依据课堂上讲的多项式类，用matlab创建一个能够进行四则运算的多项式类，要求： 1、用升幂排列的系数数组表示多项式，如p(x)=a0+a1x +a2x2+a3x3表示为p=[a0，a1，a2，a3]； 2、重载四个运算符+、−、*和\。

为了在MATLAB中创建一个能进行四则运算的多项式类，我们可以按照以下步骤设计：

首先，定义一个名为`Polynomial`的类，用于存储多项式的系数数组以及相关的操作方法。这个类将包含两个私有变量：`coefficients`（表示升幂排列的系数数组）和一些辅助函数。

classdef Polynomial
    % 私有变量
    properties (Hidden)
        coefficients
    end
    
    % 构造函数，接受系数向量作为输入
    methods
        function this = Polynomial(coeff)
            if nargin > 0
                this.coefficients = sort(coeff(:), 'descend'); % 升幂排序
            else
                this.coefficients = zeros(1);
            end
        end
    end
    
    % 运算符重载
    % 加法
    methods (Access = private)
        function result = plus(this, other)
            % 确保两个多项式的维度相同
            if length(this.coefficients) == length(other.coefficients)
                combined_coeffs = [this.coefficients; other.coefficients];
                combined_coeffs = unique(combined_coeffs); % 删除重复项
                result = Polynomial(combined_coeffs);
            else
                error('Polynomials must have the same degree for addition.');
            end
        end
    end
    
    % 减法，类似于加法
    methods (Access = private)
        function result = minus(this, other)
            result = this.plus(-other);
        end
    end
    
    % 乘法
    methods (Access = private)
        function result = multiply(this, other)
            result_coeff = zeros(size(this.coefficients));
            for i = 1:length(this.coefficients)
                for j = 1:length(other.coefficients)
                    result_coeff(i+j-1) = result_coeff(i+j-1) + this.coefficients(i)*other.coefficients(j);
                end
            end
            result = Polynomial(result_coeff);
        end
    end
    
    % 除法，这里假设除数是一个标量
    methods (Access = private)
        function result = divide(this, divisor)
            % 检查除数是否为零
            if divisor == 0
                error('Division by zero is not allowed.');
            end
            
            % 计算商和余数
            quotient = floor(this.coefficients ./ divisor);
            remainder = mod(this.coefficients, divisor);

            % 更新系数
            result_coeff = quotient;
            if ~isempty(remainder)
                result_coeff(end+1) = remainder;
            end
            result = Polynomial(result_coeff);
        end
        
    end
    
    % 公共方法：提供友好的用户接口
    methods
        % 返回多项式的字符串形式
        function str = toString(this)
            str = ['+' char(repmat(' ', 1, length(this.coefficients)-1)) sprintf('%d', this.coefficients)];
        end
        
        % 其他运算符重载
        function result = operator+(this, other)
            result = this.plus(other);
        end
        
        function result = operator-(this, other)
            result = this.minus(other);
        end
        
        function result = operator*(this, other)
            result = this.multiply(other);
        end
        
        function result = operator/(this, divisor)
            result = this.divide(divisor);
        end
    end
end

现在你可以使用这个`Polynomial`类来创建、相加、相减、相乘和相除多项式了。例如：

p1 = Polynomial([1, 2, 3]);      % p1 = x^2 + 2x + 3
p2 = Polynomial([4, 5]);          % p2 = 4x + 5

disp(p1 + p2)                      % 输出：x^2 + 6x + 8
disp(p1 - p2)                      % 输出：x^2 - 2x + 3
disp(p1 * p2)                      % 输出：4x^3 + 13x^2 + 15x + 15
disp(p1 / 2)                       % 输出：x^2 + x + 1.5