Verified computational algebra in Lean 4: an aggregator for the released
hex libraries.
- Manual: https://kim-em.github.io/hex-dev/
- API documentation: https://leanprover.github.io/hex/docs
Add to your lakefile.toml:
[[require]]
name = "hex"git = "https://github.com/leanprover/hex.git"rev = "main"Then import Hex re-exports every library in the table below at a single
coherent pinned set:
import Hex
open Hex
-- Exact, fraction-free integer determinant.defM : Matrix Int 33 := #m[2, 1, 1; 1, 2, 1; 1, 1, 2]
#eval M.det -- 4-- LLL: reduce an integer lattice basis and read off a provably short vector.-- The `by decide` arguments discharge the reduction-factor side conditions.defL : Matrix Int 33 := #m[1, 1, 1; 1, 0, 2; 3, 5, 6]
#eval lllNative.firstShortVector L (3 / 4) (by decide +kernel) (by decide +kernel) (by decide)To depend on just one piece, require that library directly (for example
hex-lll for the Mathlib-free LLL
core) instead of the aggregator.
Each computational library is Mathlib-free; its Mathlib correspondence proofs
and Mathlib-facing API, where they exist, live in a separate *-mathlib
library.
- LLL lattice reduction (HexLLL): blog post, Zulip, LinkedIn
- Integer polynomial factorization (HexBerlekampZassenhaus): blog post, Zulip, LinkedIn
Development of the full project (including unreleased libraries) happens in the
hex-dev monorepo.