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5d5048e | 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 | import OAI.Combinatorics.LowSpaceSubsetSum.Counting.ScalarSamplerArrays
namespace OAI
/-! # The extra prime drawn at the stored fourth width -/
noncomputable section
namespace LowSpaceSubsetSum.RepresentationExtraDraw
variable {n : ℕ}
def transport {ell ell' : ℕ} {h : 4 ≤ ell} {h' : 4 ≤ ell'}
(he : ell = ell') (s : (primeCoupling h' n).Seed) : (primeCoupling h n).Seed := by
subst ell'
exact s
def draw (R : RepresentationSetup n) (z : RepresentationSetup.Layout n) (hn : 100 ≤ n)
(ell : ℕ) (he : ell = R.extraPrimeParameter z) (s : (R.extraPrimeCoupling z hn).Seed) :
Option ℕ × ℕ :=
ScalarSamplerArrays.extra (he.symm ▸ (R.extraPrimeParameter_range z hn).1) n
(transport he s)
theorem value (R : RepresentationSetup n) (z : RepresentationSetup.Layout n) (hn : 100 ≤ n)
(ell : ℕ) (he : ell = R.extraPrimeParameter z) (s : (R.extraPrimeCoupling z hn).Seed) :
(draw R z hn ell he s).1 = ((R.extraPrimeCoupling z hn).bounded s).map Subtype.val := by
subst ell
exact ScalarSamplerArrays.extra_value _ _ s
theorem work (R : RepresentationSetup n) (z : RepresentationSetup.Layout n) (hn : 100 ≤ n)
(ell : ℕ) (he : ell = R.extraPrimeParameter z) (s : (R.extraPrimeCoupling z hn).Seed) :
(draw R z hn ell he s).2 ≤ n ^ 3 + SamplerExecution.primeTestBudget n + 1 := by
subst ell
exact ScalarSamplerArrays.extra_work _ (R.extraPrimeParameter_range z hn).2 s
end LowSpaceSubsetSum.RepresentationExtraDraw
end
end OAI
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