Resolution Global GMS ES Strata Build. Blocks Comb. Appl. HCA Proving Arrangements Branches Classify Coding Deformations Equidim Part Existence Finite Groups Flatness Genus Hilbert Series Membership Nonnormal Locus Normalization Primdec Puiseux Plane Curves Saturation Solving Space Curves Spectrum	Symbolic Numerical Solving Solving polynomial systems using Gröbner bases and triangular sets: Input: Zero-dimensional system f1 ,..., fk in K[x1 ,..., xn] Output: Complex roots of f1 = ... = fk = 0 The algorithm proceeds in 3 steps: Step 1: Compute a reduced lexicographical Gröbner basis of the ideal I. Step 2: Compute a triangular system T1 ,..., Ts . V(I) is the union of the V(Ti ). Step 3: Use a numerical solver (e.g. Laguerre's method) to find all zeros of Ti , i=1,..., s .
KL, 06/03	http://www.singular.uni-kl.de