Hensel's lemma [SEP] named after
Hensel's lemma
In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a polynomial equation has a simple root modulo a prime number , then this root corresponds to a unique root of the same equation modulo any higher power of , which can be found by iteratively "lifting" the solution modulo successive powers of . More generally it is used as a generic name for analogues for complete commutative rings (including "p"-adic fields
Berlekamp–Zassenhaus algorithm
In mathematics, in particular in computational algebra, the Berlekamp–Zassenhaus algorithm is an algorithm for factoring polynomials over the integers, named after Elwyn Berlekamp and Hans Zassenhaus. As a consequence of Gauss's lemma, this amounts to solving the problem also over the rationals.
The algorithm starts by finding factorizations over suitable finite fields using Hensel's lemma to lift the solution from modulo a prime "p" to a convenient power of "p". After this the right factors are found