grammaticality - What’s the correct usage of “modulo”?

The most syntactically sound way I can say "10 modulo 3 equals 1" is

(10 % 3) == 1

That holds in a great many languages, but not spoken English. I do hear it spoken often enough as a computer scientist, though, and when it's not simply, "ten mod three," it's "ten modulo three," and occasionally "ten modulus three." There are other ways you could phrase it, but these are all that I have heard spoken, and this from the lips of exceedingly well educated computer science profs.

Modulus comes from Latin; it means "little measure." "Modulus" uses the the nominative ending, which is for subjects. "Modulo" uses the ablative ending, so you can translate as "from the little measure," "with the little measure," "by the little measure," or "in the little measure," among other possibilities depending on the context. In English, "modulo" simply becomes a preposition, like "plus." You could say, "the modulus of ten with respect to three," or, "ten modulo three," but "ten modulus three" is pretty shaky. The operator "%" I have seen called both a "modulus operator" and a "modulo operator," but my texts all say "modulus operator."

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