Use QQ[x[1..8],y[1..8]];
HPPI8 := [x[1]^I x[I+2] y[2]^(I+1) - y[1]^I y[I+2] x[2]^(I+1) | I In 1..6];
BL := Toric(HPPI8, [x[1],y[2]]);
Len(BL.Gens);
340
-------------------------------
Use QQ[x[1..9],y[1..9]];
HPPI9 := [x[1]^I x[I+2] y[2]^(I+1) - y[1]^I y[I+2] x[2]^(I+1) | I In 1..7];
BL := Toric(HPPI9, [x[1],y[2]]);
Len(BL.Gens);
798
-------------------------------
Use R ::= QQ[x,y,z,w];
Toric(Ideal(xz-y^2, xw-yz));
Ideal(-y^2 + xz, -yz + xw, z^2 - yw)
-------------------------------
Toric([xz-y^2, xw-yz]);
Ideal(-y^2 + xz, -yz + xw, z^2 - yw)
-------------------------------
Toric([xz-y^2, xw-yz], [y]);
Ideal(-y^2 + xz, -yz + xw, z^2 - yw)
-------------------------------
Use R ::= QQ[x,y,z];
Toric([[1,3,2],[3,4,8]]);
Ideal(-x^16 + y^2z^5)
-------------------------------
Toric(Mat([[1,3,2],[3,4,8]]));
Ideal(-x^16 + y^2z^5)
-------------------------------
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