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D.13.6.42 groebnerComplex

Procedure from library tropical.lib (see tropical_lib).

Usage:
groebnerComplex(f,p); f poly, p number
groebnerComplex(I,p); I ideal, p number

Assume:
I homogeneous, p prime number

Return:
fan, the Groebner complex of f resp. I with respect to 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;
groebnerComplex(I,number(2));
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==> 
==> AMBIENT_DIM
==> 5
==> 
==> DIM
==> 5
==> 
==> LINEALITY_DIM
==> 1
==> 
==> RAYS
==> -2 -1 1 -1 1	# 0
==> -1 1 -1 1 -1	# 1
==> 0 -3 1 1 1	# 2
==> 0 -1 -1 -1 3	# 3
==> 0 -1 -1 3 -1	# 4
==> 0 -1 3 -1 -1	# 5
==> 0 1 -3 1 1	# 6
==> 0 1 1 -3 1	# 7
==> 0 1 1 1 -3	# 8
==> 0 3 -1 -1 -1	# 9
==> 
==> N_RAYS
==> 10
==> 
==> 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 10 23 22 8
==> 
==> SIMPLICIAL
==> 0
==> 
==> PURE
==> 1
==> 
==> CONES
==> {}	# Dimension 1
==> {0}	# Dimension 2
==> {1}
==> {2}
==> {3}
==> {4}
==> {5}
==> {6}
==> {7}
==> {8}
==> {9}
==> {0 1}	# Dimension 3
==> {0 2}
==> {0 3}
==> {0 5}
==> {0 7}
==> {1 4}
==> {1 6}
==> {1 8}
==> {1 9}
==> {2 3}
==> {2 4}
==> {2 5}
==> {2 7}
==> {3 6}
==> {4 6}
==> {3 7}
==> {4 8}
==> {5 7}
==> {5 8}
==> {6 8}
==> {6 9}
==> {7 9}
==> {8 9}
==> {0 1 2 4}	# Dimension 4
==> {0 1 3 6}
==> {0 1 5 8}
==> {0 1 7 9}
==> {0 2 3}
==> {0 2 5}
==> {0 2 7}
==> {0 3 7}
==> {0 5 7}
==> {1 4 6}
==> {1 4 8}
==> {1 6 8}
==> {1 6 9}
==> {1 8 9}
==> {2 3 4 6}
==> {2 4 5 8}
==> {2 3 7}
==> {2 5 7}
==> {4 6 8}
==> {3 6 7 9}
==> {5 7 8 9}
==> {6 8 9}
==> {0 1 2 3 4 6}	# Dimension 5
==> {0 1 2 4 5 8}
==> {0 1 3 6 7 9}
==> {0 1 5 7 8 9}
==> {0 2 3 7}
==> {0 2 5 7}
==> {1 4 6 8}
==> {1 6 8 9}
==> 
==> MAXIMAL_CONES
==> {0 1 2 3 4 6}	# Dimension 5
==> {0 1 2 4 5 8}
==> {0 1 3 6 7 9}
==> {0 1 5 7 8 9}
==> {0 2 3 7}
==> {0 2 5 7}
==> {1 4 6 8}
==> {1 6 8 9}
==> 
groebnerComplex(I,number(3));
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==> 
==> AMBIENT_DIM
==> 5
==> 
==> DIM
==> 5
==> 
==> LINEALITY_DIM
==> 1
==> 
==> RAYS
==> -2 -1 -1 1 1	# 0
==> -2 1 1 -1 -1	# 1
==> 0 -3 1 1 1	# 2
==> 0 -1 -1 -1 3	# 3
==> 0 -1 -1 3 -1	# 4
==> 0 -1 3 -1 -1	# 5
==> 0 1 -3 1 1	# 6
==> 0 1 1 -3 1	# 7
==> 0 1 1 1 -3	# 8
==> 0 3 -1 -1 -1	# 9
==> 
==> N_RAYS
==> 10
==> 
==> 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 10 23 22 8
==> 
==> SIMPLICIAL
==> 0
==> 
==> PURE
==> 1
==> 
==> CONES
==> {}	# Dimension 1
==> {0}	# Dimension 2
==> {1}
==> {2}
==> {3}
==> {4}
==> {5}
==> {6}
==> {7}
==> {8}
==> {9}
==> {0 1}	# Dimension 3
==> {0 2}
==> {0 3}
==> {0 4}
==> {0 6}
==> {1 5}
==> {1 7}
==> {1 8}
==> {1 9}
==> {2 3}
==> {2 4}
==> {2 5}
==> {2 6}
==> {3 6}
==> {4 6}
==> {3 7}
==> {4 8}
==> {5 7}
==> {5 8}
==> {7 8}
==> {6 9}
==> {7 9}
==> {8 9}
==> {0 1 2 5}	# Dimension 4
==> {0 1 3 7}
==> {0 1 4 8}
==> {0 1 6 9}
==> {0 2 3}
==> {0 2 4}
==> {0 2 6}
==> {0 3 6}
==> {0 4 6}
==> {1 5 7}
==> {1 5 8}
==> {1 7 8}
==> {1 7 9}
==> {1 8 9}
==> {2 3 5 7}
==> {2 4 5 8}
==> {2 3 6}
==> {2 4 6}
==> {5 7 8}
==> {3 6 7 9}
==> {4 6 8 9}
==> {7 8 9}
==> {0 1 2 3 5 7}	# Dimension 5
==> {0 1 2 4 5 8}
==> {0 1 3 6 7 9}
==> {0 1 4 6 8 9}
==> {0 2 3 6}
==> {0 2 4 6}
==> {1 5 7 8}
==> {1 7 8 9}
==> 
==> MAXIMAL_CONES
==> {0 1 2 3 5 7}	# Dimension 5
==> {0 1 2 4 5 8}
==> {0 1 3 6 7 9}
==> {0 1 4 6 8 9}
==> {0 2 3 6}
==> {0 2 4 6}
==> {1 5 7 8}
==> {1 7 8 9}
==> 
groebnerComplex(I,number(5));
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==> 
==> AMBIENT_DIM
==> 5
==> 
==> DIM
==> 5
==> 
==> LINEALITY_DIM
==> 1
==> 
==> RAYS
==> -4 -1 -1 -1 3	# 0
==> 0 -3 1 1 1	# 1
==> 0 -1 -1 -1 3	# 2
==> 0 -1 -1 3 -1	# 3
==> 0 -1 3 -1 -1	# 4
==> 0 1 -3 1 1	# 5
==> 0 1 1 -3 1	# 6
==> 0 1 1 1 -3	# 7
==> 0 3 -1 -1 -1	# 8
==> 
==> N_RAYS
==> 9
==> 
==> 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 9 20 18 6
==> 
==> SIMPLICIAL
==> 0
==> 
==> PURE
==> 1
==> 
==> CONES
==> {}	# Dimension 1
==> {0}	# Dimension 2
==> {1}
==> {2}
==> {3}
==> {4}
==> {5}
==> {6}
==> {7}
==> {8}
==> {0 1}	# Dimension 3
==> {0 2}
==> {0 3}
==> {0 4}
==> {0 5}
==> {0 6}
==> {0 7}
==> {0 8}
==> {1 2}
==> {1 3}
==> {1 4}
==> {2 5}
==> {3 5}
==> {2 6}
==> {3 7}
==> {4 6}
==> {4 7}
==> {5 8}
==> {6 8}
==> {7 8}
==> {0 1 2}	# Dimension 4
==> {0 1 3}
==> {0 1 4}
==> {0 2 5}
==> {0 3 5}
==> {0 2 6}
==> {0 3 7}
==> {0 4 6}
==> {0 4 7}
==> {0 5 8}
==> {0 6 8}
==> {0 7 8}
==> {1 2 3 5}
==> {1 2 4 6}
==> {1 3 4 7}
==> {2 5 6 8}
==> {3 5 7 8}
==> {4 6 7 8}
==> {0 1 2 3 5}	# Dimension 5
==> {0 1 2 4 6}
==> {0 1 3 4 7}
==> {0 2 5 6 8}
==> {0 3 5 7 8}
==> {0 4 6 7 8}
==> 
==> MAXIMAL_CONES
==> {0 1 2 3 5}	# Dimension 5
==> {0 1 2 4 6}
==> {0 1 3 4 7}
==> {0 2 5 6 8}
==> {0 3 5 7 8}
==> {0 4 6 7 8}
==> 
groebnerComplex(I,number(7));
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==> 
==> AMBIENT_DIM
==> 5
==> 
==> DIM
==> 5
==> 
==> LINEALITY_DIM
==> 1
==> 
==> RAYS
==> -1 0 0 0 0	# 0
==> 0 -3 1 1 1	# 1
==> 0 -1 -1 -1 3	# 2
==> 0 -1 -1 3 -1	# 3
==> 0 -1 3 -1 -1	# 4
==> 0 1 -3 1 1	# 5
==> 0 1 1 -3 1	# 6
==> 0 1 1 1 -3	# 7
==> 0 3 -1 -1 -1	# 8
==> 
==> N_RAYS
==> 9
==> 
==> 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 9 20 18 6
==> 
==> SIMPLICIAL
==> 0
==> 
==> PURE
==> 1
==> 
==> CONES
==> {}	# Dimension 1
==> {0}	# Dimension 2
==> {1}
==> {2}
==> {3}
==> {4}
==> {5}
==> {6}
==> {7}
==> {8}
==> {0 1}	# Dimension 3
==> {0 2}
==> {0 3}
==> {0 4}
==> {0 5}
==> {0 6}
==> {0 7}
==> {0 8}
==> {1 2}
==> {1 3}
==> {1 4}
==> {2 5}
==> {3 5}
==> {2 6}
==> {3 7}
==> {4 6}
==> {4 7}
==> {5 8}
==> {6 8}
==> {7 8}
==> {0 1 2}	# Dimension 4
==> {0 1 3}
==> {0 1 4}
==> {0 2 5}
==> {0 3 5}
==> {0 2 6}
==> {0 3 7}
==> {0 4 6}
==> {0 4 7}
==> {0 5 8}
==> {0 6 8}
==> {0 7 8}
==> {1 2 3 5}
==> {1 2 4 6}
==> {1 3 4 7}
==> {2 5 6 8}
==> {3 5 7 8}
==> {4 6 7 8}
==> {0 1 2 3 5}	# Dimension 5
==> {0 1 2 4 6}
==> {0 1 3 4 7}
==> {0 2 5 6 8}
==> {0 3 5 7 8}
==> {0 4 6 7 8}
==> 
==> MAXIMAL_CONES
==> {0 1 2 3 5}	# Dimension 5
==> {0 1 2 4 6}
==> {0 1 3 4 7}
==> {0 2 5 6 8}
==> {0 3 5 7 8}
==> {0 4 6 7 8}
==>