# Singular

#### D.16.1.5 groebnerFan

`Syntax:`
`groebnerFan(` poly g `)`
`groebnerFan(` ideal I `)`
`Assume:`
I homogeneous, ground field is the field of rational numbers
`Type:`
fan
`Purpose:`
the Groebner fan of g or the Groebner fan I
`Note:`
set printlevel > 0 for status updates on the computation
`Example:`
 ```LIB "gfanlib.so"; ring r = 0,(x,y),dp; poly g = x+y+1; fan f = groebnerFan(g); f; ==> _application PolyhedralFan ==> _version 2.2 ==> _type PolyhedralFan ==> ==> AMBIENT_DIM ==> 2 ==> ==> DIM ==> 2 ==> ==> LINEALITY_DIM ==> 0 ==> ==> RAYS ==> -1 0 # 0 ==> 0 -1 # 1 ==> 1 1 # 2 ==> ==> N_RAYS ==> 3 ==> ==> LINEALITY_SPACE ==> ==> ORTH_LINEALITY_SPACE ==> -1 0 # 0 ==> 0 -1 # 1 ==> ==> F_VECTOR ==> 1 3 3 ==> ==> SIMPLICIAL ==> 1 ==> ==> PURE ==> 1 ==> ==> CONES ==> {} # Dimension 0 ==> {0} # Dimension 1 ==> {1} ==> {2} ==> {0 1} # Dimension 2 ==> {0 2} ==> {1 2} ==> ==> MAXIMAL_CONES ==> {0 1} # Dimension 2 ==> {0 2} ==> {1 2} ==> ==> MULTIPLICITIES ==> 1 # Dimension 2 ==> 1 ==> 1 ==> ring s = 0,(x,y,z),dp; ideal I = x2z-y3,x3-y2z-xz2; fan f = groebnerFan(I); ==> // ** redefining f ** f; ==> _application PolyhedralFan ==> _version 2.2 ==> _type PolyhedralFan ==> ==> AMBIENT_DIM ==> 3 ==> ==> DIM ==> 3 ==> ==> LINEALITY_DIM ==> 1 ==> ==> RAYS ==> -5 4 1 # 0 ==> -4 -1 5 # 1 ==> -4 5 -1 # 2 ==> -4 11 -7 # 3 ==> -2 3 -1 # 4 ==> -2 7 -5 # 5 ==> -1 -4 5 # 6 ==> -1 -2 3 # 7 ==> -1 -1 2 # 8 ==> -1 0 1 # 9 ==> -1 2 -1 # 10 ==> 1 -5 4 # 11 ==> 1 -2 1 # 12 ==> 1 -1 0 # 13 ==> 1 4 -5 # 14 ==> 2 -1 -1 # 15 ==> 4 1 -5 # 16 ==> 5 -4 -1 # 17 ==> 7 -2 -5 # 18 ==> 13 -5 -8 # 19 ==> ==> N_RAYS ==> 20 ==> ==> LINEALITY_SPACE ==> -1 -1 -1 # 0 ==> ==> ORTH_LINEALITY_SPACE ==> 1 -1 0 # 0 ==> 1 0 -1 # 1 ==> ==> F_VECTOR ==> 1 20 20 ==> ==> SIMPLICIAL ==> 1 ==> ==> PURE ==> 1 ==> ==> CONES ==> {} # Dimension 1 ==> {0} # Dimension 2 ==> {1} ==> {2} ==> {3} ==> {4} ==> {5} ==> {6} ==> {7} ==> {8} ==> {9} ==> {10} ==> {11} ==> {12} ==> {13} ==> {14} ==> {15} ==> {16} ==> {17} ==> {18} ==> {19} ==> {0 2} # Dimension 3 ==> {0 9} ==> {2 4} ==> {3 5} ==> {1 8} ==> {1 9} ==> {3 10} ==> {4 10} ==> {6 7} ==> {7 8} ==> {5 14} ==> {6 11} ==> {11 12} ==> {12 13} ==> {14 16} ==> {13 17} ==> {15 17} ==> {16 18} ==> {15 19} ==> {18 19} ==> ==> MAXIMAL_CONES ==> {0 2} # Dimension 3 ==> {0 9} ==> {2 4} ==> {3 5} ==> {1 8} ==> {1 9} ==> {3 10} ==> {4 10} ==> {6 7} ==> {7 8} ==> {5 14} ==> {6 11} ==> {11 12} ==> {12 13} ==> {14 16} ==> {13 17} ==> {15 17} ==> {16 18} ==> {15 19} ==> {18 19} ==> ==> MULTIPLICITIES ==> 1 # Dimension 3 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> 1 ==> ```