Irreducible Integer Coefficients Polynomial Table Production Method Of Realization

Factorization of Integer Polynomial is one of the basic research topics in Fundamental Mathematics. However, as there is no existed easy ways of Factorization, it is commonly difficult for looking for any ways of Determination of reducibility of an Integer Polynomial and its Factorization. We assume that Integer could be classified into two groups according to its reducibility and irreducibility, then pick up the entire Integer that is irreducibility, we get Nature mathematical table. If the hypothesis is positive, then in the researches in reducibility of Polynomial, the solution of irreducibility of Integer Polynomial could not depend on the Determination of reducibility and looking for the ways of Factorization. The answer could be found easily by searching the Nature mathematical table directly. The solution of this problem will have significant contribution to the enhancement of the way of teaching Fundamental Mathematics and application of the Engineering Mathematics. This dissertation did some researches in solution and implication of this problem and has made some achievements.The main objectives are as follows:1.Establish the Corresponding relationships between all the Fractions and all the Polynomial by using Enumerability of rational numbers. That could make the transforming from Polynomial research to Integer research possible.2.Rational numbers. Establish the corresponding between multiplication of Polynomial and Second-level multiplication of rational numbers. The Correspondence of the operation relations could ensure the Feasibility of transformation of the researches.3.Establish a Second-level sieve of Common fraction. Build a relationship between fractions, which could correspond to the factor relations of the polynomial. Moreover, the determination of the relations in the form of twice can indirectly determine relationships between the Polynomial, which could make the transforming from Aliquot relations of the polynomial to the relations in the form of twice possible.4.Conduct the Second-level sieve of Common fraction. The rest of fractions will be accordingly arranged to form an Order permutation of the polynomial. 5.Make a programme of the Diagram plan and programming for all the steps mentioned above in the form of fraction in order to ensure all the objectives could be achieved in the form of fraction.6.Make a programme for outputting the fraction formed results in the form of the Polynomial. That could make the output result appear, as an order permutation of irreducible Polynomial, which is also is a table of irreducible Polynomial.