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What is the difference between the two following notations.

  1. function $f(.)$ over $\mathbb{Z}_q$ .

  2. function $f(x)$ where $x$ takes values from $\mathbb{Z}_q$

I think that both are same. Is there any difference between the two notations?

hanugm
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    It's all notation, they are used to designate the same mathematical object... – 5xum Aug 17 '15 at 09:49
  • I am making an educated guess that the OP may be interested in the difference between a (formal) polynomial $f(x)$ with coefficients in $\Bbb{Z}_q$ and the polynomial function $f:a\mapsto f(a)$ from $\Bbb{Z}_q$ to itself that it yields. Those two ARE different objects. For example the polynomial $x^q-x$ that has degree $q$, and is thus different from a constant polynomial, yields the constant function zero. See e.g. this discussion in case that is what's bothering you. – Jyrki Lahtonen Aug 17 '15 at 10:57
  • some context, id est, the book you see this in, would be appropriate. Notation means whatever the author intends it to mean. – mebassett Aug 18 '15 at 17:47

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