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D.13.6.39 tropicalVariety
Procedure from library tropical.lib (see tropical_lib).
- Usage:
- tropicalVariety(f[,p]); f poly, p optional number
tropicalVariety(I[,p]); I ideal, p optional number
- Assume:
- I homogeneous, p prime number
- Return:
- fan, the tropical variety of f resp. I with respect to the trivial valuation or the p-adic valuation
- Note:
- set printlevel=1 for output during traversal
Example:
| | LIB "tropical.lib";
ring r = 0,(x,y,z,w),dp;
ideal I = x-2y+3z,3y-4z+5w;
tropicalVariety(I);
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==>
==> AMBIENT_DIM
==> 4
==>
==> DIM
==> 2
==>
==> LINEALITY_DIM
==> 1
==>
==> RAYS
==> -3 1 1 1 # 0
==> 1 -3 1 1 # 1
==> 1 1 -3 1 # 2
==> 1 1 1 -3 # 3
==>
==> N_RAYS
==> 4
==>
==> 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 4
==>
==> SIMPLICIAL
==> 1
==>
==> PURE
==> 1
==>
==> CONES
==> {} # Dimension 1
==> {0} # Dimension 2
==> {1}
==> {2}
==> {3}
==>
==> MAXIMAL_CONES
==> {0} # Dimension 2
==> {1}
==> {2}
==> {3}
==>
tropicalVariety(I,number(2));
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==>
==> AMBIENT_DIM
==> 5
==>
==> DIM
==> 3
==>
==> LINEALITY_DIM
==> 1
==>
==> RAYS
==> -2 -1 1 -1 1 # 0
==> -1 1 -1 1 -1 # 1
==> 0 -3 1 1 1 # 2
==> 0 1 -3 1 1 # 3
==> 0 1 1 -3 1 # 4
==> 0 1 1 1 -3 # 5
==>
==> N_RAYS
==> 6
==>
==> LINEALITY_SPACE
==> 0 -1 -1 -1 -1 # 0
==>
==> ORTH_LINEALITY_SPACE
==> -1 0 0 0 0 # 0
==> 0 1 -1 0 0 # 1
==> 0 1 0 -1 0 # 2
==> 0 1 0 0 -1 # 3
==>
==> F_VECTOR
==> 1 6 5
==>
==> SIMPLICIAL
==> 1
==>
==> PURE
==> 1
==>
==> CONES
==> {} # Dimension 1
==> {0} # Dimension 2
==> {1}
==> {2}
==> {3}
==> {4}
==> {5}
==> {0 1} # Dimension 3
==> {0 2}
==> {0 4}
==> {1 3}
==> {1 5}
==>
==> MAXIMAL_CONES
==> {0 1} # Dimension 3
==> {0 2}
==> {0 4}
==> {1 3}
==> {1 5}
==>
tropicalVariety(I,number(3));
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==>
==> AMBIENT_DIM
==> 5
==>
==> DIM
==> 3
==>
==> LINEALITY_DIM
==> 1
==>
==> RAYS
==> -2 -1 -1 1 1 # 0
==> -2 1 1 -1 -1 # 1
==> 0 -3 1 1 1 # 2
==> 0 1 -3 1 1 # 3
==> 0 1 1 -3 1 # 4
==> 0 1 1 1 -3 # 5
==>
==> N_RAYS
==> 6
==>
==> LINEALITY_SPACE
==> 0 -1 -1 -1 -1 # 0
==>
==> ORTH_LINEALITY_SPACE
==> -1 0 0 0 0 # 0
==> 0 1 -1 0 0 # 1
==> 0 1 0 -1 0 # 2
==> 0 1 0 0 -1 # 3
==>
==> F_VECTOR
==> 1 6 5
==>
==> SIMPLICIAL
==> 1
==>
==> PURE
==> 1
==>
==> CONES
==> {} # Dimension 1
==> {0} # Dimension 2
==> {1}
==> {2}
==> {3}
==> {4}
==> {5}
==> {0 1} # Dimension 3
==> {0 2}
==> {0 3}
==> {1 4}
==> {1 5}
==>
==> MAXIMAL_CONES
==> {0 1} # Dimension 3
==> {0 2}
==> {0 3}
==> {1 4}
==> {1 5}
==>
tropicalVariety(I,number(5));
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==>
==> AMBIENT_DIM
==> 5
==>
==> DIM
==> 3
==>
==> LINEALITY_DIM
==> 1
==>
==> RAYS
==> -4 -1 -1 -1 3 # 0
==> 0 -3 1 1 1 # 1
==> 0 1 -3 1 1 # 2
==> 0 1 1 -3 1 # 3
==> 0 1 1 1 -3 # 4
==>
==> N_RAYS
==> 5
==>
==> LINEALITY_SPACE
==> 0 -1 -1 -1 -1 # 0
==>
==> ORTH_LINEALITY_SPACE
==> -1 0 0 0 0 # 0
==> 0 1 -1 0 0 # 1
==> 0 1 0 -1 0 # 2
==> 0 1 0 0 -1 # 3
==>
==> F_VECTOR
==> 1 5 4
==>
==> SIMPLICIAL
==> 1
==>
==> PURE
==> 1
==>
==> CONES
==> {} # Dimension 1
==> {0} # Dimension 2
==> {1}
==> {2}
==> {3}
==> {4}
==> {0 1} # Dimension 3
==> {0 2}
==> {0 3}
==> {0 4}
==>
==> MAXIMAL_CONES
==> {0 1} # Dimension 3
==> {0 2}
==> {0 3}
==> {0 4}
==>
tropicalVariety(I,number(7));
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==>
==> AMBIENT_DIM
==> 5
==>
==> DIM
==> 3
==>
==> LINEALITY_DIM
==> 1
==>
==> RAYS
==> -1 0 0 0 0 # 0
==> 0 -3 1 1 1 # 1
==> 0 1 -3 1 1 # 2
==> 0 1 1 -3 1 # 3
==> 0 1 1 1 -3 # 4
==>
==> N_RAYS
==> 5
==>
==> LINEALITY_SPACE
==> 0 -1 -1 -1 -1 # 0
==>
==> ORTH_LINEALITY_SPACE
==> -1 0 0 0 0 # 0
==> 0 1 -1 0 0 # 1
==> 0 1 0 -1 0 # 2
==> 0 1 0 0 -1 # 3
==>
==> F_VECTOR
==> 1 5 4
==>
==> SIMPLICIAL
==> 1
==>
==> PURE
==> 1
==>
==> CONES
==> {} # Dimension 1
==> {0} # Dimension 2
==> {1}
==> {2}
==> {3}
==> {4}
==> {0 1} # Dimension 3
==> {0 2}
==> {0 3}
==> {0 4}
==>
==> MAXIMAL_CONES
==> {0 1} # Dimension 3
==> {0 2}
==> {0 3}
==> {0 4}
==>
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