SymPy 虚数 [英] SymPy Imaginary Number

问题描述

我正在忙着编写一些 SymPy 代码来处理带有虚数的符号表达式.

I'm messing around with writing some SymPy code to handle symbolic expressions with imaginary numbers.

首先，我想让它把 x 和 y 作为实数，然后找到 x=iy 的解.所以我可以这样做.

To start out, I want to get it to take x and y as real numbers and find the solution where x=iy. So I can do this as follows.

x, y = sympy.symbols("x y", real=True)  
print(sympy.solve([x-sympy.I*y]))

(SymPy 求解需要一个值列表，所有这些值都必须为 0.所以 x-iy=0 => x=iy).SymPy 会正确地告诉我

(SymPy solve takes a list of values, all of which must be 0. So x-iy=0 => x=iy). SymPy will correctly tell me

[{x: 0, y: 0}]

但是，如果我以(理论上相同的)方式执行此操作:

However, if I do this a (theoretically identical) way:

x, y = sympy.symbols("x y")
print(sympy.solve([x-sympy.I*y, sympy.im(y), sympy.im(x)]))

那么现在SymPy告诉我

Then now SymPy tells me

[{re(y): y, re(x): I*y, im(x): 0, x: I*y, im(y): 0}]

这在技术上是正确的，但并没有为我完成所有事情.这只是 SymPy 中的一个限制，还是我可以通过以这种方式约束复数 x 和 y 来给我 x=y=0?

And this is technically correct, but hasn't done everything for me. Is this just a limitation in SymPy, or can I get it to give me x=y=0 by constraining complex x and y in this way?

推荐答案

因为 SymPy 比复数更擅长简化实数对，以下策略有帮助:为实部/虚部设置实变量，然后形成复变量来自他们.

Because SymPy is better at simplifying pairs of real numbers than complex numbers, the following strategy helps: set up real variables for real/imaginary parts, then form complex variables from them.

from sympy import *
x1, x2, y1, y2 = symbols("x1 x2 y1 y2", real=True)  
x = x1 + I*x2
y = y1 + I*y2

现在 x 和 y 可以用作像您这样的方程中的复变量

Now x and y can be used as complex variables in an equation such as yours

sol = solve([x-I*y, im(y), im(x)])
print(x.subs(sol[0]), y.subs(sol[0])) 

输出:0 0.

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