Singular

LIB "tropical.lib";
==> Welcome to polymake version
==> Copyright (c) 1997-2015
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
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