Singular Manual: groebnerCone

| #### 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

User manual for Singular version 4-1-0, 2016, generated by texi2html.