User:D.Lazard/Hensel


 * $$h=fg \pmod I^k$$
 * $$af+bg=1+i; \quad i\in I$$


 * $$h=fg+i_1=fg+i_1(af+bg-i)= (f+i_1b)(g+i_1a)-ii_1-i_1^2ab$$

Thus factorization modulo $$I^{k+1}$$

For quadratic lifting: $$k=1$$, but Bézout must be lifted also
 * $$a(f+i_1b)+b(g+i_1a)= 1+i+2abi_1=1+j$$
 * $$a(1-j)(f+i_1b)+b(1-j)(g+i_1a)=1-j^2$$

Uniqueness?