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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写抽象代数abstract algebra方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写抽象代数abstract algebra代写方面经验极为丰富，各种代写抽象代数abstract algebra相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|抽象代数作业代写abstract algebra代考|Inversions of a Permutation

Permutations play a central role in combinatorics, a field that studies techniques for counting the possible arrangements in any kind of discrete structure. We end this section with a brief discussion on the inversions of a permutation. This concept will come in handy when we discuss even and odd permutations in the next sections.

As a motivating example, suppose that we consider 5 events in history and attempt to remember the order in which they occurred. There are $5 !=120$ possible orderings of this time line. Suppose that we number the events in historical order as $E_1, E_2, E_3, E_4, E_5$ and suppose that someone guesses the historical order as $G_1, G_2, G_3, G_4, G_5$. Any guess about their historical order corresponds to a permutation $\sigma \in S_5$ via
$$G_{\sigma(i)}=E_i \quad \text { for all } i \in{1,2,3,4,5} .$$
This means that the person guessed the actual $i$ th historical event to be the $\sigma(i)$ th event in chronological order.

Suppose that someone guesses the chronological order of the births of five mathematicians and puts them in the following order.

The corresponding permutation is $\sigma=(132)(45)$.
What is a natural way to evaluate how incorrect the guess is? If a guess was correct except for interchanging the first two, i.e., $\sigma=(12)$, that should not be considered egregious. The worst guess would completely reverse the chronological order, i.e., $\sigma=(15)(24)$. A measure of incorrectness for the guessed ordering is to count the number of inversions.

## 数学代写|抽象代数作业代写abstract algebra代考|Useful CAS Commands

Both Maple and SAGE offer commands to determine the order, the parity, the cycle type and many other properties of permutations. We encourage the reader to explore these.

In Maple, the command Perm to define a permutation is immediately available but some of the commands for computing with permutations are in the GroupTheory package. The Maple help files provide a tutorial entitled Working with Permutations. The following code illustrates a few commands that are relevant to the content of this section.

The first and second lines define the permutations $s$ and $t$, the first in standard cycle notation, the second using the $n$-tuple notation. The third line shows how to apply the permutation $s$ as a function to the input of 2 . The next line brings in the GroupTheory package that contains commands and methods to operate on permutations. The last two lines calculate the inverse $s^{-1}$ and composition st.

Illustrating Maple’s programming language, the next block of code defines a procedure that counts the number of inversions of a permutation.

There are a number of ways to define permutations in SAGE and we encourage the reader to consult the documentation files online entitled “Permutations” or “Permutation group elements.” The first of the webpages describes methods associated with permutations that are more relevant for combinatorics with the latter focus more on applications to group theory. The following code illustrates the same commands as the Maple code, but then shows a few commands related to inversions.

# 抽象代数代写

## 数学代写|抽象代数作业代写abstract algebra代考| a- Permutation的倒置

$$G_{\sigma(i)}=E_i \quad \text { for all } i \in{1,2,3,4,5} .$$

## 数学代写|抽象代数作业代写abstract -algebra代考|有用的CAS命令

. sh . sh Maple和SAGE都提供命令来确定排列的顺序、奇偶校验、循环类型和许多其他属性。我们鼓励读者去探索这些 在Maple中，定义排列的命令Perm立即可用，但一些用于计算排列的命令在GroupTheory包中。Maple帮助文件提供了一个名为“使用排列”的教程。下面的代码演示了一些与本节内容相关的命令 第一行和第二行定义了排列$s$和$t$，第一行使用标准循环符号，第二行使用$n$ -tuple符号。第三行显示了如何将排列$s$作为函数应用于2的输入。下一行引入GroupTheory包，其中包含操作排列的命令和方法。最后两行计算逆$s^{-1}$和合成st.

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师