Maxima:如何替换方程中的变量 [英] Maxima: how to replace variables in equations

问题描述

我正在尝试写下我的工作笔记.Maxima 简化我的工作的方式是，一旦我写了一堆方程，我想改变一个变量的定义，我就这样做并重新评估整个文件.

I'm trying to write down some notes of my work. The way Maxima would simplify my work is that once I write bunch of equations and I want to change the definition of a variable, I do it and re-evaluate the entire file.

以下是我尝试完成的示例:

Here is an example of what I'm trying to accomplish:

问题 1:我有一个方程组，我想从 Maxima 得到的只是变量替换.

Question 1: I have a system of equations and all I want from Maxima is just variables replacement.

eq1: x=a+b+c
eq2: y=d+e+f
eq3: x+y=0

如何让 Maxima 输出

How do I get Maxima to output

eq3: a+b+c+d+e+f = 0

所以以后如果我想让 x 变成 a+b-c，我就改变它并重新评估

So in the future if I want x to be a+b-c, I just change it and re-evaluate

问题 2:与之前类似，但稍微复杂一些

Question 2: Similar to before but a bit more complex

eq1: x=a+b+c
eq2: y=d+e+f
eq3: x=y
eq4: a+s+e=0

如何让 Maxima 输出

How do I get Maxima to output

eq3 a+b+c=d+e+f

如何让 Maxima 为 a 求解 eq1 并为 e 和输出求解 eq2

How do I get Maxima to solve eq1 for a and solve eq2 for e and output

eq4: x-b-c+s+y-d-f = 0

预先感谢您的帮助，圭多

Thank you in advance for your help, Guido

推荐答案

我认为 subst 和 solve 可以在这里处理你想要的操作.

I think subst and solve can handle the operations you want here.

(%i1) eq1: x=a+b+c;
(%o1)                            x = c + b + a
(%i2) eq2: y=d+e+f;
(%o2)                            y = f + e + d
(%i3) eq3: x+y=0;
(%o3)                              y + x = 0
(%i4) subst ([eq1, eq2], eq3);
(%o4)                      f + e + d + c + b + a = 0

好的，现在这是您的第二个示例.注意 solve 返回一个方程列表.

OK, now here's your second example. Note that solve returns a list of equations.

(%i5) eq3: x=y;
(%o5)                                x = y
(%i6) eq4: a+s+e=0;
(%o6)                            s + e + a = 0
(%i7) subst ([eq1, eq2], eq3);
(%o7)                        c + b + a = f + e + d
(%i8) solve (eq1, a);
(%o8)                           [a = x - c - b]
(%i9) solve (eq2, e);
(%o9)                           [e = y - f - d]
(%i10) append (%o8, %o9);
(%o10)                  [a = x - c - b, e = y - f - d]
(%i11) subst (%o10, eq4);
(%o11)                   y + x + s - f - d - c - b = 0

Maxima 的solve 功能不是太强大；它不能解的方程有很多种.但它可以解线性方程.

Maxima's solve function is not too powerful; there are many kinds of equations it cannot solve. But it can solve linear equations.

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