Two torus-invariant Weil divisors are equal when their underlying normal toric varieties are equal and, for each irreducible torus-invariant divisor, the corresponding coefficients are equal.
i1 : X = normalToricVariety(id_(ZZ^3) | -id_(ZZ^3)); |
i2 : D1 = toricDivisor({2,-7,3,0,7,5,8,-8}, X)
o2 = 2*X - 7*X + 3*X + 7*X + 5*X + 8*X - 8*X
0 1 2 4 5 6 7
o2 : ToricDivisor on X
|
i3 : D2 = 2 * X_0 - 7 * X_1 + 3 * X_2 + 7 * X_4 + 5 * X_5 + 8 * X_6 - 8 * X_7
o3 = 2*X - 7*X + 3*X + 7*X + 5*X + 8*X - 8*X
0 1 2 4 5 6 7
o3 : ToricDivisor on X
|
i4 : D1 == D2 o4 = true |
i5 : D1 == - D2 o5 = false |
i6 : assert (D1 == D2 and D2 == D1 and D1 =!= - D2) |
Since the group of torus-equivariant Weil divisors form an abelian group, it also makes sense to compare a toric divisor with the zero integer (which we identify with the toric divisor whose coefficients are equal to zero).
i7 : D1 == 0 o7 = false |
i8 : 0*D1 == 0 o8 = true |
i9 : assert (D1 =!= 0 and 0*D1 == 0 and 0 == 0*D2) |