论文标题
证明Z [X]中的不可约性
Certifying Irreducibility in Z[x]
论文作者
论文摘要
我们考虑了证明$ {\ mathbb z}中的多项式的问题[x] $或$ {\ mathbb q} [x] $是不可约的。知道多项式是不可约的，让我们认识到商环实际上是一个场扩展（等价〜，多项式理想是最大的）。通过对多项式进行分解是不可信的，因为它需要信任一个相对较大且相对复杂的程序（无法轻易验证其正确性）。我们提出了一种实用方法来生成不可约性证书，可以通过相对简单的计算来验证。我们假设$ {\ mathbb f} _p [x] $中的Primes和Inrreducibles是自我认证。
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.
