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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
==> 

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