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D.13.6.40 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";
==> Welcome to polymake version
==> Copyright (c) 1997-2015
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
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}
==>