Singular Manual: maximalGroebnerCone

| #### D.13.4.37 maximalGroebnerCone Procedure from library `tropical.lib` (see tropical_lib). Usage: maximalGroebnerCone(I); I ideal or poly Assume: I a reduced standard basis Return: cone, the maximal Groebner cone of I with respect to the current ordering 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";) ./examples/maximalGroebnerCone.si\
       ng:2
    ==> // ** redefining hilbPoly (LIB "poly.lib";) ./examples/maximalGroebnerCon\
       e.sing:2
    ==> // ** redefining hilbPoly (LIB "poly.lib";) ./examples/maximalGroebnerCon\
       e.sing:2
    ==> // ** redefining substitute (LIB "poly.lib";) ./examples/maximalGroebnerC\
       one.sing:2
    ==> // ** redefining substitute (LIB "poly.lib";) ./examples/maximalGroebnerC\
       one.sing:2
    ==> // ** redefining cyclic (LIB "poly.lib";) ./examples/maximalGroebnerCone.\
       sing:2
    ==> // ** redefining cyclic (LIB "poly.lib";) ./examples/maximalGroebnerCone.\
       sing:2
    ==> // ** redefining elemSymmPoly (LIB "poly.lib";) ./examples/maximalGroebne\
       rCone.sing:2
    ==> // ** redefining elemSymmPoly (LIB "poly.lib";) ./examples/maximalGroebne\
       rCone.sing:2
    ==> // ** redefining elemSymmId (LIB "poly.lib";) ./examples/maximalGroebnerC\
       one.sing:2
    ==> // ** redefining elemSymmId (LIB "poly.lib";) ./examples/maximalGroebnerC\
       one.sing:2
    ==> // ** redefining katsura (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining katsura (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining kat_var (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining kat_var (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining freerank (LIB "poly.lib";) ./examples/maximalGroebnerCon\
       e.sing:2
    ==> // ** redefining freerank (LIB "poly.lib";) ./examples/maximalGroebnerCon\
       e.sing:2
    ==> // ** redefining is_zero (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining is_zero (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining maxcoef (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining maxcoef (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining maxdeg (LIB "poly.lib";) ./examples/maximalGroebnerCone.\
       sing:2
    ==> // ** redefining maxdeg (LIB "poly.lib";) ./examples/maximalGroebnerCone.\
       sing:2
    ==> // ** redefining maxdeg1 (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining maxdeg1 (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining mindeg (LIB "poly.lib";) ./examples/maximalGroebnerCone.\
       sing:2
    ==> // ** redefining mindeg (LIB "poly.lib";) ./examples/maximalGroebnerCone.\
       sing:2
    ==> // ** redefining mindeg1 (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining mindeg1 (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining normalize (LIB "poly.lib";) ./examples/maximalGroebnerCo\
       ne.sing:2
    ==> // ** redefining normalize (LIB "poly.lib";) ./examples/maximalGroebnerCo\
       ne.sing:2
    ==> // ** redefining rad_con (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining rad_con (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining lcm (LIB "poly.lib";) ./examples/maximalGroebnerCone.sin\
       g:2
    ==> // ** redefining lcm (LIB "poly.lib";) ./examples/maximalGroebnerCone.sin\
       g:2
    ==> // ** redefining content (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining content (LIB "poly.lib";) ./examples/maximalGroebnerCone\
       .sing:2
    ==> // ** redefining mod2id (LIB "poly.lib";) ./examples/maximalGroebnerCone.\
       sing:2
    ==> // ** redefining mod2id (LIB "poly.lib";) ./examples/maximalGroebnerCone.\
       sing:2
    ==> // ** redefining id2mod (LIB "poly.lib";) ./examples/maximalGroebnerCone.\
       sing:2
    ==> // ** redefining id2mod (LIB "poly.lib";) ./examples/maximalGroebnerCone.\
       sing:2
    ==> // ** redefining subrInterred (LIB "poly.lib";) ./examples/maximalGroebne\
       rCone.sing:2
    ==> // ** redefining subrInterred (LIB "poly.lib";) ./examples/maximalGroebne\
       rCone.sing:2
    ==> // ** redefining newtonDiag (LIB "poly.lib";) ./examples/maximalGroebnerC\
       one.sing:2
    ==> // ** redefining newtonDiag (LIB "poly.lib";) ./examples/maximalGroebnerC\
       one.sing:2
    ring r = 0,(x,y,z),dp;
    ideal I = cyclic(3);
    option(redSB);
    ideal stdI = std(I);
    cone CI = maximalGroebnerCone(stdI);
    print(rays(CI));
    ==> 1,1,0,
    ==> 1,0,0,
    ==> 1,1,1
    ring s = 0,(x,y,z,u),dp;
    ideal Ih = homog(cyclic(3),u);
    ideal stdI = std(Ih);
    cone CIh = maximalGroebnerCone(stdI);
    print(rays(CIh));
    ==> 1, 1,-1,-1,
    ==> 3,-1,-1,-1,
    ==> 1, 1, 1,-3
    print(generatorsOfLinealitySpace(CIh));
    ==> -1,-1,-1,-1
    ring rw = 0,(x,y,z),(a(1,0,1),lp);
    ideal I = cyclic(3);
    ideal stdI = std(I);
    CI = maximalGroebnerCone(stdI);
    print(rays(CI));
    ==> 1,0,0,
    ==> 1,0,1,
    ==> 1,1,1

User manual for Singular version 4-1-2p4, 2020, generated by texi2html.