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)} )) 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)) o5 = true |
i6 : isWellDefined(divisor({1}, {ideal(x,y)})) (isWellDefined, BasicDivisor): Not all ideals are height one o6 = false |
i7 : isWellDefined(divisor({1}, {ideal(x^2)})) (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 |