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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|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.

## 数学代写|抽象代数作业代写abstract algebra代考|Definition and Examples

Since a subgroup $H$ of a group $G$ must be nonempty, there exists some $x \in H$. Since $H$ is closed under taking inverses, then $x^{-1} \in H$. Since $H$ is closed under the group operation, then $e=x x^{-1} \in H$. Hence, a subgroup contains the identity element. The property of associativity is inherited from associativity in $G$ and so since $e \in H$ and $H$ is closed under taking inverses, $H$ equipped with the binary operation on $G$ is a group in its own right. (As a point of terminology, it is important to understand that we do not say that “a group is closed under an operation.” Such a statement is circular since a binary operation on $G$ by definition maps any pair of elements in $G$ back into $G$. The terminology of “closed under an operation” is a matter of concern only for strict subsets of $G$.)

Example 1.6.2. With the usual addition operation, $\mathbb{Z} \leq \mathbb{Q} \leq \mathbb{R} \leq \mathbb{C}$. With the multiplication operation we have $\mathbb{Q}^* \leq \mathbb{R}^* \leq \mathbb{C}^$. However, $\mathbb{Z}^$ is not a subgroup of $\mathbb{Q}^$, written $\mathbb{Z}^ \mathbb{Z}^$, because even though $\mathbb{Z}^$ is closed under multiplication, it is not closed under taking multiplicative inverses. For example $2^{-1}=\frac{1}{2} \notin \mathbb{Z}^*$.

Example 1.6.3. Any group $G$ always has at least two subgroups, the trivial subgroup ${c}$ and all of $G$.

Example 1.6.4. If $G=D_n$, then $R=\left{\iota, r, r^2, \ldots, r^{n-1}\right}$ is a subgroup. This is the subgroup of rotations. Also for all integers $i$ between 0 and $n-1$, the subsets $H_i=\left{l, s r^i\right}$ are subgroups. These subgroups of two elements correspond to reflection about various lines of symmetry.

Fxample 1.6.5. I.et $G=S_n$ and consider the subset of permutations that leave the elements ${m+1, m+2, \ldots n}$ fixed. This is a subgroup of $S_n$ that consists of all elements in $S_m$.

# 抽象代数代写

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

Maple 和 SAGE 都提供命令来确定排列的顺序、奇偶性、循环类型和许多其他属性。我们鼓励读者探索这些。

## 有限元方法代写

assignmentutor™作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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