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Discusses the entire coefficient multinomial shallowly in region of rationality indivisible distinction method
This article introduced first some basic definitions, the theorem, then gave have judged a coefficient multinomial in the region of rationality whether improper several methods. First gave renowned Ison Stein to distinguish the method, but it also had the limitation: It is only a sufficient condition, uses it only to be possible to determine some special entire coefficient multinomial on the region of rationality irreducibility. Therefore we can not but explore some other methods, including: Ison Stein distinguishes method equal form, counter-evidence method, substitution method, use rational root distinction method, use factorisation uniqueness theorem and so on.

整系数多项式；Entire coefficient multinomial
数域；Number field
不可约多项式；Irreducible polynomial
艾森斯坦因判别法
Ison Stein distinguishes method

Discussed shallowly the entire coefficient multinomial this article introduced first in region of rationality's indivisible distinction law some basic definitions, the theorem, then gave have judged a coefficient multinomial in the region of rationality whether improper several methods. First gave renowned Ison Stein to distinguish the law, but it also had the limitation: It is only a sufficient condition, uses it only to be possible to determine some special entire coefficient multinomial on the region of rationality irreducibility. Therefore we can not but explore some other methods, including: Ison Stein distinguishes method equal form, reduction to absurdity, substitution law, use rational root distinction law, use factorisation uniqueness theorem and so on.

key word: Entire coefficient multinomial; Number field; Irreducible polynomial; Ison Stein distinguishes the law

On the whole polynomial coefficient in the domain can not be rational about discrimination law
This article first introduced some basic definitions, theorems, and then gives the judge a whole polynomial coefficient in the rational domain about whether the several ways. First is the famous Eisenstein because of discrimination law, but it also has limitations: it is only a sufficient condition, use it only can determine the whole of some special factor polynomials in the domain can not be rational about sexual. Therefore, we have to explore some other ways, including: Eisenstein criterion for the equivalent form of reduction to absurdity, the substitution law, rational use of Gen-discrimination law, use of factorization, and so the only theorem.
Key words: the whole factor polynomials; several domain; not about polynomials; Eisenstein because of discrimination law