# Modulo operation notation

I would like to write that some polynomial $p(x)$ is the sum of polynomial $d(x)$ and the remainder of division of polynomial $b(x)$ by polynomial $w(x)$:

$$p(x) = d(x) + b(x)\bmod w(x)$$

But from what I saw in books, this can mean something different which is:

$$p(x) = (d(x) + b(x))\bmod w(x)$$

So, what is a good way to write what I mean?

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When in doubt, add brackets. – Zhen Lin May 24 '11 at 10:09
(b mod w) is a shorthand for the set {b+qw ; q polynomial}. Hence d+(b mod w)=(d+b) mod w since both are {d+b+qw ; q polynomial}. – Did May 24 '11 at 10:15
@Didier: I think it's clear from context that the OP wants to discuss an operation which returns the remainder. But I agree that the use of $\text{mod}$ for this is an abuse of notation and should be replaced with something else. – Zhen Lin May 24 '11 at 10:37
I would write it exactly like you, but add brackets. So $p(x) = (d(x) + b(x)\bmod w(x))$ but $p(x)\not=d(x)+b(x)\mod w(x)$. Notice also, that the spacing is also different. – FUZxxl May 24 '11 at 12:22
Write it as $\rm\ p = d + (b\ mod\ w)\$ to avoid confusion with $\rm p = d + b\ (mod\ w)\:,\$ or use $\rm\:(b\ rem\ w)\:.$ – Bill Dubuque Jul 26 '11 at 17:52