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D.13.4.38 homogeneitySpace

Procedure from library tropical.lib (see tropical_lib).

Usage:
homogeneitySpace(I); I ideal or poly

Assume:
I a reduced standard basis

Return:
cone, the set of all weight vectors with respect to whom I is weighted homogeneous

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/homogeneitySpace.sing:\
   2
==> // ** redefining hilbPoly (LIB "poly.lib";) ./examples/homogeneitySpace.s\
   ing:2
==> // ** redefining hilbPoly (LIB "poly.lib";) ./examples/homogeneitySpace.s\
   ing:2
==> // ** redefining substitute (LIB "poly.lib";) ./examples/homogeneitySpace\
   .sing:2
==> // ** redefining substitute (LIB "poly.lib";) ./examples/homogeneitySpace\
   .sing:2
==> // ** redefining cyclic (LIB "poly.lib";) ./examples/homogeneitySpace.sin\
   g:2
==> // ** redefining cyclic (LIB "poly.lib";) ./examples/homogeneitySpace.sin\
   g:2
==> // ** redefining elemSymmPoly (LIB "poly.lib";) ./examples/homogeneitySpa\
   ce.sing:2
==> // ** redefining elemSymmPoly (LIB "poly.lib";) ./examples/homogeneitySpa\
   ce.sing:2
==> // ** redefining elemSymmId (LIB "poly.lib";) ./examples/homogeneitySpace\
   .sing:2
==> // ** redefining elemSymmId (LIB "poly.lib";) ./examples/homogeneitySpace\
   .sing:2
==> // ** redefining katsura (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining katsura (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining kat_var (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining kat_var (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining freerank (LIB "poly.lib";) ./examples/homogeneitySpace.s\
   ing:2
==> // ** redefining freerank (LIB "poly.lib";) ./examples/homogeneitySpace.s\
   ing:2
==> // ** redefining is_zero (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining is_zero (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining maxcoef (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining maxcoef (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining maxdeg (LIB "poly.lib";) ./examples/homogeneitySpace.sin\
   g:2
==> // ** redefining maxdeg (LIB "poly.lib";) ./examples/homogeneitySpace.sin\
   g:2
==> // ** redefining maxdeg1 (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining maxdeg1 (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining mindeg (LIB "poly.lib";) ./examples/homogeneitySpace.sin\
   g:2
==> // ** redefining mindeg (LIB "poly.lib";) ./examples/homogeneitySpace.sin\
   g:2
==> // ** redefining mindeg1 (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining mindeg1 (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining normalize (LIB "poly.lib";) ./examples/homogeneitySpace.\
   sing:2
==> // ** redefining normalize (LIB "poly.lib";) ./examples/homogeneitySpace.\
   sing:2
==> // ** redefining rad_con (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining rad_con (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining lcm (LIB "poly.lib";) ./examples/homogeneitySpace.sing:2
==> // ** redefining lcm (LIB "poly.lib";) ./examples/homogeneitySpace.sing:2
==> // ** redefining content (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining content (LIB "poly.lib";) ./examples/homogeneitySpace.si\
   ng:2
==> // ** redefining mod2id (LIB "poly.lib";) ./examples/homogeneitySpace.sin\
   g:2
==> // ** redefining mod2id (LIB "poly.lib";) ./examples/homogeneitySpace.sin\
   g:2
==> // ** redefining id2mod (LIB "poly.lib";) ./examples/homogeneitySpace.sin\
   g:2
==> // ** redefining id2mod (LIB "poly.lib";) ./examples/homogeneitySpace.sin\
   g:2
==> // ** redefining subrInterred (LIB "poly.lib";) ./examples/homogeneitySpa\
   ce.sing:2
==> // ** redefining subrInterred (LIB "poly.lib";) ./examples/homogeneitySpa\
   ce.sing:2
==> // ** redefining newtonDiag (LIB "poly.lib";) ./examples/homogeneitySpace\
   .sing:2
==> // ** redefining newtonDiag (LIB "poly.lib";) ./examples/homogeneitySpace\
   .sing:2
ring r = 0,(x,y,z),dp;
ideal I = cyclic(3);
option(redSB);
ideal stdI = std(I);
cone C0I = homogeneitySpace(stdI);
print(generatorsOfLinealitySpace(C0I));
==> 
ring s = 0,(x,y,z,u),dp;
ideal Ih = homog(cyclic(3),u);
ideal stdI = std(Ih);
cone C0Ih = homogeneitySpace(stdI);
print(generatorsOfLinealitySpace(C0Ih));
==> -1,-1,-1,-1