Explicit coefficient-height bounds for the bounded integral shear.
theorem
CCDN.bivariateShear_bounded_coefficient_bound
(a d : ℕ)
(ha : a ≤ d)
(f : Polynomial (Polynomial ℤ))
(hd : bivariateTotalDegree f ≤ d)
(H : ℝ)
(hH : 0 ≤ H)
(hf : BivariateCoefficientBound f H)
:
BivariateCoefficientBound ((bivariateShear ℤ ↑a) f) ((↑d + 1) ^ (d + 2) * H)
For the selected parameter 0<=a<=d, the sheared height is at most H*(d+1)^(d+2), hence its logarithm costs only O(d log d).