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# gfanSecondaryFan -- computes the secondary fan of a vector configuration

## Synopsis

• Usage:
F = gfanSecondaryFan L
• Inputs:
• L, a list, of integer vectors
• Optional inputs:
• scale
• symmetry
• unimodular
• Outputs:
• F, an instance of the type Fan, the secondary fan of L

## Description

This method computes the secondary fan of a list of vectors.

 i1 : gfanSecondaryFan {{1,0},{1,1}, {1,2}, {1,2}} o1 = Fan{...1...} o1 : Fan

gfan Documentation

This program computes the secondary fan of a vector configuration. The configuration is given as an ordered list of vectors. In order to compute the secondary fan of a point configuration an additional coordinate of ones must be added. For example {(1,0),(1,1),(1,2),(1,3)}.
Options:
--unimodular:
Use heuristics to search for unimodular triangulation rather than computing the complete secondary fan
--scale value:
Assuming that the first coordinate of each vector is 1, this option will take the polytope in the 1 plane and scale it. The point configuration will be all lattice points in that scaled polytope. The polytope must have maximal dimension. When this option is used the vector configuration must have full rank. This option may be removed in the future.
--restrictingfan value:
Specify the name of a file containing a polyhedral fan in Polymake format. The computation of the Secondary fan will be restricted to this fan. If the --symmetry option is used then this restricting fan must be invariant under the symmetry and the orbits in the file must be with respect to the specified group of symmetries. The orbits of maximal cones of the file are then read in rather than the maximal cones.

--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 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.
--interrupt value:
Interrupt the enumeration after a specified number of facets have been computed (works for usual symmetric traversals, but may not work in general for non-symmetric traversals or for traversals restricted to fans).


## Ways to use gfanSecondaryFan :

• gfanSecondaryFan(List)

## For the programmer

The object gfanSecondaryFan is .