Implicitization of a general union of parametric varieties. (English) Zbl 0969.14041
Summary: We reconduct the computation of the equations defining a union \(V\) of parametric varieties, up to a given degree \(d\), to the computation of the equations, of degree \(\leq d\), vanishing on a finite set of points of \(V\). If \(V\) is general this gives a new algorithm for implicitizing \(V\). We have compared the implementation of this algorithm with the Hilbert-driven elimination algorithm included in the software packages CoCoA 3.7 and Singular 1.2, obtaining significant time savings. Moreover, the implementation of the algorithm leads to two intriguing conjectures on the natural number of generators of the union of general parametric curves or surfaces.
MSC:
| 14Q15 | Computational aspects of higher-dimensional varieties |
| 68W40 | Analysis of algorithms |
| 68W30 | Symbolic computation and algebraic computation |
| 14-04 | Software, source code, etc. for problems pertaining to algebraic geometry |
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