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Is the hyphen that we often see in words such as "non-zero", "non-trivial", etc. optional?

In case the answer is negative, is there any rule of thumb on which one may rely in order to recall when it is OK to leave it out?

Thanks in advance for your knowledgeable replies.

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    Almost every one of hundreds of words in the full OED starting with non is listed as a hyphenated form. A couple of exceptions that stood out to me when scrolling through them were the historical US noun nonslaveholder and adjectival / adverbial nonverbal / nonverbally (but for some reason they do actually hyphenate non-verbalized). So by far the best rule of thumb is to hyphenate in all cases.
    – FumbleFingers
    Aug 29, 2018 at 17:20
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    @FumbleFingers is that a British thing or a quirk of the OED? I don't have access to it, but most other places I've checked show many of the non constructions without the dash.
    – Kevin
    Aug 29, 2018 at 17:30
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    @Kevin: So far as I'm aware, the OED is the definitive English dictionary (they specifically identify AmE and BrE usages as such where relevant). In practice there's been an ongoing move towards using less "punctuation marks" in general over at least the past century, and if you ask me, BrE is less "conservative" than (post-Webster) AmE anyway....
    – FumbleFingers
    Aug 29, 2018 at 17:39
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    (Is that one of those "Jinx! You owe me a Coke!" moments? :)
    – FumbleFingers
    Aug 29, 2018 at 17:45
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    In any case, using the hyphen is never wrong, and is required in some cases. I'd say when in doubt use the hyphen, and only omit it if you memorize words that don't need it or look it up.
    – Kevin
    Aug 29, 2018 at 17:48

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To record and summarize the discussion in the comments, while the OED mostly uses the hyphen, many other dictionaries don't, and the ngrams show higher non-hyphenated usage than hyphenated.

Since using the hyphen is never wrong, and is preferred in some cases, when in doubt use the hyphen, and only omit it if you happen to know a word is commonly spelled without it.

And it's a true hyphen, not an en- or em-dash.

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