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D.13.4.36 groebnerCone
Procedure from library tropical.lib (see tropical_lib).
- Usage:
- groebnerCone(I,w); I ideal or poly, w intvec or bigintmat
- Assume:
- I a reduced standard basis and w contained in the maximal Groebner cone
- Return:
- cone, the Groebner cone of I with respect to w
Example:
| | LIB "tropical.lib";
==> Welcome to polymake version
==> Copyright (c) 1997-2015
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
LIB "poly.lib";
==> // ** redefining bino (LIB "poly.lib";)
==> // ** redefining hilbPoly (LIB "poly.lib";)
==> // ** redefining hilbPoly (LIB "poly.lib";)
==> // ** redefining substitute (LIB "poly.lib";)
==> // ** redefining substitute (LIB "poly.lib";)
==> // ** redefining cyclic (LIB "poly.lib";)
==> // ** redefining cyclic (LIB "poly.lib";)
==> // ** redefining elemSymmPoly (LIB "poly.lib";)
==> // ** redefining elemSymmPoly (LIB "poly.lib";)
==> // ** redefining elemSymmId (LIB "poly.lib";)
==> // ** redefining elemSymmId (LIB "poly.lib";)
==> // ** redefining katsura (LIB "poly.lib";)
==> // ** redefining katsura (LIB "poly.lib";)
==> // ** redefining kat_var (LIB "poly.lib";)
==> // ** redefining kat_var (LIB "poly.lib";)
==> // ** redefining freerank (LIB "poly.lib";)
==> // ** redefining freerank (LIB "poly.lib";)
==> // ** redefining is_zero (LIB "poly.lib";)
==> // ** redefining is_zero (LIB "poly.lib";)
==> // ** redefining maxcoef (LIB "poly.lib";)
==> // ** redefining maxcoef (LIB "poly.lib";)
==> // ** redefining maxdeg (LIB "poly.lib";)
==> // ** redefining maxdeg (LIB "poly.lib";)
==> // ** redefining maxdeg1 (LIB "poly.lib";)
==> // ** redefining maxdeg1 (LIB "poly.lib";)
==> // ** redefining mindeg (LIB "poly.lib";)
==> // ** redefining mindeg (LIB "poly.lib";)
==> // ** redefining mindeg1 (LIB "poly.lib";)
==> // ** redefining mindeg1 (LIB "poly.lib";)
==> // ** redefining normalize (LIB "poly.lib";)
==> // ** redefining normalize (LIB "poly.lib";)
==> // ** redefining rad_con (LIB "poly.lib";)
==> // ** redefining rad_con (LIB "poly.lib";)
==> // ** redefining lcm (LIB "poly.lib";)
==> // ** redefining lcm (LIB "poly.lib";)
==> // ** redefining content (LIB "poly.lib";)
==> // ** redefining content (LIB "poly.lib";)
==> // ** redefining mod2id (LIB "poly.lib";)
==> // ** redefining mod2id (LIB "poly.lib";)
==> // ** redefining id2mod (LIB "poly.lib";)
==> // ** redefining id2mod (LIB "poly.lib";)
==> // ** redefining subrInterred (LIB "poly.lib";)
==> // ** redefining subrInterred (LIB "poly.lib";)
==> // ** redefining newtonDiag (LIB "poly.lib";)
==> // ** redefining newtonDiag (LIB "poly.lib";)
ring r = 0,(x,y,z),dp;
ideal I = cyclic(3);
option(redSB);
ideal stdI = std(I);
// w lies in the interior of a maximal Groebner cone
intvec w = 3,2,1;
cone CwI = groebnerCone(stdI,w);
print(rays(CwI));
==> 1,1,0,
==> 1,0,0,
==> 1,1,1
// v lies on a facet of a maximal Groebner cone
intvec v = 2,1,0;
cone CvI = groebnerCone(stdI,v);
print(rays(CvI));
==> 1,0,0,
==> 1,1,0
// v lies on a ray of a maximal Groebner cone
intvec u = 1,1,1;
cone CuI = groebnerCone(stdI,u);
print(rays(CuI));
==> 1,1,1
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