sympy - 替代特定的权力

Question

I have this equality.

import sympy as sp
D, L, V = sp.symbols("D, L, V", real=True, positive=True)
Veq = sp.Eq(V, sp.pi * D**3 / 4 * (sp.Rational(2, 3) + L / D))

I would like to solve Veq for D**3 . If I try a direct approach, sp.solve(Veq, D**3) the computation is going to take a while eventually giving me a tremendously long result (useless to me).

My attempt: trying to substitute D**3 with a new symbol, then solve for it. Unfortunately, the substitution is also going to replace the other D in the equality:

t = sp.symbols("t")
print(Veq.subs(D**3, t))

>>> Eq(V, pi*t*(L/t**(1/3) + 2/3)/4)

Note the term L/t**(1/3) . I would like it to be L/D after the substitution. So far I've managed to manipulate the expression and reaching my goal with this code:

res = sp.Mul(*[a.subs(D**3, sp.symbols("t")) if a.has(D**3) else a for a in asd.args[1].args])
Veq = sp.Eq(V, res)
print(Veq)

>>> Eq(V, pi*t*(2/3 + L/D)/4)

I'm wondering, is there some flag for subs that I can use to reach my goal? Or some other method?

Answer 1

If you want the substitution to be exact you can use the exact flag:

>>> var('D V L')
(D, V, L)
>>> Veq = sp.Eq(V, sp.pi * D**3 / 4 * (sp.Rational(2, 3) + L / D))
>>> Veq.subs(D**3,y,exact=True)
Eq(V, pi*y*(2/3 + L/D)/4)
>>> solve(Veq.subs(D**3,y,exact=True),y)
[12*D*V/(pi*(2*D + 3*L))]

The exact flag appears to be ignore when assumptions are given:

>>> D, L, V = symbols("D, L, V", real=True, positive=True)
>>> (D**3+D).subs(D**3,y,exact=True)
y**(1/3) + y
>>> D, L, V = symbols("D, L, V")
>>> (D**3+D).subs(D**3,y,exact=True)
D + y

You can use replace for your situation:

>>> D, L, V = symbols("D, L, V", real=True, positive=True)
>>> (D**3+D).replace(D**3,y)
D + y

But since your expression is a Relational you have to use replace on the arguments, not the Relational (or else you will get an error):

>>> eq = Eq(D**3, D - 1)
>>> eq.func(*[a.replace(D**3,y) for a in eq.args])
Eq(y, D - 1)