3 Affine toric varieties This chapter concerns toric commands which deal with the coordinate rings of affine toric varieties U_σ. 3.1 Ideals defining affine toric varieties 3.1-1 EmbeddingAffineToricVariety EmbeddingAffineToricVariety( L )  function Input: L is a list generating a cone (as in DualSemigroupGenerators). Output: the toroidal embedding of X=Spec(I), where I is the ideal of the affine toric variety (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 ]