4.6 Saturation

The saturation $(I:J)^\infty$ of I with respect J can be computed by computing $(I:J),((I:J):J), \ldots$ until it stabilizes.

SINGULAR example:

ring R=...;
ideal I=...;
ideal J=...;
int ii;
I = std(I);
while ( ii<=size(II))
{
  II=quotient(I,J);
  for ( ii=1; ii <=size(II); ii=ii++)
  {
    if (reduce(II[ii],I)!=0) break;
  }
  I=std(II);
}

// II is now (I:J)$^\infty$.