18.2. Direct integer coordinates🔗

Let f have leading coefficient c. The finite-field target is the monic unit multiple c⁻¹ f mod p.

Hex.ZPoly.monicTarget is its canonical integer lift modulo p^a. This multiplication by a unit in 𝔽_p does not change the integer variable or apply a coefficient-swelling substitution. During recombination, scaling a selected lifted product by c returns it to the coordinates of f. Centred coefficient recovery, primitive-part extraction, and sign normalization then give a factor of the original polynomial.

Classical and lattice recombination use the same modular factorization, factor indices, and direct-coordinate Hensel lift.