gfan.sm1 is a package to compute global and local Grobner fans. See R.Bahloul and N.Takayama, arxiv, math.AG/0412044 and references as to algorithms. At the beginning of the source code gfan.sm1, there are sample inputs cone.sample and cone.sample2. gfan.sm1 works only with polymake 2.0. We provide a web service of computing with polymake 2.0. /@@@polymake.web 1 def is set by default in gfan.sm1. See changelog-ja.tex as to details on the difference between 2.0 and later versions. *cone.sample ; is an example. See the source code. The state polytope is the hexagon. *cone.Wt cone.Lpt {vertices in the output} are weights on the rays of the Grobner cone. *cone.L gives a basis of the linearity space. *cone.Lp gives a basis of the pointed cone. cone.Lpt is the transpose of cone.Lp. *When v is a row vector in an ouput cone, (v cone.Lp cone.W) gives the corresponding weight vector in the full variable space in D *cone.incidence is a list of [[cone num1,facet num1], [cone num2,facet num2]] which means that cone num1 and cone num2 are adjacent and shares the facet num1 and the facet num2 */cone.withGblist 1 def saves the Grobner basis standing for each cone. *Cone descriptions: cone.fan **A facet is given by its normal vector n of a cone. It gives facet num of the cone. **A cone is defined by facet normal vectors n1, n2, ... as n1.x>=0 and n2.x >=0 and ... **facetsv is a list of facets expressed by generators. **nextcid is a list of the adjacent cone numbers. **nextfid is a list of the shared facet numbers. **vertices is the generators of a cone. **inequalities are not necessarily unique.

Nobuki Takayama 2020-11-24