  
  [1m[4m[31m3. Affine toric varieties[0m
  
  This chapter concerns [1mtoric[0m commands which deal with the coordinate rings of
  affine toric varieties U_sigma.
  
  
  [1m[4m[31m3.1 Ideals defining affine toric varieties[0m
  
  [1m[4m[31m3.1-1 IdealAffineToricVariety[0m
  
  [1m[34m> IdealAffineToricVariety( [0m[22m[34mL[0m[1m[34m ) _____________________________________[0mfunction
  
  [22m[36mInput[0m: [22m[34mL[0m is a list generating a cone (as in [22m[32mDualSemigroupGenerators[0m).
  [22m[36mOutput[0m:  the  [1mGAP[0m  ideal  defining  the toric variety associated to the cone
  generated by the vectors in [22m[34mL[0m.
  
  This  computation  is  not  very efficient and should not be used for ideals
  with      many      generators.     For     example,     if     you     take
  [22m[34mL:=[[1,2,3,4],[0,1,0,7],[3,1,0,2],[0,0,1,0]];[0m                           then
  [22m[32mIdealAffineToricVariety(L);[0m can exhaust GAP's memory allocation.
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35mgap> J:=IdealAffineToricVariety([[1,0],[3,4]]);[0m
    [22m[35m[ two-sided ideal in PolynomialRing(..., [ x_1, x_2 ]), (3 generators) ][0m
    [22m[35mgap> GeneratorsOfIdeal(J);[0m
    [22m[35m[ -x_2^2+x_1, -x_2^3+x_1^2, -x_2^4+x_1^3 ][0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m3.1-2 EmbeddingAffineToricVariety[0m
  
  [1m[34m> EmbeddingAffineToricVariety( [0m[22m[34mL[0m[1m[34m ) _________________________________[0mfunction
  
  [22m[36mInput[0m: [22m[34mL[0m is a list generating a cone (as in [22m[32mDualSemigroupGenerators[0m).
  [22m[36mOutput[0m:  the toroidal embedding of X=Spec([22m[32mIdealAffineToricVariety(L)[0m) (given
  as a list of multinomials).
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35mgap> phi:=EmbeddingAffineToricVariety([[1,0],[3,4]]);[0m
    [22m[35m[ x_2, x_1, x_1^2/x_4, x_1^3/x_4^2, x_1^4/x_4^3 ][0m
    [22m[35mgap> L:=[[1,0,0],[1,1,0],[1,1,1],[1,0,1]];;[0m
    [22m[35mgap> phi:=EmbeddingAffineToricVariety(L);[0m
    [22m[35m[ x_3, x_2, x_1/x_5, x_1/x_6 ][0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
