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isWellDefined(BasicDivisor) -- whether a divisor is valid

Description

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

See also

Ways to use this method:

The source of this document is in WeilDivisors.m2:2210:0.