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Python - Sympy Minima和Maxima

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我正在尝试学习sympy的微积分函数，并且我能够通过以下方式获得极值关键点的二阶导数的根：

import numpy as np
    from numpy import linspace, math, arange, linspace
    from sympy import *
    import sympy as sp
    import math

    x = Symbol('x')
    f = (x**4) - (24*x**2) + 80  
    fd = diff(f)
    fdd = diff(fd)
    print(fd)
    print(fdd)

    polyRoots = solveset(f,x)
    dRoots = solveset(fd,x) #gets critical x values
    ddRoots = solveset(fdd,x)

如何将我从dRoots获得的值替换为原始等式f，并输出一个值列表？

python sympy calculus

1 回答

  • 1
    >>> from sympy import *
>>> x = Symbol('x')
>>> f = x**4 - 24*x**2 + 80
>>> fd = diff(f)
>>> fdd = diff(fd)
>>> polyRoots = solveset(f, x)
>>> dRoots = solveset(fd, x)
>>> ddRoots = solveset(fdd, x)
>>> dRoots
{0, -2*sqrt(3), 2*sqrt(3)}
>>> [_ for _ in dRoots]
[0, -2*sqrt(3), 2*sqrt(3)]
>>> [f.subs(x, _) for _ in dRoots]
[80, -64, -64]

    您可以通过执行以下操作验证这是否有意义：

    >>> [f.subs(x, _) for _ in polyRoots]
[0, 0, 0, 0]
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