Also, it is proved that many algebraic number fields of finite degree are not elementarily equivalent to the above-mentioned ultraproducts.
还证明了很多有限次代数数域不与上述的超积初等等价。
Then he considers the case of algebraic numbers and obtains some results like the following: Every real algebraic number field of finite degree is non-inductive;
然后着重在代数范围内进行讨论，得到下列的结果：每个有限次实代数数域都不是归纳域；
Diophantine equation is an important subject in number theory and closely connected with algebraic number theory, combinatorics, algebraic geometry and computer science etc.
丢番图方程是数论中一个十分重要的研究课题，与代数数论、组合数学、代数几何等有密切联系。
In the nineteenth century, the system of algebraic knowledge is enormous, which contains the permutation group, matrix, algebraic number theory, algebraic geometry and other branches.
十九世纪的代数学知识体系庞大，它包含置换群、矩阵、代数数论、代数几何等多个分支。
Many of the familiar algebraic rules for real number arithmetic do not always hold for floating-point arithmetic.
对于浮点算法而言，许多惯用的实数算法代数规则有时并不适用。
If the number of faults in a circuit does not greater than the number of ports, the faults can be analysed by this method only using some algebraic computations.
如果电路中故障数不超出端口数，则利用这个方法只要经过一些代数运算就可以分析电路中的故障。
There exist a number of typical systems and models which possess the three generator Lie algebraic structure in quantum optics, atomic and molecular physics and condensed matter physics.
在量子光学、凝聚态物理、原子分子物理中存在许多典型的具有三生成元李代数结构的量子系统或模型。
They are one of only four number systems in which division is possible, and so allow the full range of algebraic operations to be performed.
八元数实在是个古怪的东西，它们是仅有的可能做除法的四种数制中之一，因此容许运行满量程的代数运算。
In the field of optical computing and parallel information processing, several number systems have been used for different arithmetic and algebraic operations.
在光计算和并行信息处理领域中，用多种数位系统进行不同的算术和代数运算。
In solving rational inequalities, using the number line yields a higher correctness rate than using algebraic manipulations.
解答分式不等式，选用数轴标根法比代数方法有更高的正确率。
Octonions are indeed odd creatures. They are one of only four number systems in which division is possible, and so allow the full range of algebraic operations to be performed.
八元数实在是个古怪的东西，它们是仅有的可能做除法的四种数制中之一，因此容许运行满量程的代数运算。
While most of the students use algebraic manipulations, some adopted the method of using the number line, and still some few solve by sketching the graphs.
解答二次不等式，选用代数方法比数轴标根法有更高的正确率；
It's a recursive construction. Given any odd number, we can construct Boolean function with optimum algebraic immunity in the same number of variables.
这是一个递归构造的方法，利用该方法，对任意的奇数，都可以构造相同变元数量的代数免疫最优布尔函数。
In this lecture the speaker will demonstrate sample algebraic and number theory applications in information security, in particular, in the design of cryptosystems.
在此讲座中，报告人将用实例展示代数和数论在信息安全，特别是密码系统设计中的应用。
Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups.
直达数论和量组，题目由于计算的复杂性，代数学的几何学，力学包括范围。
Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups.
直达数论和量组，题目由于计算的复杂性，代数学的几何学，力学包括范围。
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