next | previous | forward | backward | up | index | toc

# gfanResultantFan -- Tropical variety of the sparse (toric) resultant variety.

## Synopsis

• Usage:
gfanRenderStaircase(L)
• Inputs:
• Optional inputs:
• special
• vectorinput

## Description

This method computes the tropical variety of a sparse (toric) resultant variety.

gfan Documentation

This program computes the resultant fan as defined in "Computing Tropical Resultants" by Jensen and Yu. The input is a polynomial ring followed by polynomials, whose coefficients are ignored. The output is the fan of coefficients such that the input system has a tropical solution.
Options:
--codimension:
Compute only the codimension of the resultant fan and return.

--symmetry:
Tells the program to read in generators for a group of symmetries (subgroup of $S_n$) after having read in the vector configuration. The program DOES NOT checks that the configuration stays fixed when permuting the variables with respect to elements in the group. The output is grouped according to the symmetry.

--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.

--special:
Read in a zero-one vector from the standard input and specialize all variables with a one. That is, compute the stable intersection of the resultant fan with the subspace where the variables with a one in the vector are forced to zero. AT THE MOMENT ALSO A RELATIVE INTERIOR POINT OF A STARTING CONE IS READ.

--vectorinput:
Read in a list of point configurations instead of a polynomial ring and a list of polynomials.

--projection:
Use the projection method to compute the resultant fan. This works only if the resultant fan is a hypersurface. If this option is combined with --special, then the output fan lives in the subspace of the non-specialized coordinates.



## Ways to use gfanResultantFan :

• gfanResultantFan(List)

## For the programmer

The object gfanResultantFan is .