Check whether m times a Weil or Q-divisor D is Cartier for each m from 1 to a fixed positive integer n1 (if the divisor is a QWeilDivisor, it can search slightly higher than n1). If m * D1 is Cartier, it returns m. If it fails to find an m, it returns 0.
i1 : R = QQ[x, y, z] / ideal(x * y - z^2 );
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i2 : D1 = divisor({1, 2}, {ideal(x, z), ideal(y, z)})
o2 = 2*Div(y, z) + Div(x, z)
o2 : WeilDivisor on R
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i3 : D2 = divisor({1/2, 3/4}, {ideal(y, z), ideal(x, z)}, CoeffType => QQ)
o3 = 1/2*Div(y, z) + 3/4*Div(x, z)
o3 : QWeilDivisor on R
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i4 : isQCartier(10, D1)
o4 = 2
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i5 : isQCartier(10, D2)
o5 = 8
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i6 : R = QQ[x, y, u, v] / ideal(x * y - u * v);
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i7 : D1 = divisor({1, 2}, {ideal(x, u), ideal(y, v)})
o7 = 2*Div(y, v) + Div(x, u)
o7 : WeilDivisor on R
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i8 : D2 = divisor({1/2, -3/4}, {ideal(y, u), ideal(x, v)}, CoeffType => QQ)
o8 = -3/4*Div(x, v) + 1/2*Div(y, u)
o8 : QWeilDivisor on R
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i9 : isQCartier(10, D1)
o9 = 0
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i10 : isQCartier(10, D2)
o10 = 0
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i11 : R = QQ[x, y, z] / ideal(x * y - z^2 );
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i12 : D1 = divisor({1, 2}, {ideal(x, z), ideal(y, z)})
o12 = 2*Div(y, z) + Div(x, z)
o12 : WeilDivisor on R
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i13 : D2 = divisor({1/2, 3/4}, {ideal(y, z), ideal(x, z)}, CoeffType => QQ)
o13 = 1/2*Div(y, z) + 3/4*Div(x, z)
o13 : QWeilDivisor on R
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i14 : isQCartier(10, D1, IsGraded => true)
o14 = 1
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i15 : isQCartier(10, D2, IsGraded => true)
o15 = 4
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