leanprover-community / leanprover-community/mathlib4
Define `Asymptotics.IsSubpolynomial`
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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?
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by searching the existing Asymptotics API and downstream projects for related definitions. Establish the proposed IsSubpolynomial definition and its intended filter and norm parameters, then add the requested stability, equivalence, and uniform-constants lemmas; done means the API supports the motivating temperate-growth proofs.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Quiet
- Clarity
- Mostly clear
- Newbie friendliness
- 38/100