (C) 2001 Academic Press.