invariants

简明释义

英[ɪnˈvɛərɪənts]美[ɪnˈvɛrɪənts]

n. [数]不变量（invariant 的复数）；不变性

英英释义

单词用法

同义词

反义词

例句

1.A simple proof of six invariants under the transformation of spin axis is put forward.

给出了二次曲面在转轴变换下的六个不变量的简易证明。

2.Yet another approach to adding much more powerful invariants is that of dependent types.

添加更加强大的不变量的另一种方法是从属类型。

3.Let's tackle invariants and consider the code in Figure 1.

让我们来解决不变量和考虑中的代码图1。

4.A simple proof of six invariants under the transformation of spin axis is put forward.

给出了二次曲面在转轴变换下的六个不变量的简易证明。

5.The field need not obey any invariants with respect to others.

该字段不遵循其他字段的不变式。

6.In computer science, we often use invariants to ensure the correctness of algorithms.

在计算机科学中，我们经常使用不变量来确保算法的正确性。

7.The study of invariants is crucial in understanding the symmetry of geometric figures.

研究不变量对理解几何图形的对称性至关重要。

8.In mathematics, invariants are properties that remain unchanged under certain transformations.

在数学中，不变量是指在某些变换下保持不变的性质。

9.In programming, maintaining invariants within a class helps to prevent bugs.

在编程中，保持类中的不变量有助于防止错误。

10.Physics relies on certain invariants to describe the fundamental laws of nature.

物理学依赖于某些不变量来描述自然的基本法则。

作文

In the world of mathematics and computer science, the concept of invariants (不变式) plays a crucial role in ensuring the correctness and stability of algorithms and systems. An invariant is a property or condition that remains unchanged throughout the execution of a process or algorithm. Understanding invariants is essential for both theoretical and practical applications, as they provide a foundation for reasoning about the behavior of programs and mathematical structures.For instance, consider a simple sorting algorithm, such as bubble sort. During the execution of this algorithm, one can define an invariant that states: "At the end of each pass through the list, the largest unsorted element will be in its correct position." This invariant holds true for every iteration of the sorting process, allowing us to conclude that once the algorithm completes, the entire list will be sorted. By identifying and maintaining invariants, programmers can ensure that their algorithms function correctly and efficiently.In addition to sorting algorithms, invariants are also used in various areas of computer science, including data structures, where they help maintain the integrity of the data being processed. For example, in a binary search tree, an invariant might be that for any given node, all values in the left subtree are less than the node’s value, and all values in the right subtree are greater. This invariant allows for efficient searching, inserting, and deleting operations, as it guarantees the structure's properties are preserved.The significance of invariants extends beyond just programming; they also appear in fields like physics and engineering. In these disciplines, invariants can refer to physical quantities that remain constant throughout a process, such as the conservation of energy or momentum in closed systems. This understanding aids scientists and engineers in predicting outcomes and designing systems that behave reliably under various conditions.Moreover, invariants can be found in everyday life, often in the form of principles or rules that guide our actions and decisions. For instance, the principle of equality in mathematics asserts that if two quantities are equal, they remain equal even when manipulated by adding or subtracting the same number from both sides. This invariant serves as a foundational concept that supports more complex mathematical theories and applications.In conclusion, invariants (不变式) are fundamental concepts that help us understand and reason about the stability and correctness of processes across various domains. Whether in computer science, mathematics, physics, or everyday life, recognizing and maintaining invariants can lead to more effective problem-solving and decision-making. As we delve deeper into these subjects, the importance of invariants becomes increasingly evident, highlighting their role as cornerstones of logical reasoning and systematic thinking.