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; |
i2 : R = QQ[x,y]; |
i3 : isWellDefined(divisor({1}, {ideal(x)} ))
-- (minimalPrimes,Ideal) with Strategy => Monomial from -*Function[/usr/share/Macaulay2/MinimalPrimes.m2:315:27-324:61]*-
-- (trim,Module) with Strategy => Complement from -*Function[/usr/share/Macaulay2/Core/matrix2.m2:243:62-243:113]*-
-- (codim,Module) with Strategy => Default from -*Function[/usr/share/Macaulay2/Core/monideal.m2:30:57-42:52]*-
-- (codim,Module) with Strategy => Default from -*Function[/usr/share/Macaulay2/Core/monideal.m2:30:57-42:52]*-
o3 = true
|
i4 : isWellDefined(divisor({1/2}, {ideal(x)} ))
(isWellDefined, BasicDivisor): Not all coefficients are integers
o4 = false
|
i5 : isWellDefined(divisor({1/2}, {ideal(x)}, CoefficientType=>QQ))
-- (minimalPrimes,Ideal) with Strategy => Monomial from -*Function[/usr/share/Macaulay2/MinimalPrimes.m2:315:27-324:61]*-
-- (trim,Module) with Strategy => Complement from -*Function[/usr/share/Macaulay2/Core/matrix2.m2:243:62-243:113]*-
-- (codim,Module) with Strategy => Default from -*Function[/usr/share/Macaulay2/Core/monideal.m2:30:57-42:52]*-
-- (codim,Module) with Strategy => Default from -*Function[/usr/share/Macaulay2/Core/monideal.m2:30:57-42:52]*-
o5 = true
|
i6 : isWellDefined(divisor({1}, {ideal(x,y)}))
-- (minimalPrimes,Ideal) with Strategy => Monomial from -*Function[/usr/share/Macaulay2/MinimalPrimes.m2:315:27-324:61]*-
-- (trim,Module) with Strategy => Complement from -*Function[/usr/share/Macaulay2/Core/matrix2.m2:243:62-243:113]*-
-- (codim,Module) with Strategy => Default from -*Function[/usr/share/Macaulay2/Core/monideal.m2:30:57-42:52]*-
-- (codim,Module) with Strategy => Default from -*Function[/usr/share/Macaulay2/Core/monideal.m2:30:57-42:52]*-
(isWellDefined, BasicDivisor): Not all ideals are height one
o6 = false
|
i7 : isWellDefined(divisor({1}, {ideal(x^2)}))
-- (minimalPrimes,Ideal) with Strategy => Monomial from -*Function[/usr/share/Macaulay2/MinimalPrimes.m2:315:27-324:61]*-
-- (trim,Module) with Strategy => Complement from -*Function[/usr/share/Macaulay2/Core/matrix2.m2:243:62-243:113]*-
-- (codim,Module) with Strategy => Default from -*Function[/usr/share/Macaulay2/Core/monideal.m2:30:57-42:52]*-
(isWellDefined, BasicDivisor): Not all ideals are prime
o7 = false
|
i8 : S = QQ[a,b]; |
i9 : isWellDefined(divisor({1,2}, {ideal(x), ideal(a)}))
(isWellDefined, BasicDivisor): Not all ideals have the same ambient ring
o9 = false
|