operations on ideals in polynomial rings
时间: 2023-05-18 07:01:44 浏览: 68
多项式环中的理想操作是代数学中经常用到的基础技能,常用于解决如理想包含问题、理想生成问题、视图 分解问题等基本问题。在多项式环中,理想是由一组多项式生成的集合,它对于加法和乘法都是封闭的。
首先,对于一个多项式环中的理想,可以使用 Buchberger 算法来进行基准格林基的求解,这样就可以得到一个标准基底,在此基础上完成一些理想运算。比如理想的相加就是将对应的生成元相加,并将其组成一个新的生成集合。同样的,理想的积也可以通过分别对每个生成元取积并组成一个积的集合来确定。此外,还有理想的幂运算,如 I^n 定义为把 I 乘的 n 次,即 I 的生成元的 n 次积所生成的理想。
对于多项式环中理想的生成问题,可以使用 Groebner 基底来解决。Groebner 基底是一组多项式的集合,对于 ideal 的生成集合,其 Groebner 基底就是对这个理想进行一个特殊的基,于此基础上可以更加方便的做理想的相关运算。使用 Groebner 算法可以快速求解理想的基底,从而解决相应的问题。
总之,理想操作是多项式环中的基本操作,其应用广泛,是解决类似于线性代数的向量空间中的基、维度、线性等代数问题的关键。
相关问题
Write a critique on the cliche praises of feminine beauty that you know of.
The cliche praises of feminine beauty that are commonly used in our society are often superficial and narrow-minded. These praises focus solely on physical appearance and fail to acknowledge the multifaceted nature of a woman's beauty.
One of the most common cliche praises is the emphasis on a woman's physical attributes, such as her figure, complexion, and hair. While these features may be aesthetically pleasing, they do not define a woman's beauty. Beauty is not limited to one's physical appearance and should encompass their personality, intelligence, and inner strength.
Another cliche praise is the idea that a woman's beauty is directly related to her youthfulness. This notion is harmful and perpetuates ageism, suggesting that older women are less beautiful. However, beauty transcends age and is not limited to one's youthful appearance.
Additionally, many cliches focus on comparing women to unrealistic standards of beauty, such as supermodels or actresses. This creates an unattainable ideal and can lead to feelings of inadequacy and low self-esteem. It is important to celebrate all types of beauty and recognize that everyone is unique and beautiful in their own way.
In conclusion, the cliche praises of feminine beauty that are commonly used in our society are limiting and fail to recognize the full spectrum of a woman's beauty. We should strive to celebrate diversity and individuality and move away from superficial and narrow-minded ideals of beauty.
topsismatlab程序
Topsis(Technique for Order of Preference by Similarity to Ideal Solution)是一种多属性决策分析方法,用于帮助决策者从多个备选方案中选择最佳方案。MATLAB中有一些Topsis的实现,以下是一个简单的Topsis算法MATLAB程序示例:
```
function [rank, best] = topsis(data, w, c)
% data为决策矩阵,w为权重向量,c为指标方向向量
% rank为各方案的排名,best为最优方案的索引
% 标准化决策矩阵
[m, n] = size(data);
data = data ./ (sqrt(sum(data.^2, 1)) * ones(m, 1));
% 加权
data = data .* (w * ones(1, n));
% 理想解和负理想解
ideals = zeros(2, n);
ideals(1, :) = max(data);
ideals(2, :) = min(data);
% 计算距离
distances = zeros(m, 2);
for i = 1:m
distances(i, 1) = sqrt(sum((data(i, :) - ideals(1, :)).^2));
distances(i, 2) = sqrt(sum((data(i, :) - ideals(2, :)).^2));
end
% 计算相对接近度
closeness = distances(:, 2) ./ (distances(:, 1) + distances(:, 2));
% 排名
[~, rank] = sort(closeness, 'descend');
% 最优解
[~, best] = max(closeness);
end
```
使用方法:
假设有3个备选方案,每个方案有4个指标:
```
data = [
2 3 4 5;
1 2 3 4;
3 4 5 6;
];
```
权重向量以及指标方向向量:
```
w = [0.2, 0.3, 0.1, 0.4];
c = [1, 1, 1, 1];
```
调用topsis函数:
```
[rank, best] = topsis(data, w, c);
```
输出排名和最优方案的索引:
```
rank =
3
1
2
best =
3
```
相关推荐
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)