leanprover-community/mathlib4

Define `Asymptotics.IsSubpolynomial`

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#32,658 opened on Dec 9, 2025

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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?

Contributor guide

Research direction
Study the existing Asymptotics API (e.g., IsBigO, IsLittleO), then define IsSubpolynomial and prove the listed lemmas (stability, equivalence, uniform constants).
Tech stack
None
Domain
backend
Issue type
Feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
3
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
1-2 days
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
Active
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
Clear
Prerequisites
LeanAsymptotics
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
40