问题
I am trying to calculate general composite function derivative using sympy. In my specific case script is the following:
from sympy import *
t=symbols('t')
p=Function('p')
x=Function('x')
v=diff(x(p(t)),t)
a=diff(v,t)
for variable a it yields:
Derivative(p(t), t)**2*Derivative(x(p(t)), p(t), p(t)) + Derivative(p(t), t, t)*Subs(Derivative(x(_xi_1), _xi_1), (_xi_1,), (p(t),))
If I call doit(), answer still contains subs object
a.doit() #answer: Derivative(p(t), t)**2*Subs(Derivative(x(_xi_3), _xi_3, _xi_3), (_xi_3,), (p(t),)) + Derivative(x(p(t)), p(t))*Derivative(p(t), t, t)
Mathematically the answer is correct but I still need output in following format (without Subs objects):
Derivative(p(t), t)**2*Derivative(x(p(t)), p(t), p(t)) + Derivative(x(p(t)), p(t))*Derivative(p(t), t, t)
Is there any way to achieve desired result? To be clear this example is very simplified compared to my original expression so I need general way to get desired output.
回答1:
Indeed, repeated applications of doit() in this case result in flip-flopping between two forms of the expression: half the time the first addend has Subs, half the time it's the second.
But you can deal with the issue as follows:
for b in a.atoms(Subs):
a = a.xreplace({b: b.doit()})
This returns Derivative(p(t), t)**2*Derivative(x(p(t)), p(t), p(t)) + Derivative(x(p(t)), p(t))*Derivative(p(t), t, t) as desired.
The trick is that atoms(Subs) is the set of all Subs objects in the expression, and doit is applied only to them, not to Derivative objects where it only messes things up. (Ideally, doit would not mess Derivative objects up in the first place...)
来源：https://stackoverflow.com/questions/48123138/subs-object-still-remains-after-calling-doit-method-in-sympy