|
|
D.16.1.8 tropicalVariety
Syntax:
tropicalVariety( poly g )
tropicalVariety( poly g, number p )
tropicalVariety( ideal I )
tropicalVariety( ideal I, number p )
Assume:
- I homogeneous, ground field are the rational numbers, p prime
Type:
- fan
Purpose:
- the tropical variety of g or the tropical variety of I, either without or with p-adic valuation
Note:
- set printlevel > 0 for status updates on the computation
Example:
| | LIB "gfanlib.so";
ring r = 0,(x,y),dp;
poly g1 = x+y+1;
fan f1 = tropicalVariety(g1);
f1; // tropical line with vertex at (0,0)
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==>
==> AMBIENT_DIM
==> 2
==>
==> DIM
==> 1
==>
==> 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
==>
==> SIMPLICIAL
==> 1
==>
==> PURE
==> 1
==>
==> CONES
==> {} # Dimension 0
==> {0} # Dimension 1
==> {1}
==> {2}
==>
==> MAXIMAL_CONES
==> {0} # Dimension 1
==> {1}
==> {2}
==>
==> MULTIPLICITIES
==> 1 # Dimension 1
==> 1
==> 1
==>
poly g2 = 2x+y+4;
fan f2 = tropicalVariety(g2,number(2));
f2; // tropical line with vertex at (0,1)
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==>
==> AMBIENT_DIM
==> 3
==>
==> DIM
==> 2
==>
==> LINEALITY_DIM
==> 0
==>
==> RAYS
==> -1 -1 -2 # 0
==> 0 -1 0 # 1
==> 0 0 -1 # 2
==> 0 1 1 # 3
==>
==> N_RAYS
==> 4
==>
==> LINEALITY_SPACE
==>
==> ORTH_LINEALITY_SPACE
==> -1 0 0 # 0
==> 0 -1 0 # 1
==> 0 0 -1 # 2
==>
==> F_VECTOR
==> 1 4 3
==>
==> SIMPLICIAL
==> 1
==>
==> PURE
==> 1
==>
==> CONES
==> {} # Dimension 0
==> {0} # Dimension 1
==> {1}
==> {2}
==> {3}
==> {0 1} # Dimension 2
==> {0 2}
==> {0 3}
==>
==> MAXIMAL_CONES
==> {0 1} # Dimension 2
==> {0 2}
==> {0 3}
==>
==> MULTIPLICITIES
==> 1 # Dimension 2
==> 1
==> 1
==>
ring s = 0,x(1..4),wp(1,11,3,19);
ideal I =
2*x(1)^2+3*x(1)*x(2)+24*x(3)*x(4),
8*x(1)^3+x(2)*x(3)*x(4)+18*x(3)^2*x(4);
fan f = tropicalVariety(I,number(3));
f;
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==>
==> AMBIENT_DIM
==> 5
==>
==> DIM
==> 3
==>
==> LINEALITY_DIM
==> 1
==>
==> RAYS
==> -2 -1 1 5 -5 # 0
==> -1 0 -1 1 0 # 1
==> -1 0 1 3 -4 # 2
==> 0 -1 1 1 -1 # 3
==> 0 0 0 -1 1 # 4
==> 0 1 -3 1 1 # 5
==> 0 1 1 5 -7 # 6
==>
==> N_RAYS
==> 7
==>
==> 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 7 7
==>
==> SIMPLICIAL
==> 1
==>
==> PURE
==> 1
==>
==> CONES
==> {} # Dimension 1
==> {0} # Dimension 2
==> {1}
==> {2}
==> {3}
==> {4}
==> {5}
==> {6}
==> {0 1} # Dimension 3
==> {0 2}
==> {0 3}
==> {1 4}
==> {2 4}
==> {1 5}
==> {2 6}
==>
==> MAXIMAL_CONES
==> {0 1} # Dimension 3
==> {0 2}
==> {0 3}
==> {1 4}
==> {2 4}
==> {1 5}
==> {2 6}
==>
==> MULTIPLICITIES
==> 1 # Dimension 3
==> 1
==> 1
==> 1
==> 1
==> 1
==> 1
==>
|
|
Online Manual
