# Singular

#### D.13.4.41 groebnerFan

Procedure from library `tropical.lib` (see tropical_lib).

Usage:
groebnerFan(f); f poly
groebnerFan(I); I ideal

Assume:
I homogeneous

Return:
fan, the Groebner fan of f resp. I

Note:
set printlevel=1 for output during traversal

Example:
 ```LIB "tropical.lib"; ==> Welcome to polymake version ==> Copyright (c) 1997-2015 ==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt) ==> http://www.polymake.org ring r = 0,(x,y,z,w),dp; ideal I = x-2y+3z,3y-4z+5w; groebnerFan(I); ==> _application PolyhedralFan ==> _version 2.2 ==> _type PolyhedralFan ==> ==> AMBIENT_DIM ==> 4 ==> ==> DIM ==> 4 ==> ==> LINEALITY_DIM ==> 1 ==> ==> RAYS ==> -3 1 1 1 # 0 ==> -1 -1 -1 3 # 1 ==> -1 -1 3 -1 # 2 ==> -1 3 -1 -1 # 3 ==> 1 -3 1 1 # 4 ==> 1 1 -3 1 # 5 ==> 1 1 1 -3 # 6 ==> 3 -1 -1 -1 # 7 ==> ==> N_RAYS ==> 8 ==> ==> LINEALITY_SPACE ==> -1 -1 -1 -1 # 0 ==> ==> ORTH_LINEALITY_SPACE ==> 1 -1 0 0 # 0 ==> 1 0 -1 0 # 1 ==> 1 0 0 -1 # 2 ==> ==> F_VECTOR ==> 1 8 12 6 ==> ==> SIMPLICIAL ==> 0 ==> ==> PURE ==> 1 ==> ==> CONES ==> {} # Dimension 1 ==> {0} # Dimension 2 ==> {1} ==> {2} ==> {3} ==> {4} ==> {5} ==> {6} ==> {7} ==> {0 1} # Dimension 3 ==> {0 2} ==> {0 3} ==> {1 4} ==> {2 4} ==> {1 5} ==> {2 6} ==> {3 5} ==> {3 6} ==> {4 7} ==> {5 7} ==> {6 7} ==> {0 1 2 4} # Dimension 4 ==> {0 1 3 5} ==> {0 2 3 6} ==> {1 4 5 7} ==> {2 4 6 7} ==> {3 5 6 7} ==> ==> MAXIMAL_CONES ==> {0 1 2 4} # Dimension 4 ==> {0 1 3 5} ==> {0 2 3 6} ==> {1 4 5 7} ==> {2 4 6 7} ==> {3 5 6 7} ==> ```