GeneralHenselPackage(RP, TP)

ghensel.spad line 1 [edit on github]

• RP : EuclideanDomain
• TP : UnivariatePolynomialCategory(RP)

This package is used for factorization of bivariate polynomials over a finite field and univariate polynomials with integer coefficients.

HenselLift : (TP, List(TP), RP, PositiveInteger) -> Record(plist : List(TP), modulo : RP)

HenselLift(pol, lfacts, prime, bound) lifts lfacts, that are the factors of pol mod prime, to factors of pol mod prime^k > bound. No recombining is done .

completeHensel : (TP, List(TP), RP, PositiveInteger) -> List(TP)

completeHensel(pol, lfact, prime, bound) lifts lfact, the factorization mod prime of pol, to the factorization mod prime^k>bound. Factors are recombined on the way.

reduction : (TP, RP) -> TP

reduction(u, pol) computes the symmetric reduction of u mod pol