Uniform estimates for finite coefficient assembly, including zero and terminal grades.
theorem
EulerPacketCylinderField.Field.wordBound_truncateFamily
{P T : ℝ}
[Fact (0 < P)]
(M : ℕ)
(f : ℕ → EulerPacketProfileRecursion.VectorField)
(G : (i : ℕ) → i ≤ M → Field P T (f i))
(q : ℕ)
(R : ℝ)
(A : ℕ → ℝ)
(d : ℕ → ℕ)
(hR : 0 ≤ R)
(hA : ∀ (i : ℕ), 0 ≤ A i)
(hG : ∀ (i : ℕ) (hi : i ≤ M), (G i hi).WordBound q R (A i) (d i))
(n : ℕ)
:
(truncateFamily M f G n).WordBound q R (A n) (d n)
theorem
EulerPacketCylinderField.Field.wordBound_assembleFamily
{P T : ℝ}
[Fact (0 < P)]
(M : ℕ)
(f c : ℕ → EulerPacketProfileRecursion.VectorField)
(G : (i : ℕ) → i ≤ M → Field P T (f i))
(H : (i : ℕ) → i ≤ M → Field P T (c i))
(R A : ℝ)
(hR : 1 ≤ R)
(hA : 1 ≤ A)
(hG : ∀ (i : ℕ) (hi : i ≤ M), (G i hi).WordBound 6 R (2 * A ^ (2 * i)) (EulerPacketShiftArithmetic.highShift i))
(hH : ∀ (i : ℕ) (hi : i ≤ M), (H i hi).WordBound 6 R (A ^ (2 * i)) (EulerPacketShiftArithmetic.highShift i))
(n : ℕ)
:
(assembleFamily M f c G H n).WordBound 6 R (3 * A ^ (2 * n)) (EulerPacketShiftArithmetic.highShift n)