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@ -42,9 +42,9 @@ To make things more concrete, consider the $\{\mathbb{N}, \times, +, 1, 0\}$ bag
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For the general commutative semiring,\AR{Why are you introducing the general semi-ring case if we are only using the polynomial semi-ring?} denote the plus and multiplication operators as $\oplus$ and $\otimes$ respectively, where summation represents summing over $\oplus$. Operations in $\query$ are translated into the following polynomial operations.
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\OK{
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Eventually, you probably want a little more background here, depending on the query notation you choose to use. The simplest approach would be basing it on the Green et. al. Provenance Semirings paper. As we discussed, that would make $\query(\mathcal D)(t)$ the query polynomial.
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}
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%\OK{
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% Eventually, you probably want a little more background here, depending on the query notation you choose to use. The simplest approach would be basing it on the Green et. al. Provenance Semirings paper. As we discussed, that would make $\query(\mathcal D)(t)$ the query polynomial.
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%}
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%
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%\OK{
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% I don't think we're on the same page here. From the Prov. Semirings perspective, the entire $\poly(X_i)$ is the annotation of a tuple in an arbitrary query over a $\mathbb R[x]$-relation (i.e., a relation who's tuples are annotated by polynomials over the reals). The $X_i$s are not annotations, they're the variables of that polynomial. (footnote: Presumably, there are tuples in the database who's annotations are just a single variable, but that's not the general case).
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