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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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