/**
 * Multifactor Hensel lifting for the univariate factorization engine
 * (`functions/src/typed/factorization/`).
 *
 * Given a MONIC integer polynomial `f` and its MONIC irreducible factors over
 * 𝔽_p (whose product is ≡ f mod p), lift that factorization to a factorization
 * modulo `p^k` whose product is ≡ f (mod p^k), with each lifted factor still
 * ≡ its input factor (mod p). The target modulus `p^k` is chosen by the caller
 * so that `p^k ≥ 2·landauMignotte(f)+1`, i.e. large enough that the true
 * integer factors of `f` are uniquely recovered by symmetric reduction.
 *
 * Strategy: LINEAR (iterated) two-factor Hensel lifting from `p^i` to `p^{i+1}`
 * up to `p^k`, combined with a recursive FACTOR TREE for more than two factors.
 * Bézout cofactors `s, t` with `s·g + t·h ≡ 1 (mod p)` are computed once per
 * two-factor split via the extended Euclidean algorithm over 𝔽_p; because the
 * per-step diophantine correction is solved only mod p, the fixed mod-p
 * cofactors remain valid at every lifting step (the standard property of linear
 * Hensel lifting — see Geddes/Czapor/Labahn §6.4 or von zur Gathen & Gerhard
 * §15). All factors are monic and `f` is monic, so the lifted factors stay
 * monic and no leading-coefficient imposition is required.
 *
 * `bigint`-only by design: float64 loses correctness once `p^k > 2^53`.
 */
import { type IntPoly } from './integer-poly.js';
/**
 * Multifactor Hensel lift. Lifts the mod-`p` factorization `factorsModP` of the
 * monic integer polynomial `f` (with `∏ factorsModP ≡ f mod p`) to monic
 * integer factors whose product is `≡ f (mod targetPk)` and each of which is
 * `≡ its input factor (mod p)`. Coefficients are returned in the symmetric
 * range modulo `targetPk = p^k` (via `modSymmetric`).
 *
 * More than two factors are handled by a recursive factor tree: `factorsModP`
 * is split into two halves, the two half-products are lifted together by
 * `henselLiftTwo`, and each lifted half is recursively split into its own
 * factors.
 */
export declare function henselLift(f: IntPoly, factorsModP: IntPoly[], p: bigint, targetPk: bigint): IntPoly[];
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