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BasicDivisor -- the Types of divisors


The BasicDivisor is the class of divisors whose coefficients are unspecified, a base class. Not typically for use. All subtypes have the same essential structure.

RWeilDivisor is a subclass which has real coefficients.

QWeilDivisor is a further subclass with rational coefficients.

WeilDivisor is a subclass with integer coefficients.

The basic structure is a HashTable. There is one key which has a value which specifies the ambient ring. Another key is cache which points to a CacheTable. The remaining keys are a Groebner basis $L$ for each prime ideal $P$ in the support with corresponding value a list with one entry {$n$} where $n$ is the coefficient of the height one prime.

i1 : R = QQ[x,y,z];
i2 : D = divisor(x*y^2*z^3)

o2 = 2*Div(y) + 3*Div(z) + Div(x)

o2 : WeilDivisor on R
i3 : H = new HashTable from D

o3 = HashTable{{x} => {1}                  }
               {y} => {2}
               {z} => {3}
               cache => CacheTable{...1...}
               ring => R

o3 : HashTable
i4 : (2/3)*D

o4 = 2*Div(z) + 4/3*Div(y) + 2/3*Div(x)

o4 : QWeilDivisor on R
i5 : 0.6*D

o5 = 1.8*Div(z) + 1.2*Div(y) + .6*Div(x)

o5 : RWeilDivisor on R

Types of BasicDivisor :

Functions and methods returning an object of class BasicDivisor :

Methods that use an object of class BasicDivisor :

For the programmer

The object BasicDivisor is a type, with ancestor classes HashTable < Thing.