Hensel lifting and bivariate polynomial factorisation over finite fields
نویسندگان
چکیده
This paper presents an average time analysis of a Hensel lifting based factorisation algorithm for bivariate polynomials over finite fields. It is shown that the average running time is almost linear in the input size. This explains why the Hensel lifting technique is fast in practice for most polynomials.
منابع مشابه
An efficient sparse adaptation of the polytope method over I and a record-high binary bivariate factorisation
A recent bivariate factorisation algorithm appeared in (Abu-Salem et al., 2004) based on the use of Newton polytopes and a generalisation of Hensel lifting. Although possessing a worst case exponential running time like the Hensel lifting algorithm, the polytope method should perform well for sparse polynomials whose Newton polytopes have very few Minkowski decompositions. A preliminary impleme...
متن کاملGCD and Factorisation of multivariate polynomials
Some widely known techniques can be used to factorise univariate polynomials over the domain of integers. However, finding algorithms which factorise univariate and multivariate polynomials over Z and other domains is a little trickier. Several factorisation algorithms first need GCDs of the polynomials. Computing GCDs of polynomials is also necessary for adding rational functions. Both problem...
متن کاملFactoring bivariate polynomials using adjoints
We relate factorization of bivariate polynomials to singularities of projective plane curves. We prove that adjoint polynomials of a polynomial F ∈ k[x, y] with coefficients in a field k permit to recombinations of the factors of F (0, y) induced by both the absolute and rational factorizations of F , and so without using Hensel lifting. We show in such a way that a fast computation of adjoint ...
متن کاملAlgebraic Osculation and Factorization of Sparse Polynomials
We prove a theorem on algebraic osculation and we apply our result to the Computer Algebra problem of polynomial factorization. We consider X a smooth completion of C and D an effective divisor with support ∂X = X \ C. Our main result gives explicit conditions equivalent to that a given Cartier divisor on the subscheme (|D|,OD) extends to X. These osculation criterions are expressed with residu...
متن کاملFactorization of Polynomials by E. Kaltofen Abstract Algorithms for factoring polynomials in one or more variables over various coefficient
Algorithms for factoring polynomials in one or more variables over various coefficient domains are discussed. Special emphasis is given to finite fields, the integers, or algebraic extensions of the rationals, and to multivariate polynomials with integral coefficients. In particular, various squarefree decomposition algorithms and Hensel lifting techniques are analyzed. An attempt is made to es...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Comput.
دوره 71 شماره
صفحات -
تاریخ انتشار 2002