canonical form

简明释义

典式

英英释义

例句

1.The database uses a canonical form 标准形式 to eliminate redundancy in its records.

数据库使用canonical form 标准形式 来消除记录中的冗余。

2.In mathematics, every polynomial can be expressed in its canonical form 标准形式 for easier analysis.

在数学中，每个多项式都可以以其canonical form 标准形式 表达，以便于分析。

3.When normalizing data, it's important to convert it into a canonical form 标准形式 to ensure consistency.

在规范化数据时，将其转换为canonical form 标准形式 是确保一致性的重要步骤。

4.The XML document was transformed into a canonical form 标准形式 for better interoperability.

XML 文档被转换为 canonical form 标准形式 以提高互操作性。

5.In programming, a URL is often stored in a canonical form 标准形式 to avoid duplicates.

在编程中，URL 通常以 canonical form 标准形式 存储，以避免重复。

作文

In mathematics and computer science, the concept of canonical form plays a crucial role in simplifying complex structures and making them easier to work with. The term canonical form refers to a standard or normalized representation of an object or a mathematical expression that allows for easier analysis and manipulation. For instance, in linear algebra, matrices can be transformed into their canonical form, which simplifies the process of solving systems of equations. This transformation helps to identify the properties of the matrix more clearly, such as its rank and eigenvalues.Moreover, in the realm of programming, the idea of canonical form is often applied to data structures. When we talk about data serialization, we refer to the process of converting data into a format that can be easily stored or transmitted. By converting data into its canonical form, we ensure that it remains consistent and can be interpreted correctly across different systems. This is particularly important in distributed systems where data integrity and consistency are paramount.The significance of canonical form extends beyond mathematics and computer science; it also finds applications in linguistics and logic. In linguistics, a canonical form can refer to the base form of a word, which serves as a reference point for inflected forms. For example, the verb "to run" has a canonical form that represents its infinitive state, while other forms like "running" or "ran" are derived from it. Understanding these forms helps linguists analyze language structure and usage effectively.In logic, the concept of canonical form is used to express logical formulas in a standardized way, making them easier to evaluate and compare. For example, propositional logic can be represented in a canonical form known as conjunctive normal form (CNF) or disjunctive normal form (DNF). These representations allow for systematic approaches to logical reasoning and problem-solving.The importance of canonical form lies in its ability to streamline processes and enhance clarity. By adhering to a canonical form, individuals and systems can communicate more effectively, reducing ambiguity and potential errors. Whether in mathematics, programming, linguistics, or logic, the use of canonical form facilitates a deeper understanding of underlying structures and relationships.In conclusion, the concept of canonical form is integral to various fields of study, providing a foundation for analysis, comparison, and communication. It serves as a powerful tool for simplifying complex ideas and ensuring consistency across different contexts. As we continue to explore the intricacies of mathematics, computer science, linguistics, and logic, the relevance of canonical form will undoubtedly remain significant, guiding us toward clearer insights and more efficient problem-solving strategies.

在数学和计算机科学中，规范形式的概念在简化复杂结构并使其更易于处理方面发挥着关键作用。术语规范形式指的是对象或数学表达式的标准或规范化表示，这种表示使分析和操作变得更容易。例如，在线性代数中，矩阵可以转换为其规范形式，这简化了求解方程组的过程。这种转换有助于更清晰地识别矩阵的属性，例如其秩和特征值。此外，在编程领域，规范形式的概念通常应用于数据结构。当我们谈论数据序列化时，我们指的是将数据转换为可以轻松存储或传输的格式。通过将数据转换为其规范形式，我们确保其保持一致，并可以在不同系统之间正确解释。这在分布式系统中尤为重要，因为数据的完整性和一致性至关重要。规范形式的重要性超越了数学和计算机科学；它在语言学和逻辑学中也有应用。在语言学中，规范形式可以指一个词的基本形式，它作为变形形式的参考点。例如，动词“跑”的规范形式代表其不定式状态，而其他形式如“正在跑”或“跑过”是从中派生的。理解这些形式有助于语言学家有效分析语言结构和用法。在逻辑学中，规范形式的概念用于以标准化方式表达逻辑公式，使其更容易评估和比较。例如，命题逻辑可以用一种称为合取范式（CNF）或析取范式（DNF）的规范形式表示。这些表示法允许对逻辑推理和问题解决采取系统的方法。规范形式的重要性在于其能够简化过程并增强清晰度。通过遵循规范形式，个人和系统可以更有效地沟通，减少歧义和潜在错误。无论是在数学、编程、语言学还是逻辑中，使用规范形式都有助于深入理解基础结构和关系。总之，规范形式的概念对于各个研究领域至关重要，为分析、比较和沟通提供了基础。它作为简化复杂思想和确保不同背景下的一致性的强大工具。随着我们继续探索数学、计算机科学、语言学和逻辑学的复杂性，规范形式的相关性无疑将继续显著，引导我们朝着更清晰的见解和更有效的问题解决策略迈进。