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