如何解含有多个变量的线性方程组? - V2EX
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Jay54520

如何解含有多个变量的线性方程组?

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  •   Jay54520 May 7, 2021 3333 views
    This topic created in 1832 days ago, the information mentioned may be changed or developed.
    b = c - d * a f = d + d * a g = f * h e = g * i + b 

    除了 a 都是变量(在运行时都是常量),所以这是一个只含有一个未知数的方程组,求 a 的表达式。 Symbolab 好像不支持用字母表示常量,是不是用法不对?

    Supplement 1    May 7, 2021
    还遗漏了一个等式
    j = e / f 或 j = e / (f - b)
    Supplement 2    May 7, 2021

    通过 SymPy 解决,#5 提供的方法。

    11 replies    2021-05-07 20:28:41 +08:00
    weizhen199
        1
    weizhen199  
       May 7, 2021
    这种电脑用矩阵法来解比较合适吧(猜测
    Jay54520
        2
    Jay54520  
    OP
       May 7, 2021
    还遗漏了一个等式
    j = e / f 或 j = e / (f - b)
    misdake
        3
    misdake  
       May 7, 2021
    没看懂。既然只有 a 是未知数,那随便拿一个方程不就能求出来了么
    Jay54520
        4
    Jay54520  
    OP
       May 7, 2021
    @misdake 求的是用其他变量如何表示 a 。比如 a = (变量 1 + 变量 2) / (变量 3 - 变量 4)。
    princelai
        5
    princelai  
       May 7, 2021   4
    ```python
    from sympy import symbols, init_printing, solve

    init_printing(use_unicode=True)

    a, c, d, h, i = symbols('a c d h i')

    b = c - d * a
    f = d + d * a
    g = f * h
    e = g * i + b
    j = e / f

    solve(j, a)
    ```

    Out[53]:
    -(c + dhi)
    ─────────────
    d(hi - 1)
    Imindzzz
        6
    Imindzzz  
    PRO
       May 7, 2021
    这个网站不错
    cartmanie
        7
    cartmanie  
       May 7, 2021 via iPhone
    Wolfram alpha
    LeeReamond
        8
    LeeReamond  
       May 7, 2021
    算法的话,个人想法是,首先将每个等式标准化,然后依次搜索出现频率最低的变量,将其消去,最后求解。循环直到所有变量都解明
    Jooooooooo
        9
    Jooooooooo  
       May 7, 2021
    线性方程组本质是个矩阵
    YvesX
        10
    YvesX  
       May 7, 2021
    你学线性代数的时候有没有好奇过解方程组为什么要做得这么机械
    这就是它的典型用途
    maxwel1
        11
    maxwel1  
       May 7, 2021 via Android
    mathematica:就这?还需要喊我?
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