Factorization Module Based On The Ntl Platform

Calculation plays an important role in the development of human society,every major scientific and technological breakthrough depend on the calculation.At first,the number range expressed by computer is limited,the calculation is numerical,and gets the approximate results. In fact, in the natural science and engineering,not only approximate calculation,the formula derivation and simplifying expressions are more important,need to obtain accurate results,these calculations named symbolic computation are formula derivation in accordance with established rules.The main features of symbolic computaion are accurate results and stable process, the symbolic computaion has been widely used where needs accurate results,such as the computer automated reasoning and verifiable calculation. Numerical calculation has the advantages which are using floating-point to deal with approximate issues and solving large-scale problems,and has been widely used in engineering areas ,but it's calculation process is not stable,while generally only get partial solution,and miss some meaningful solutions.The basic idea of polynomial factorization is to transform multivariate polynomial factorization into univariate polynomial factorization,so, firstly univariate polynomial factorization must be solved. But prior to this,we have to know the the basic knowledge of algebra, the large integer representation and operations,polynomial representation and operations, the Euclidean algorithm for seeking the greatest common factor.The classical symbolic computation method Hensel lifting is our final goal,the basic idea is to get a initial factorization when module the prime p,by squarefree-factorization distinct-degree factorization,equal-degree factorization, then lift it to a new factorization while module prime p power.Factorization is a basic function of a computer algebra system, and is widely used in symbolic computaion and automated reasoning. Although,Maple has the function of polynomial factorization,it shows many disadvantages,for example,software system is too large,low efficiency, different program languages between different versions,and poor portability. NTL is a GNU library and the source code is open for us. It can operate large integer and univariate polynomials,unlucky,it only has the univariate polynomial factorization,no multivariate polynomial factorization. Someone has worked in the NTL library to implement the function of multivariate polynomial factorization,but the program is not stable,can only resolve small-scale problems. for these disadvantages, author append new class libraries,and develop multivariate polynomial factorization program on the NTL library using C++ language, compare it to Maple ,it has greater efficiency.