commutability

简明释义

英[kəmjuːtəˈbɪlɪti]美[kəˌmjuːtəˈbɪləti]

n. 可代替；[物] 可对易性

英英释义

单词用法

同义词

反义词

例句

1.The performance of the sketch dint have mightiness of image pleasant impression with not commutability of alone of art magic power.

素描的表现力具有强烈的形象美感和不可代替的单独的艺术魅力。

2.The performance of the sketch dint have mightiness of image pleasant impression with not commutability of alone of art magic power.

素描的表现力具有强烈的形象美感和不可代替的单独的艺术魅力。

3.The concept of commutability is crucial in mathematics, especially in group theory.

在数学中，可交换性的概念是至关重要的，尤其是在群论中。

4.In programming, the commutability of functions can simplify code and improve readability.

在编程中，函数的可交换性可以简化代码并提高可读性。

5.The commutability of certain operations determines how they can be rearranged without affecting the result.

某些操作的可交换性决定了它们如何可以重新排列而不影响结果。

6.In physics, the commutability of observables is a key factor in quantum mechanics.

在物理学中，观测量的可交换性是量子力学中的一个关键因素。

7.Understanding the commutability of different tasks can help in optimizing workflow.

理解不同任务的可交换性可以帮助优化工作流程。

作文

In the realm of mathematics and computer science, the concept of commutability plays a crucial role in understanding how operations can be rearranged without altering the outcome. Commutability refers to the property that allows two elements or operations to be interchanged. For example, in arithmetic, the addition of two numbers is commutative because changing the order of the numbers does not change the sum. This fundamental principle extends beyond simple arithmetic to more complex mathematical structures and algorithms. The significance of commutability can be seen in various fields, including algebra, where the commutative property of addition and multiplication is foundational. In algebraic structures such as groups, rings, and fields, understanding whether operations are commutative helps mathematicians categorize and work with these structures effectively. In computer science, commutability is essential when designing algorithms. For instance, when processing data, if certain operations can be performed in any order without affecting the final result, developers can optimize their code for efficiency. This is particularly relevant in parallel computing, where tasks can be executed simultaneously. If operations are commutable, they can be distributed across multiple processors, significantly speeding up computation times. Moreover, the concept of commutability is not limited to mathematics and computer science; it also has implications in physics and engineering. For example, in quantum mechanics, the commutation relations between observables determine the nature of physical systems. Understanding which measurements can be performed simultaneously without interference is critical for experimental design and interpretation of results. In everyday life, we encounter commutability in various forms, often without realizing it. Consider the act of preparing a meal: the order in which you chop vegetables and cook them may vary, but as long as you follow the recipe, the final dish remains the same. This illustrates the practical importance of commutability in our daily routines, emphasizing its relevance beyond theoretical contexts. In conclusion, commutability is a fundamental concept that permeates multiple disciplines, from mathematics and computer science to physics and everyday activities. Recognizing and leveraging commutability allows for greater flexibility and efficiency in problem-solving and decision-making processes. As we continue to explore and innovate in various fields, the awareness of commutability will undoubtedly enhance our understanding and capabilities, leading to more effective solutions and advancements in technology and science.

在数学和计算机科学领域，可交换性的概念在理解操作如何重新排列而不改变结果方面发挥着至关重要的作用。可交换性指的是允许两个元素或操作互换的性质。例如，在算术中，两个数字的加法是可交换的，因为改变数字的顺序不会改变和。这一基本原则不仅限于简单的算术运算，还扩展到更复杂的数学结构和算法中。 可交换性的重要性可以在多个领域中看到，包括代数，在这里，加法和乘法的可交换性质是基础。在群、环和域等代数结构中，理解操作是否可交换有助于数学家有效地对这些结构进行分类和研究。 在计算机科学中，可交换性在设计算法时至关重要。例如，在处理数据时，如果某些操作可以以任何顺序执行而不影响最终结果，开发人员就可以优化代码以提高效率。这在并行计算中特别相关，其中任务可以同时执行。如果操作是可交换的，它们可以分配到多个处理器上，从而显著加快计算时间。 此外，可交换性的概念不仅限于数学和计算机科学；它在物理学和工程学中也有影响。例如，在量子力学中，观测量之间的对易关系决定了物理系统的性质。了解哪些测量可以同时进行而不产生干扰，对于实验设计和结果解释至关重要。 在日常生活中，我们以各种形式遇到可交换性，往往没有意识到它。考虑准备一顿饭的行为：切菜和烹饪的顺序可能会有所不同，但只要遵循食谱，最终的菜肴仍然保持不变。这说明了可交换性在我们日常生活中的实际重要性，强调了它在理论背景之外的相关性。 总之，可交换性是一个基本概念，渗透到多个学科中，从数学和计算机科学到物理学和日常活动。认识到并利用可交换性可以在解决问题和决策过程中提供更大的灵活性和效率。随着我们在各个领域的不断探索和创新，对可交换性的认知无疑将增强我们的理解和能力，导致更有效的解决方案以及科技和科学的进步。