leanprover-community/mathlib4
Define `Asymptotics.IsSubpolynomial`
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#32 658 ouverte le 9 déc. 2025
good first issuet-analysis
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Description
I think we should have a definition for "along the filter l, f is a big O of 1 + ‖g‖^k for some natural k", along with some basic lemmas such as:
- stability under addition, multiplication, power, composition
- equivalence with some other definitions (e.g using
(1 + ‖g‖)^k) - if you have a finite set of functions which are subpolynomial in
g, you can pick the constants in the big O and the power uniformly.
This is motivated by proofs about functions with temperate growth, which I claim could be simpler with such an API. But this would also be useful more generally for people studying asymptotic behaviours (e.g to define groups with polynomial growth). In fact, maybe something like this exists already in downstream projects?