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I look for the opposite of "invariant" in the context of scientific language. If you look at this example sentence:

[...] Although it is translationally and rotationally invariant, it is not permutationally invariant. [...]

There is a repetition of the word "invariant" and a double negation. ("not" and "in-" as prefix)

Since I could not find any example of people saying "variant" for "not invariant", I do not know how to nicely write this sentence.

If I look at Merriam Webster and list the possible antonyms:

changing, deviating, nonuniform, unsteady, varying

I think none is fitting, but I am also not of English mother tongue.

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  • From programming contexts, constant, volatile might refer to the attributes invariant, variable.
    – FumbleFingers
    Commented Jan 5, 2022 at 12:03
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    There is a repetition of the word "invariant" and a double negation. ("not" and "in-" as prefix) There is nothing wrong with this at all. The language is perfect for the context: you change it at your peril...
    – Greybeard
    Commented Jan 5, 2022 at 12:13

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Variant is correct. It can function as an adjective meaning essentially "having variety", and it fits here as "invariant" is also an adjective.

As for why this is not a common use, I can't say. It's perfectly correct and has an appealing familiarity to it. If you're looking for advice relating to the jargon of a specific field, I suggest you consult experts of that field.

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