I commonly want to use the phrase “we have” when writing mathematics, to mean something like “most readers will know this thing and I am about to use it”. My primary question is whether this is too colloquial. My secondary question is what the alternatives are if it is too colloquial.
For example, right now I have a sentence
“Given a point P∈X we have the residue map resP:ΩK(X)→k, as defined in …”. I don’t feel saying “there exists the” is quite right. Even if it is grammatically correct, I don’t think this conveys the implication that it will be almost certainly familiar to the expected audience.
I have seen this question but I feel this is slightly different. If not then my apologies.
In my opinion it is even good style. You are involving the reader somehow to the discussion, if you write phrases like “we have”, “we consider”, “we may assume”, “one can see that” etc.
By the way, it is common in other languages as well and you can read similar phrases in papers of famous mathematicans all over the world.
Noi sappiamo (…)
(we know that, … Ref, p.6 )
(..) nehmen wir an, dass (..)
(We assume that … Ref)
However in the reducible case (..) we have to consider (..)
Furthermore I found a guide by MIT in which is said
Be forthright: write in an unhesitating, straightforward, and friendly style, ridding your language of needless and bewildering formality. Be wary of awkward and inefficient passive constructions. Often the passive voice is used simply to avo id the first person.
However, the pronoun “we” is now generally considered acceptable
in contexts where it
means the author and reader together, or less often, the author with the reader looking on.