如何使用SymPy找到两个函数的交点? [英] How to use SymPy to find the point of intersection of two functions?

问题描述

我正在尝试使用 SymPy 库来查找两个函数之间的交点:

I am trying to use the SymPy library to find the point of intersection(s) between two functions:

f(x) = e ^ (x/2) 和 g(x) = 3 - 3 * x

我试过了:

import sympy as syp

x = syp.symbols('x')

f_x = syp.E ** (x / 2)
g_x = 3 - 3 * x

print(syp.nsolve(f_x, g_x, x))

syp.nsolve(f_x, g_x, x) 吐出一个 TypeError.用 syp.solve([f_x, g_x], x) 替换该行会产生一个空列表 [].这是错误的，因为 f(x) 和 g(x) 恰好在一点相交.

syp.nsolve(f_x, g_x, x) spits out a TypeError. Replacing that line with syp.solve([f_x, g_x], x) results in an empty list []. This is wrong because f(x) and g(x) intersect at exactly one point.

如何使用 SymPy 获取任何 f(x) 和 g(x) 之间的交点的 x 和 y 值?

How do I get the x and y values of the point of intersection(s) between any f(x) and g(x) using SymPy?

推荐答案

import sympy as syp

x = syp.symbols('x')

f_x = syp.E ** (x / 2)
g_x = 3 - 3 * x

print(syp.solve(f_x - g_x, x))

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以上代码的输出为:

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The output of the above code is:

[-2*LambertW(exp(1/2)/6) + 1]

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