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1·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。

2·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。

3·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。

4·On the dialectic point of view, the influences of Cauchy's systematical study on the theory of permutation to understanding Galois theory to mathematicians in France are appraised.

从辩证的角度，评价了柯西系统的置换理论研究对法国数学家在深刻理解伽罗瓦数学工作过程中所产生的正、反两方面的影响。

5·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。

6·The group which is founded by Galois and Abel and the theory which is proposed by Klein provide the tool from the second stage to the third stage of the geometry.

而由伽罗瓦和阿贝尔创立的群的结构并由克莱因提出的几何变换群理论为几何学从第二阶段到第三阶段的转变提供了依据。

7·What had led Galois to invent this theory?

是什么导致伽罗瓦发明这条理论？

8·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。

9·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。