在Python使用 eval() 求解线性方程

使用 a + bx = c + dx 形式的一个变量的线性方程可以在Python使用eval()函数求解。输入类型将是一个字符串形式的线性方程。

句法：

eval(expression, globals=None, locals=None)

在这里，我们将方程转换为实数和虚数的表达式，以便 eval 可以轻松处理它。

例如，通过将右侧的所有项向左移动， 5x + 4 = 2x + 10变为5j + 4 – (2j + 10) 。我们正在将这个方程转换为一个复杂的方程，因为 eval() 无法以其他方式处理方程。将其转换为复数有助于更快地进行评估。

步骤1：我们将使用Python的replace()将“=”替换为“-(”，并将“x”替换为“j”。

第 2 步：然后在字符串中添加“+)”以完成表达式。

第 3 步：然后执行 {“j”:1j} 将等式更改为易于由 eval()函数计算的格式。在这一步中，所有的常数项都被评估，x 项或虚项也被评估。

第 4 步：然后将计算出的表达式简单地分解为实部和虚部。如果虚部存在或 x 为真且不为零，则打印答案，否则如果虚部为 0 且实部为真，则没有解，否则有无限解。这里，

x = 2.000000

是最终的解决方案。

示例 1：

Python3

def solve(equation):
    
    # replacing all the x terms with j 
    # the imaginary part
    s1 = equation.replace('x', 'j')
      
    # shifting the equal sign to start 
    # an opening bracket
    s2 = s1.replace('=', '-(')
      
    # adding the closing bracket to form 
    # a complete expression
    s = s2+')'
      
    # mapping the literal j to the complex j
    z = eval(s, {'j': 1j})
    real, imag = z.real, -z.imag
      
    # if the imaginary part is true return the
    # answer
    if imag:
        return "x = %f" % (real/imag)
    else:
        if real:
            return "No solution"
        else:
            return "Infinite solutions"
  
  
equation = "2+3x=5x-7"
print(solve(equation))

输出

x = 4.500000

示例 2：

蟒蛇3

def solve(equation):
    
    # replacing all the x terms with j 
    # the imaginary part
    s1 = equation.replace('x', 'j')
      
    # shifting the equal sign to start 
    # an opening bracket
    s2 = s1.replace('=', '-(')
      
    # adding the closing bracket to form 
    # a complete expression
    s = s2+')'
      
    # mapping the literal j to the complex j
    z = eval(s, {'j': 1j})
    real, imag = z.real, -z.imag
      
    # if the imaginary part is true return the
    # answer
    if imag:
        return "x = %f" % (real/imag)
    else:
        if real:
            return "No solution"
        else:
            return "Infinite solutions"
  
  
equation = "x=x+10"
print(solve(equation))

输出

No solution

示例 3：

蟒蛇3

def solve(equation):
    
    # replacing all the x terms with j
    # the imaginary part
    s1 = equation.replace('x', 'j')
      
    # shifting the equal sign to start 
    # an opening bracket
    s2 = s1.replace('=', '-(')
      
    # adding the closing bracket to form 
    # a complete expression
    s = s2+')'
      
    # mapping the literal j to the complex j
    z = eval(s, {'j': 1j})
    real, imag = z.real, -z.imag
      
    # if the imaginary part is true return the
    # answer
    if imag:
        return "x = %f" % (real/imag)
    else:
        if real:
            return "No solution"
        else:
            return "Infinite solutions"
  
  
equation = "2x=2x"
print(solve(equation))

输出

Infinite solutions