This method intersects a list of tropical hypersurfaces. The input is a list of polynomials whose tropicalizations give the hypersurfaces.
i1 : QQ[x,y]; |
i2 : gfanTropicalHyperSurface(x+y) o2 = (Fan{...1...}, {1}) o2 : Sequence |
i3 : gfanTropicalHyperSurface(x+y+1) o3 = (Fan{...1...}, {1, 1, 1}) o3 : Sequence |
i4 : gfanTropicalIntersection {x+y, x+y+1} o4 = (Fan{...1...}, {1}) o4 : Sequence |
gfan Documentation This program computes the set theoretical intersection of a set of tropical hypersurfaces (or to be precise, their common refinement as a fan). The input is a list of polynomials with each polynomial defining a hypersurface. Considering tropical hypersurfaces as fans, the intersection can be computed as the common refinement of these. Thus the output is a fan whose support is the intersection of the tropical hypersurfaces.Options:-t: Note that the input polynomials generate an ideal. This option will make the program choose a relative interior point for each listed output cone and check if its initial ideal contains a monomial. The actual check is done on a homogenization of the input ideal, but this does not affect the result.--tplane: This option intersects the resulting fan with the plane x_0=-1, where x_0 is the first variable. To simplify the implementation the output is actually the common refinement with the non-negative half space. This means that "stuff at infinity" (where x_0=0) is not removed.--symmetryPrinting: Parse a group of symmetries after the input has been read. Used when printing with --incidence.--symmetryExploit: Restrict computation to the closed lexicographic fundamental domain of the specified symmetry group. This overwrites --restrict.--nocones: Tells the program not to output the CONES and MAXIMAL_CONES sections, but still output CONES_COMPRESSED and MAXIMAL_CONES_COMPRESSED if --symmetry is used.--restrict: Restrict the computation to a full-dimensional cone given by a list of marked polynomials. The cone is the closure of all weight vectors choosing these marked terms.--stable: Find the stable intersection of the input polynomials using tropical intersection theory. This can be slow. Most other options are ignored.
The object gfanTropicalIntersection is a method function with options.