有理数域上多项式不可约的判定

Judgment on Irreducible Polynomials over Rational Field

艾森斯坦因判别法和它的等价判定定理都只是判定有理数域上多项式不可约的充分条件,不能用于判断形式下的多项式是否可约,针对这种情况给出了艾森斯坦因判别法的推广定理,并通过例题说明了它们之间没有必然的包含关系。

Eisenstein discrimination and its equivalent determinant theorem are only sufficient condition for judging the irreducibility of the integer polynomial in rational field, while they can not be used to judge whether the polynomial with could be reduced or not. So in this paper we give the further promotion of Eisenstein discrimination, and illustrate that there have no necessary contain relation among the three theorems by some examples.