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From my understanding the standard notation for modulus is $\,x \bmod m$, but using that notation expressions like $(((x-.5) \bmod 7) -y)^2$ become quite clumsy. The Desmos graphing calculator uses the aformention notation of $\,{\rm mod}(x,m)$ which would allow the above to written as $({\rm mod}(x-.5,7)-y)^2$ which to me is much more readable. Would the average reader understand the second notation without any explanation? If not is there another notation that would make it easier to read any is more common?

Bill Dubuque
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Aaron Quitta
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  • @KajHansen It's not $\ x\pmod m.,$ Rather it's $\ x\bmod m.\ $ Please be more careful not to write text that exacerbates such common confusion. – Bill Dubuque Feb 22 '19 at 16:41
  • @Bill Oops, I'm guessing the former is referring to an equivalence class on $\mathbb{Z}$ whereas the latter is a function $\mathbb{Z} \to {0, 1, 2, \cdots, m ! - ! 1 }$? Thanks for bringing this to my attention; I was unaware that there was a standard notational distinction between the two. I always ad-hoc'd something in the past on the rare occasion I needed to refer specifically to the function. – Kaj Hansen Feb 22 '19 at 16:43
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    What is the difference between a parenthesized mod and a binary mod ? –  Feb 22 '19 at 16:43
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    At any rate, @Aaron, there's no reason you can't invent your own notation if you're really set on changing it (though this certainly can annoy your readers if done to excess). Your reasoning for the change is perfectly rational: go for it if you want. But there's also no reason you shouldn't write a single explanatory sentence along the lines of "By [new notation], we mean [old notation]". Don't leave any room in your writing for your readers to have to guess at what you mean. – Kaj Hansen Feb 22 '19 at 16:56
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    @Roddy $\ r = (x\bmod m), $ denotes the normalized remainder $,r,$ left after dividing $x$ by $m,,$ i.e. $, x = r + qm,$ for integers $q,r,$ with the remainder $r$ typically normalized in the range $, 0\le r < m., $ Otoh $\ r\equiv x\pmod{! m}\ $ means the same but without any remainder normalization i.e. $,r,$ can be any integer. Finally, the notation $, x\pmod m, $ is nonstandard, but is sometimes used for the equivalence class $,x+m\Bbb Z,$ in the quotient ring $,\Bbb Z/m\Bbb Z.\ \ $ – Bill Dubuque Feb 22 '19 at 17:13
  • @Kaj Please see above. – Bill Dubuque Feb 22 '19 at 17:14
  • it's in MathJax as \pmod –  Feb 22 '19 at 17:17
  • @RoddyMacPhee \bmod, not \pmod – Bill Dubuque Feb 22 '19 at 17:33
  • *Thanks for you advice @KajHansen! Can I ask what the difference between \pmod and \bmod is? – Aaron Quitta Feb 23 '19 at 17:35

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It is the notation used by computers. Other than that, if you say what it means, most people will understand it. Otherwise, I can give you little. But I would say it is an accepted notation.

Math Bob
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