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D.16.1.7 groebnerComplex
Syntax:
groebnerComplex( poly g, number p )
groebnerComplex( ideal I, number p )
Assume:
- I homogeneous, ground field are the rational numbers, p prime number
Type:
- fan
Purpose:
- the Groebner complex of g or the Groebner complex I with respect to the p-adic valuation
Note:
- set printlevel > 0 for status updates on the computation
Example:
| | LIB "gfanlib.so";
ring r = 0,(x,y),dp;
poly g = 2x+y+4;
fan f = groebnerComplex(g,number(2));
f; // single vertex at (0,1)
==> _application PolyhedralFan
==> _version 2.2
==> _type PolyhedralFan
==>
==> AMBIENT_DIM
==> 3
==>
==> DIM
==> 3
==>
==> 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 6 3
==>
==> SIMPLICIAL
==> 1
==>
==> PURE
==> 1
==>
==> CONES
==> {} # Dimension 0
==> {0} # Dimension 1
==> {1}
==> {2}
==> {3}
==> {0 1} # Dimension 2
==> {0 2}
==> {0 3}
==> {1 2}
==> {1 3}
==> {2 3}
==> {0 1 2} # Dimension 3
==> {0 1 3}
==> {0 2 3}
==>
==> MAXIMAL_CONES
==> {0 1 2} # Dimension 3
==> {0 1 3}
==> {0 2 3}
==>
==> MULTIPLICITIES
==> 1 # Dimension 3
==> 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 = groebnerComplex(I,number(3));
==> // ** redefining f **
rays(f); // fan too large to display
==> -2,-1, 1, 5, -5,
==> -2, 3, 1, 3, -7,
==> -1, 0,-1, 1, 0,
==> -1, 0, 1, 3, -4,
==> -1, 1, 0, 2, -3,
==> -1, 3,-2, 0, -1,
==> 0,-3, 1,17,-15,
==> 0,-3, 5,21,-23,
==> 0,-1,-1,-1, 3,
==> 0,-1,-1, 3, -1,
==> 0,-1,-1, 7, -5,
==> 0,-1, 1, 1, -1,
==> 0,-1, 1, 3, -3,
==> 0,-1, 1, 5, -5,
==> 0,-1, 3,-1, -1,
==> 0,-1, 3,11,-13,
==> 0, 0,-1, 0, 1,
==> 0, 0,-1, 1, 0,
==> 0, 0, 0,-1, 1,
==> 0, 0, 0, 1, -1,
==> 0, 0, 1, 1, -2,
==> 0, 0, 1, 2, -3,
==> 0, 0, 1, 3, -4,
==> 0, 1,-3, 1, 1,
==> 0, 1,-1, 0, 0,
==> 0, 1, 0, 1, -2,
==> 0, 1, 1, 1, -3,
==> 0, 1, 1, 5, -7,
==> 0, 2,-1, 0, -1,
==> 0, 2, 0,-1, -1,
==> 0, 3,-1,-1, -1,
==> 0, 3,-1, 1, -3,
==> 0, 3,-1, 3, -5,
==> 0, 5,-3,-3, 1,
==> 0, 5,-3,-1, -1,
==> 0, 5,-3, 1, -3,
==> 0, 7,-5,-1, -1,
==> 0,11,-5, 3, -9,
==> 0,13,-3, 5,-15
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