Numerical calculation of H-bases for positive dimensional varieties
Barry H. Dayton · 2012
A symbolic-numeric method for calculating an H-basis for the ideal of a positive dimensional complex affine algebraic variety, possibly defined numerically, is given. H-bases for ideals I in I, introduced by Macaulay and later studied by Möller and Sauer, are an analog of Gröbner bases with respect to a global degree ordering: f is an element of I of total degree n if and only f is a C-linear combination of polynomials of total degree n or less which are monomial multiples of members of the H-basis. The method uses the interplay of local and global duality.