Singular Manual: homogeneitySpace

| #### 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

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