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不同区间上不同公式函数的导数

sympy

1

Rastapopoulos · 技术社区 · 8 年前

是否有一种规范化的方法按部分声明函数症状 ?我试过

import sympy
import sympy.functions.special.delta_functions as special

sympy.init_printing()
x = sympy.symbols('x', real=True)
V = x*x * (special.Heaviside(x + 1) - special.Heaviside(x - 1)) \
    + (1 + 2*sympy.log(x)) * special.Heaviside(x - 1) \
    + (1 + 2*sympy.log(-x)) * special.Heaviside(-x - 1)

它定义了一个可微函数,但是

print(V.diff(x).simplify())
# Prints: (x*(x**2*(-DiracDelta(x - 1) + DiracDelta(x + 1)) - 2*x*(Heaviside(x - 1) - Heaviside(x + 1)) - (2*log(-x) + 1)*DiracDelta(x + 1) + (2*log(x) + 1)*DiracDelta(x - 1)) + 2*Heaviside(-x - 1) + 2*Heaviside(x - 1))/x

有什么方法可以告诉你症状简化 DiracDelta(x - a)*f(x) 到 DiracDelta(x - a)*f(a) ?

1 回复 | 直到 8 年前

1

2

user6655984 8 年前

Piecewise

V = sympy.Piecewise((1 + 2*sympy.log(-x), x < -1),
                    (x**2, x < 1),
                    (1 + 2*sympy.log(x), True))
print(V.diff(x))

Piecewise((2/x, x < -1), (2*x, x < 1), (2/x, True))

(expr, cond) Piecewise cond expr