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(xzy^2, xwyz));
Ideal(y^2 + xz, yz + xw, z^2  yw)

Toric([xzy^2, xwyz]);
Ideal(y^2 + xz, yz + xw, z^2  yw)

Toric([xzy^2, xwyz], [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)

