3. Affine toric varieties
  
  This chapter concerns toric commands which deal with the coordinate rings of
  affine toric varieties U_sigma.
  
  
  3.1 Ideals defining affine toric varieties
  
  3.1-1 IdealAffineToricVariety
  
  > IdealAffineToricVariety( L ) _____________________________________function
  
  Input: L is a list generating a cone (as in DualSemigroupGenerators).
  Output:  the  GAP  ideal  defining  the toric variety associated to the cone
  generated by the vectors in L.
  
  This  computation  is  not  very efficient and should not be used for ideals
  with      many      generators.     For     example,     if     you     take
  L:=[[1,2,3,4],[0,1,0,7],[3,1,0,2],[0,0,1,0]];                           then
  IdealAffineToricVariety(L); can exhaust GAP's memory allocation.
  
  ---------------------------  Example  ----------------------------
    gap> J:=IdealAffineToricVariety([[1,0],[3,4]]);
    [ two-sided ideal in PolynomialRing(..., [ x_1, x_2 ]), (3 generators) ]
    gap> GeneratorsOfIdeal(J);
    [ -x_2^2+x_1, -x_2^3+x_1^2, -x_2^4+x_1^3 ]
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  3.1-2 EmbeddingAffineToricVariety
  
  > EmbeddingAffineToricVariety( L ) _________________________________function
  
  Input: L is a list generating a cone (as in DualSemigroupGenerators).
  Output:  the toroidal embedding of X=Spec(IdealAffineToricVariety(L)) (given
  as a list of multinomials).
  
  ---------------------------  Example  ----------------------------
    gap> phi:=EmbeddingAffineToricVariety([[1,0],[3,4]]);
    [ x_2, x_1, x_1^2/x_4, x_1^3/x_4^2, x_1^4/x_4^3 ]
    gap> L:=[[1,0,0],[1,1,0],[1,1,1],[1,0,1]];;
    gap> phi:=EmbeddingAffineToricVariety(L);
    [ x_3, x_2, x_1/x_5, x_1/x_6 ]
    
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