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1·What had led Galois to invent this theory?

是什么导致伽罗瓦发明这条理论？

2·And once Galois had started to work on it, had he made any false starts, gone down any dead ends?

一旦伽罗瓦开始研究，他有没有犯过错误，最终走进了死胡同？

3·The main means used in the paper are group theory, Galois field, module algebra and linear algebra.

文中涉及的主要理论有群论，伽罗华域，模代数和线性代数。

4·Long standing questions about compass and straightedge construction were finally settled by Galois theory.

长期存在的问题，指南针和直尺建设的最后解决伽罗瓦理论。

5·A number of ancient problems concerning Compass and straightedge constructions were finally solved using Galois theory.

从目前的罗盘和直尺古代建筑的一些问题终于解决了使用伽罗瓦理论。

6·Modular inversion is a part of the kernel for computations in the Galois field GF (p) used by many public key cryptosystems.

有限域上的模逆运算是许多公钥密码系统使用的算法中的核心域运算之一。

7·Based on Galois theory of definite field, using the square prime sequence, the code function of basic prime code is modified and extended.

在伽罗华有限域理论的基础上，用素域上的二次素数序列对素数码的码函数进行改进。

8·I was not able to bring my un-ease into focus, to get hold of it, find words for it, until I had finished their book on Galois and the Theory of Groups.

在读他们关于伽罗瓦及阶群理论之前，我无法理解自己的这种不满足，既无法掌握也无以言表。

9·The polarities check ability, minimum code distance and capacity of correct single bit error of CRC-CCITT are proved by using galois field polynomial theory.

以国际标准CRC-CCITT循环冗余校验码为研究对象，利用近世代数多项式理论证明其奇偶校验性质、最小码距和纠正单比特错误能力。

10·According to algebraic property that a direct sum of Galois fields is isomorphic to a finite ring, the linear block code for multiplexing systems is proposed.

依据有限域直和与有限环同构的代数性质，对多路复用系统构造线性分组码。