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Context I am writing a technical document about some piece of mathematics, the tone of which is intended to be formal and academic.

Question Directly after a computation comes a sentence, in which I am unsure how to best position the preposition 'above'. The two alternatives are:

(1) 'The reader should find no difficulty in identifying the six implicit steps in the above computation.'

and

(2) 'The reader should find no difficulty in identifying the six implicit steps in the computation above.'

In this context, is one of these alternatives to be preferred over the other? I am leaning towards alternative (1), but I am no native speaker of English.

Edit It has been suggested that my question may be a duplicate. The suggested duplicate fails to address a context and appears to pertain more to grammar than to formal style. I think my question is different.

Edit 2 Davo suggests alternative (2) be replaced by

(3) 'The reader should find no difficulty in identifying the six implicit steps in the computation shown above.'

I agree with this suggestion; see this comment of mine. Thus I wonder if one of alternatives (1) and (3) is to be preferred over the other? I still lean towards alternative (1), simply because it consists of one less word.

It has also been suggested I number the relevant computation and thereafter refer to this number. Whereas this is appropriate in many cases, I find it unnatural to do so here. See my comment on Carl Witthoft's answer for an explanation.

Edit 3 This comment (in another thread) links to a graph showing which formulation is more common. It suggests alternative (1), and the question is answered.

Qeeko
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    I'm no academic, but I would say either one is fine. #1 sounds a little formal and forced to me, but that could be because I'm a pretty informal person. – Roger Sinasohn Jul 12 '17 at 17:34
  • Personally, I would use ... in the above computation. or ...in the computation shown above. or, more formally, ...in computation example X. – Davo Jul 12 '17 at 17:41
  • If you just displayed your computation, couldn't you say "in the (or this) computation"? What other steps would you be referring to? Your reader is not stupid and can easily get from point A to point A without road signs. – Yosef Baskin Jul 12 '17 at 18:27
  • @RogerSinasohn I think alternative (2) may at first mislead some readers to expect another computation than the one I intend; as in 'In the computation above what?'. Then they may come to the realisation that it was in fact the computation just shown. This brings us to Davo's suggestion, where one modifies alternative (2) to read '(…) in the computation shown above.', clearing up this confusion. I therefore think alternative (1) or Davo's modification of alternative (2) is better, but I still prefer (1), as it consists of one less word. – Qeeko Jul 12 '17 at 19:01
  • @YosefBaskin Your alternative seems less formal and suggestive to me. – Qeeko Jul 12 '17 at 19:50
  • @Davo I have replaced alternative (2) in my question with your second suggestion. – Qeeko Jul 12 '17 at 19:55
  • 'This computation' is not informal, just clear and simple. What do you mean by suggestive? That word has one main connotation, not this setting. – Yosef Baskin Jul 12 '17 at 19:56
  • @YosefBaskin I did not say that it was informal, but only that, to me, it seems less formal (in this setting). I think my alternatives are more explicit, thus more suggestive as to what is being referred to (am I using this word incorrectly?). In mathematical writing, the word 'computation' has its traditional meaning, or it could refer to the proof of a theorem (especially when said proof is computational in nature). In the document, the computation being referred to is placed inside a proof which is computational in nature. 'This computation' thus leaves it unclear what is referred to. – Qeeko Jul 12 '17 at 20:17
  • You are right that less formal does not mean informal in the absolute. Moving on, the denotation of 'suggestive of X 'is 'hinting at X.' The connotation of 'suggestive,' without a specific X, is hinting at sex. – Yosef Baskin Jul 12 '17 at 21:17

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While both are just fine, I'll propose a more formal alternative as well. In technical publications (papers or books), each equation or formula is given a number. It's then far preferable to refer to each such item by its assigned number. Not only is that unambiguous -- after all "above" covers a lot of ground -- but the reference remains valid even if you happen to move the referring text to some location above the formula (at which point otherwise you'd have to change it to read ".l. below..."

Carl Witthoft
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  • Numbering the equations/formulas is a practice I usually follow, but I think it is unnatural in this case. Firstly, the computation is enclosed within a 'proof-environment', so it is logically separated from the other parts of the text; thus restricting the scope of 'above'. Secondly, the computation spans six lines, and numbering any one of them and then refer to this number may incorrectly suggest that the implicit steps occur on this line. Lastly, all the other computations in the proof are completely explicit, so there should be no ambiguity as to what 'above' refers. – Qeeko Jul 12 '17 at 18:35