Non-sequential substitution in SymPy

Question

I\'m trying to use [SymPy][1] to substitute multiple terms in an expression at the same time. I tried the [subs function][2] with a dictionary as parameter, but found out that i

Answer 1

Answering the edited question.

In your example you can use some temporary variables which will not be over-written be subsequent substitutions. Then, once all of the potentially overlapping substitutions have been made, you can replace the temporary variables with the real ones.

This example works for the question, if your full problem contains more complex substitutions, I think you should still be able to create temporary variables to avoid overlapping substitutions.

from sympy import Symbol, sin, cos, pi

I_x, I_y, I_z = Symbol("I_x"), Symbol("I_y"), Symbol("I_z")
S_x, S_y, S_z = Symbol("S_x"), Symbol("S_y"), Symbol("S_z")
J_is = Symbol("J_IS")
t = Symbol("t")
I_x_temp, I_y_temp, I_z_temp = Symbol("I_x_temp"), Symbol("I_y_temp"), Symbol("I_z_temp")

f = 2*I_x*S_z
answer = I_y*sin(2*pi*J_is*t) + 2*I_x*S_z*cos(2*pi*J_is*t)

subs1a = [
    (2*I_x*S_z, 2*I_x_temp*S_z*cos(2*pi*J_is*t) + I_y_temp*sin(2*pi*J_is*t)),
    (I_x,  I_x_temp*cos(2* pi*J_is*t) + 2*I_x_temp*S_z*sin(2*pi*J_is*t)),
    (I_y,  I_y_temp*cos(2*pi*J_is*t) - 2*I_x_temp*S_z* sin(2*pi*J_is*t))
]

subs_temp = [(I_x_temp, I_x), (I_y_temp, I_y), (I_z_temp, I_z)]

print f
f = f.subs(subs1a)
print f
f = f.subs(subs_temp)
print f
print f == answer # True

Note, you can also perform two substitutions back to back:

f.subs(subs1a).subs(subs_temp) == answer