Sympy Substitution on the output of variable-CodePudding

In my code I have a variable h set to an integration. I would like to perform a coordinate change on the output of that integration. Using a computer algebra software like Maple this is achieved by substituting the coordinate change into the variable h, where the substitution takes place on the output of the integration. I tried the following code:

import sympy as sp

r = sym.Symbol('r')
R = sym.Symbol('R')
theta00 = sp.pi*sp.exp(-(r**2-1)/2)

h = sp.integrate((r**2/2)*sp.diff(theta00, r), (r, -sp.oo, R))
hxy = h.subs(sp.sqrt((x-1)**2   y**2), R)

The output of hxy is the same as the output of h, without the required substitution. I think the substitution is being applied before the integration. Is there a way to work with the output of the integration in the variable h?

CodePudding user response：

You have to make sure that the veariables you are using are sympy symbols. Here I am using the symbols from sympy.abc directly.

Then for the substitution you can create use a dictionary mapping variables in your formulas to the substituted value.

import sympy as sp
from sympy.abc import r, R, x, y
theta00 = sp.pi*sp.exp(-(r**2-1)/2)
h = sp.integrate((r**2/2)*sp.diff(theta00, r), (r, -sp.oo, R))

hxy = h.subs({R: sp.sqrt((x-1)**2   y**2)})

You could also replace by a numeric value

h.subs({R: 3})