We are discussing the sentence "We can obtain the result by analytic inversion." It's from a math context.
Is this an OK sentence, or does it have to be "an inversion"? If so, why? If not, why? Is this sentence particularly problematic because "inversion" can have both a non-countable (the process of inverting) and a countable (if you have different ways of inverting) interpretation?
If this is an OK sentence, why is the sentence so much different if you replace "inversion" by "algorithm"? Clearly, in this case, you do need "an".