# positivePart -- get the effective part or anti-effective part of a divisor

## Synopsis

• Usage:
positivePart( F1 )
negativePart( F1 )
• Inputs:
• Outputs:
• an instance of the type RWeilDivisor, an effective divisor

## Description

This function returns the positive part of a divisor

 i1 : R = QQ[x, y, u, v] / ideal(x * y - u * v); i2 : D = divisor({1, -2, 3, -4}, {ideal(x, u), ideal(y, u), ideal(x, v), ideal(y, v)}) o2 = -4*Div(y, v) + Div(x, u) + -2*Div(y, u) + 3*Div(x, v) o2 : WeilDivisor on R i3 : positivePart( D ) o3 = Div(x, u) + 3*Div(x, v) o3 : WeilDivisor on R i4 : negativePart( D ) o4 = 2*Div(y, u) + 4*Div(y, v) o4 : WeilDivisor on R i5 : D == positivePart(D) - negativePart(D) o5 = true i6 : E = divisor({0, 1}, {ideal(x,u), ideal(y,u)}) o6 = 0*Div(x, u) + Div(y, u) o6 : WeilDivisor on R i7 : positivePart(E) o7 = Div(y, u) o7 : WeilDivisor on R i8 : negativePart(E) o8 = 0, the zero divisor o8 : WeilDivisor on R i9 : E == positivePart(E) - negativePart(E) o9 = true

## Ways to use positivePart :

• "positivePart(RWeilDivisor)"

## For the programmer

The object positivePart is .