Singular

LIB "tropical.lib";
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}
==>