# RelativeCanonicalDivisor -- computes the relative canonical divisor

## Synopsis

• Usage:
RelativeCanonicalDivisor(E)
• Inputs:
• E, Intersection matrix.
• Outputs:
• The relative canonical divisor of the resolution.

## Description

Starting form the intersection matrix as presented in [AAD14], it returns the relative canonical divisor of the resolution as a matrix 1 x m.
 i1 : E = matrix({{ -5, 0, 1, 0, 1}, { 0, -2, 1, 0, 0}, { 1, 1, -1, 0, 0}, { 0, 0, 0, -2, 1}, { 1, 0, 0, 1, -1}}) o1 = | -5 0 1 0 1 | | 0 -2 1 0 0 | | 1 1 -1 0 0 | | 0 0 0 -2 1 | | 1 0 0 1 -1 | 5 5 o1 : Matrix ZZ <--- ZZ i2 : RelativeCanonicalDivisor(E) o2 = | 1 2 4 2 4 | 1 5 o2 : Matrix QQ <--- QQ

## For the programmer

The object RelativeCanonicalDivisor is .