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e5a97c6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 | import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordRangeRealization
import OAI.Combinatorics.LowSpaceSubsetSum.Counting.PrimeSamplerCoupling
import OAI.Combinatorics.LowSpaceSubsetSum.Compression.CompressionSamplerCoupling
namespace OAI
/-! # Word refinements for the prime calls used in both branches -/
noncomputable section
namespace LowSpaceSubsetSum.WordRealization
def prime (w n ell : ℕ) (hell : 4 ≤ ell) (hw : ell ≤ w) :
Realization w (n^3) (primeCoupling hell n) := by
let : Nonempty ↥(primeRange ell) := (primeRange_nonempty hell).to_subtype
let : Nonempty {x : Fin (2 ^ ell) // primeEligible ell x} :=
⟨(primeEligibleEquiv hell).symm (Classical.choice inferInstance)⟩
exact map (rejection w ell hw (n^3) (primeEligible ell)) (primeEligibleEquiv hell)
def factor (w n ell : ℕ) (hw : ell ≤ w) :
Realization w (n^3) (factorCoupling n ell) := by
unfold factorCoupling
split
next h => exact enlarge (map (pure ()) (factorOneEquiv h)) (Nat.zero_le _)
next h => exact map (prime w n ell (by omega) hw) (factorPrimeEquiv (by omega))
def triplePrime (w n a b c : ℕ) (ha : a ≤ w) (hb : b ≤ w) (hc : c ≤ w) :
Realization w (3*n^3) (triplePrimeCoupling n a b c) := by
have h := map (prod (prod (factor w n a ha) (factor w n b hb))
(factor w n c hc)) (tripleFactorEquiv a b c)
simpa only [triplePrimeCoupling, show (n^3+n^3)+n^3 = 3*n^3 by omega] using h
def compression {n : ℕ} (D : CompressionData n) (hn : 168000000 ≤ n)
(w : ℕ) (hp : Nat.clog 2 n ≤ w) (hq : compressionPrimeExponent n ≤ w) :
Realization w (n*n^3+n^3) (D.sampler hn) :=
bind (permutation w n n hp) (fun _ => CompressionSetup.PrimeSpace n)
(fun _ => primeCoupling (by unfold compressionPrimeExponent; omega) n)
(fun _ => prime w n (compressionPrimeExponent n)
(by unfold compressionPrimeExponent; omega) hq)
end LowSpaceSubsetSum.WordRealization
end
end OAI
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