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I want to have a sentence like this:

In addition, to efficiently calculate f(t) after adding an item x at position p, where there are q relevant items before, we can use Eq. 3.

Is this grammatically correct? What better phrase can I use instead of "where there are q relevant items before"

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    Yes, it works. If you are looking for alternatives, you can substitute if or in case or given that for where. – Brian Donovan Aug 9 '15 at 16:02
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    Do there have to be exactly q such items? I'm guessing probably not. So you could say, perhaps, To efficiently calculate f(t) after adding an item x at position p, [then] provided there are at least q preceding relevant items, we can use Eq. 3. I would discard the superfluous In addition, since it's contextually obvious you're writing something additional, and the sentence structure is already somewhat "sprawling". – FumbleFingers Aug 9 '15 at 16:03
  • or "such that there are ..." – Graffito Aug 9 '15 at 16:04
  • Yes. There are exactly q item. – Shayan Aug 9 '15 at 16:55
  • @Graffito: My main problem is with before and its usage – Shayan Aug 9 '15 at 16:55
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Where there are can be with.

In addition, to efficiently calculate f(t) after adding an item x at position p, with q relevant items before, we can use Eq. 3.

However, q relevant items before is a bit hard to parse, at least in this context. Does this work?

In addition, to efficiently calculate f(t) after adding an item x at position p, with q relevant items in positions prior to p, we can use Eq. 3.

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Given a set of relevant items Q={q1(x1), q2(x2), q3(x3),..., qn(xn)}, Equation 3 will efficiently calculate f(t) when we add qn+1(xn+1) to Q.

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