generating set

简明释义

发电装置

英英释义

例句

1.The engineer designed a new generating set to improve the power output of the facility.

工程师设计了一套新的发电机组以提高设施的电力输出。

2.The generating set was installed to provide electricity to remote areas.

这套发电机组被安装用来为偏远地区提供电力。

3.The generating set can run on both diesel and natural gas, making it versatile.

这套发电机组可以使用柴油和天然气运行，具有多功能性。

4.Our company specializes in manufacturing high-efficiency generating sets for industrial use.

我们公司专注于制造高效的发电机组用于工业用途。

5.In case of a power outage, we have a backup generating set ready for use.

在停电的情况下，我们有一个备用的发电机组准备使用。

作文

In the realm of mathematics and algebra, the concept of a generating set is fundamental to understanding how certain structures can be formed. A generating set refers to a collection of elements from which other elements of a particular set can be derived through various operations. For example, in linear algebra, a generating set for a vector space is a set of vectors such that any vector in that space can be expressed as a linear combination of the vectors in the generating set. This idea not only simplifies the study of vector spaces but also provides a framework for exploring more complex mathematical structures.The importance of generating sets extends beyond pure mathematics into practical applications across various fields. In computer science, for instance, when designing algorithms, understanding the generating set of a problem can lead to more efficient solutions. By identifying the minimal set of inputs necessary to produce desired outputs, programmers can optimize their code and reduce computational time.Moreover, in the context of group theory, a branch of abstract algebra, a generating set plays a crucial role in defining groups. A group can be generated by a set of elements where every element of the group can be expressed as a combination of these generators. This concept is vital for classifying groups and understanding their properties. For example, the symmetric group on three letters can be generated by two permutations, and from these, all other permutations can be obtained.In addition to mathematics and computer science, the idea of a generating set can also be found in the field of physics, particularly in quantum mechanics. The state of a quantum system can often be described using a generating set of basis states. By manipulating these basis states, physicists can predict the behavior of more complex systems. This highlights the versatility of the generating set concept across various disciplines.Furthermore, the notion of a generating set encourages critical thinking and problem-solving skills. When faced with a complex problem, identifying a generating set allows individuals to break down the problem into manageable parts. This analytical approach fosters creativity and innovation as it encourages one to think about the relationships between different elements and how they can be combined to achieve a specific outcome.In conclusion, the concept of a generating set is not merely an abstract mathematical idea; it is a powerful tool that finds applications in numerous fields. Whether in mathematics, computer science, physics, or even in everyday problem-solving, generating sets provide a framework for understanding and tackling complexity. By grasping the essence of a generating set, one can unlock new ways of thinking and enhance their ability to analyze and solve problems effectively. As we continue to explore the depths of various disciplines, the significance of generating sets will undoubtedly remain a cornerstone of intellectual inquiry and practical application.

在数学和代数的领域中，生成集合的概念对于理解某些结构是如何形成的至关重要。生成集合指的是一组元素，通过各种运算可以从中导出特定集合的其他元素。例如，在线性代数中，向量空间的生成集合是一组向量，使得该空间中的任何向量都可以表示为生成集合中向量的线性组合。这个思想不仅简化了对向量空间的研究，还提供了探索更复杂数学结构的框架。生成集合的重要性超越了纯数学，延伸到各个领域的实际应用中。例如，在计算机科学中，当设计算法时，理解问题的生成集合可以导致更高效的解决方案。通过识别产生所需输出所需的最小输入集，程序员可以优化他们的代码并减少计算时间。此外，在群论的背景下，抽象代数的一个分支，生成集合在定义群方面发挥着关键作用。一个群可以由一组元素生成，其中群的每个元素都可以表示为这些生成元的组合。这个概念对于分类群和理解其属性至关重要。例如，三元对称群可以由两个置换生成，从这些置换中可以获得所有其他置换。除了数学和计算机科学，生成集合的概念还可以在物理学领域找到，特别是在量子力学中。量子系统的状态通常可以使用生成集合的基态来描述。通过操纵这些基态，物理学家可以预测更复杂系统的行为。这突显了生成集合概念在各个学科中的多样性。此外，生成集合的概念鼓励批判性思维和解决问题的能力。当面临复杂问题时，识别生成集合使个人能够将问题分解为可管理的部分。这种分析方法促进了创造力和创新，因为它鼓励人们思考不同元素之间的关系以及如何将它们结合以实现特定结果。总之，生成集合的概念不仅仅是一个抽象的数学思想；它是一个强大的工具，在众多领域中都有应用。无论是在数学、计算机科学、物理学，还是在日常问题解决中，生成集合都提供了理解和应对复杂性的框架。通过掌握生成集合的本质，人们可以开启新的思维方式，提高分析和有效解决问题的能力。在我们继续探索各个学科的深度时，生成集合的重要性无疑将继续成为智力探究和实际应用的基石。