证明非还原菌素Z[x]
Certifying Irreducibility in Z[x]
摘要：
我们考虑的问题证明一个多项式在${\mathbb Z}[x]$或${\mathbb Q}[x]$是不可约的。知道多项式是不可约的让我们认识到商环实际上是一个域扩张（等价于~多项式理想是最大的）。通过因式分解来检查多项式是不可约的是不令人满意的，因为它需要信任一个相对较大和复杂的程序（其正确性不容易验证）。我们提出了一个实用的方法来生成证书的不可约，可以通过相对简单的计算进行验证，我们假设，素数和不可约的${\mathbb F}_p[x]$是自证明。
英文摘要：
We consider the question of certifying that a polynomial in ${\mathbb Z}[x]$ or ${\mathbb Q}[x]$ is irreducible. Knowing that a polynomial is irreducible lets us recognise that a quotient ring is actually a field extension (equiv.~that a polynomial ideal is maximal). Checking that a polynomial is irreducible by factorizing it is unsatisfactory because it requires trusting a relatively large and complicated program (whose correctness cannot easily be verified). We present a practical method for generating certificates of irreducibility which can be verified by relatively simple computations; we assume that primes and irreducibles in ${\mathbb F}_p[x]$ are self-certifying.
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