Name
Abstract | ||
|---|---|---|
We present two algorithms that compute the Newton polytope of a polynomial defining a hypersurface H in C^n using numerical computation. The first algorithm assumes that we may only compute values of f - this may occur if f is given as a straight-line program, as a determinant, or as an oracle. The second algorithm assumes that H is represented numerically via a witness set. That is, it computes the Newton polytope of H using only the ability to compute numerical representatives of its intersections with lines. Such witness set representations are readily obtained when H is the image of a map or is a discriminant. We use the second algorithm to compute a face of the Newton polytope of the L\"uroth invariant, as well as its restriction to that face. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/s11786-014-0189-6 | Mathematics in Computer Science |
Keywords | Field | DocType |
Hypersurface, Polynomial system, Newton polytope, Numerical algebraic geometry, Witness set | Discrete mathematics,Combinatorics,Polynomial,Discriminant,Numerical algebraic geometry,Polytope,Hypersurface,Invariant (mathematics),Witness set,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
8 | 2 | 1661-8270 |
Citations | PageRank | References |
1 | 0.58 | 13 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jonathan D. Hauenstein | 1 | 269 | 37.65 |
| Frank Sottile | 2 | 26 | 5.10 |