# Singular

#### 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