| Classify |
| Coding |
| Deformations |
| Equidim Part |
| Existence |
| Finite Groups |
| Flatness |
| Genus |
| Hilbert Series |
| Membership |
| Monodromy |
| Normalization |
| Primdec |
| Puiseux |
| Plane Curves |
| Solving |
| Space Curves |
| Spectrum |
Solving polynomial systems using Gröbner bases and triangular sets:
| Input: | Zero-dimensional system f1 ,..., fk in K[x1 ,..., xn] |
| Output: | Complex roots of |
| 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 . |
| Timings |