ideal( D1 )
Get an ideal associated to $O(-D)$ of a Weil Divisor $D$. Recall that on an affine scheme, $O(-D)$ is by definition the subset of the fraction field made up of elements such that $Div(f) - D \geq 0$. If $D$ is effective, this will produce the ideal corresponding to $O(-D)$. Otherwise, it will produce some ideal isomorphic to a module corresponding to $O(-D)$.
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Note, if the divisor has non-integer coefficients, their ceilings will be taken, since $O(-D) = O(floor(-D)) = O(-ceiling(D))$.
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The output value of this function is stored in the divisor's cache.