This function tries to verify that this is a valid divisor. It checks that the coefficients are from the right ring (in the WeilDivisor/QWeilDivisor/RWeilDivisor cases at least). It also checks to make sure all the ideals are from the same ring, are prime, and have height one. If debugLevel > 0, the function will print an message explaining why the divisor was not valid.
i1 : debugLevel = 1;
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i2 : R = QQ[x,y];
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i3 : isWellDefined(divisor({1}, {ideal(x)} ))
-- 1 : (ContainmentHooks) with Strategy => Inhomogeneous from FunctionClosure[/usr/local/share/Macaulay2/Core/modules2.m2:113:60-113:98]
-- (minimalPrimes,Ideal) with Strategy => Monomial from FunctionClosure[/usr/local/share/Macaulay2/MinimalPrimes.m2:304:26-313:60]
-- (trim,Module) with Strategy => PID from FunctionClosure[/usr/local/share/Macaulay2/Core/matrix2.m2:263:14-265:125]
-- (trim,Module) with Strategy => Complement from FunctionClosure[/usr/local/share/Macaulay2/Core/matrix2.m2:248:61-248:112]
-- (codim,Module) with Strategy => Default from FunctionClosure[/usr/local/share/Macaulay2/Core/monideal.m2:37:56-49:51]
-- (codim,Module) with Strategy => Default from FunctionClosure[/usr/local/share/Macaulay2/Core/monideal.m2:37:56-49:51]
o3 = true
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i4 : isWellDefined(divisor({1/2}, {ideal(x)} ))
(isWellDefined, BasicDivisor): Not all coefficients are integers
o4 = false
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i5 : isWellDefined(divisor({1/2}, {ideal(x)}, CoefficientType=>QQ))
-- 1 : (ContainmentHooks) with Strategy => Inhomogeneous from FunctionClosure[/usr/local/share/Macaulay2/Core/modules2.m2:113:60-113:98]
-- (minimalPrimes,Ideal) with Strategy => Monomial from FunctionClosure[/usr/local/share/Macaulay2/MinimalPrimes.m2:304:26-313:60]
-- (trim,Module) with Strategy => PID from FunctionClosure[/usr/local/share/Macaulay2/Core/matrix2.m2:263:14-265:125]
-- (trim,Module) with Strategy => Complement from FunctionClosure[/usr/local/share/Macaulay2/Core/matrix2.m2:248:61-248:112]
-- (codim,Module) with Strategy => Default from FunctionClosure[/usr/local/share/Macaulay2/Core/monideal.m2:37:56-49:51]
-- (codim,Module) with Strategy => Default from FunctionClosure[/usr/local/share/Macaulay2/Core/monideal.m2:37:56-49:51]
o5 = true
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i6 : isWellDefined(divisor({1}, {ideal(x,y)}))
-- 1 : (ContainmentHooks) with Strategy => Inhomogeneous from FunctionClosure[/usr/local/share/Macaulay2/Core/modules2.m2:113:60-113:98]
-- (minimalPrimes,Ideal) with Strategy => Monomial from FunctionClosure[/usr/local/share/Macaulay2/MinimalPrimes.m2:304:26-313:60]
-- (trim,Module) with Strategy => PID from FunctionClosure[/usr/local/share/Macaulay2/Core/matrix2.m2:263:14-265:125]
-- (trim,Module) with Strategy => Complement from FunctionClosure[/usr/local/share/Macaulay2/Core/matrix2.m2:248:61-248:112]
-- (codim,Module) with Strategy => Default from FunctionClosure[/usr/local/share/Macaulay2/Core/monideal.m2:37:56-49:51]
-- 1 : (ContainmentHooks) with Strategy => Inhomogeneous from FunctionClosure[/usr/local/share/Macaulay2/Core/modules2.m2:113:60-113:98]
-- 1 : (ContainmentHooks) with Strategy => Inhomogeneous from FunctionClosure[/usr/local/share/Macaulay2/Core/modules2.m2:113:60-113:98]
-- (codim,Module) with Strategy => Default from FunctionClosure[/usr/local/share/Macaulay2/Core/monideal.m2:37:56-49:51]
(isWellDefined, BasicDivisor): Not all ideals are height one
o6 = false
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i7 : isWellDefined(divisor({1}, {ideal(x^2)}))
-- 1 : (ContainmentHooks) with Strategy => Inhomogeneous from FunctionClosure[/usr/local/share/Macaulay2/Core/modules2.m2:113:60-113:98]
-- (minimalPrimes,Ideal) with Strategy => Monomial from FunctionClosure[/usr/local/share/Macaulay2/MinimalPrimes.m2:304:26-313:60]
-- (trim,Module) with Strategy => PID from FunctionClosure[/usr/local/share/Macaulay2/Core/matrix2.m2:263:14-265:125]
-- (trim,Module) with Strategy => Complement from FunctionClosure[/usr/local/share/Macaulay2/Core/matrix2.m2:248:61-248:112]
-- (codim,Module) with Strategy => Default from FunctionClosure[/usr/local/share/Macaulay2/Core/monideal.m2:37:56-49:51]
-- 1 : (ContainmentHooks) with Strategy => Inhomogeneous from FunctionClosure[/usr/local/share/Macaulay2/Core/modules2.m2:113:60-113:98]
(isWellDefined, BasicDivisor): Not all ideals are prime
o7 = false
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i8 : S = QQ[a,b];
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i9 : isWellDefined(divisor({1,2}, {ideal(x), ideal(a)}))
(isWellDefined, BasicDivisor): Not all ideals have the same ambient ring
o9 = false
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