regular chain

简明释义

直营连销

英英释义

例句

1.Each step in the production line is connected through a regular chain 常规链条 that ensures smooth operations.

生产线中的每一步都通过一个常规链条连接，确保操作顺利进行。

2.Understanding the regular chain 常规链条 of communication is vital for effective teamwork.

理解沟通的常规链条对有效团队合作至关重要。

3.The supply regular chain 常规链条 helps us track inventory and manage logistics effectively.

供应常规链条帮助我们有效跟踪库存和管理物流。

4.In the manufacturing process, we need to ensure that each component is part of a regular chain 常规链条 to maintain efficiency.

在制造过程中，我们需要确保每个组件都是常规链条的一部分，以保持效率。

5.To improve our workflow, we must analyze the regular chain 常规链条 of tasks involved in the project.

为了改善我们的工作流程，我们必须分析项目中涉及的常规链条任务。

作文

In the world of mathematics and algebraic geometry, the concept of a regular chain plays a crucial role in understanding the structure of polynomial ideals. A regular chain is a sequence of polynomials that not only generates an ideal but also satisfies certain regularity conditions that make it useful for various applications. To grasp the importance of a regular chain, one must first understand what an ideal is. An ideal is a special subset of a ring, which in this context is typically a polynomial ring. It consists of polynomials that can be combined and manipulated in specific ways to produce new polynomials within the same set. The notion of a regular chain extends this idea by ensuring that the polynomials in the sequence interact with each other in a well-behaved manner.Consider the example of a system of equations. When solving a system, we often look for solutions that satisfy all equations simultaneously. If we have a regular chain of polynomials representing these equations, it guarantees that the solutions we find will be structured in a consistent way. This is particularly important in computational algebra, where algorithms rely on the properties of these chains to efficiently find solutions or analyze the geometric properties of the solutions.Furthermore, the concept of a regular chain is not limited to theoretical mathematics; it has practical implications in fields such as robotics, computer graphics, and control theory. In robotics, for instance, a regular chain can be used to model the kinematics of robotic arms. By representing the constraints and movements of the arm with polynomials, engineers can ensure that the solutions to these constraints are both feasible and optimal.In computer graphics, the rendering of curves and surfaces often involves the use of regular chains. By defining shapes and their interactions through polynomial equations, artists and designers can create realistic models that behave predictably under transformations like rotation and scaling. This ensures that the visual output remains consistent, enhancing the viewer's experience.Moreover, in control theory, a regular chain helps in the design of systems that need to respond to inputs in a stable manner. By analyzing the behavior of systems through polynomial equations, engineers can predict how changes in input will affect system output, leading to more robust designs.In conclusion, the significance of a regular chain extends far beyond its mathematical definition. It serves as a foundation for numerous applications across various fields, ensuring that systems behave consistently and predictably. Understanding regular chains not only enriches one's knowledge of algebra but also opens doors to practical problem-solving in technology and engineering. As we continue to explore the complexities of mathematics, the regular chain remains a vital concept that bridges the gap between theory and application, demonstrating the beauty and utility of mathematical principles in our everyday lives.

在数学和代数几何的世界中，regular chain（正规链）的概念在理解多项式理想的结构方面起着至关重要的作用。regular chain是一个多项式序列，不仅生成一个理想，而且满足某些规律性条件，使其在各种应用中非常有用。要理解regular chain的重要性，首先必须了解什么是理想。理想是环的一个特殊子集，在这个上下文中，通常是一个多项式环。它由可以以特定方式组合和操作的新多项式组成，产生同一集合中的新多项式。regular chain的概念扩展了这个想法，通过确保序列中的多项式彼此以良好的方式相互作用。考虑一个方程组的例子。当解决一个系统时，我们通常寻找同时满足所有方程的解。如果我们有一个表示这些方程的regular chain多项式，它保证我们找到的解将以一致的方式结构化。这在计算代数中尤为重要，因为算法依赖于这些链的性质，以有效地找到解或分析解的几何属性。此外，regular chain的概念不仅限于理论数学；它在机器人技术、计算机图形学和控制理论等领域具有实际意义。例如，在机器人技术中，regular chain可用于建模机器人手臂的运动学。通过用多项式表示手臂的约束和运动，工程师可以确保这些约束的解既可行又最优。在计算机图形学中，曲线和表面的渲染通常涉及使用regular chains。通过通过多项式方程定义形状及其交互，艺术家和设计师可以创建在旋转和缩放等变换下表现出可预测行为的逼真模型。这确保了视觉输出的一致性，从而增强观众的体验。此外，在控制理论中，regular chain有助于设计需要以稳定方式响应输入的系统。通过分析系统的行为通过多项式方程，工程师可以预测输入变化将如何影响系统输出，从而导致更强大的设计。总之，regular chain的重要性远远超出了其数学定义。它作为多个领域各种应用的基础，确保系统以一致和可预测的方式运行。理解regular chains不仅丰富了人们对代数的知识，还为技术和工程中的实际问题解决打开了大门。随着我们继续探索数学的复杂性，regular chain仍然是一个至关重要的概念，它架起了理论与应用之间的桥梁，展示了数学原理在我们日常生活中的美丽和实用性。