CODEWITHSUNDEEP
sympysubstitution
Bill Spotz
Bill Spotz

Reputation: 33

SymPy Expr.subs() method does not work within a Sum

I am trying to use sympy to start with a PDE, manipulate it symbolically to obtain a finite element formulation, and then apply code generation to obtain a code snippet for applying the results in an application.

As such, I want to start with Derivative objects, but at some point substitute a simple function in place of those derivatives, as the basis functions and derivatives of those basis functions will be stored by the code. In simple situations, this works:

>>> from sympy import *
>>> init_printing()
>>> i = Idx('i')
>>> x = Symbol('x')
>>> phi = Function('phi')(i,x)
>>> expr = Derivative(phi,x) + phi
>>> expr
          d
φ(i, x) + ──(φ(i, x))
          dx
>>> phi_x = Function('phi_x')(i,x)
>>> expr.subs(Derivative(phi,x), phi_x)
φ(i, x) + φₓ(i, x)

But if the derivatives appear within a summation, the substitution fails:

>>> N = Symbol('N', integer=True)
>>> expr = summation(Derivative(phi,x) + phi, (i,0,N-1))
>>> expr
N - 1
 ____
 ╲
  ╲   ⎛          d          ⎞
   ╲  ⎜φ(i, x) + ──(φ(i, x))⎟
   ╱  ⎝          dx         ⎠
  ╱
 ╱
 ‾‾‾‾
i = 0
>>> expr.subs(Derivative(phi,x), phi_x)
N - 1
 ____
 ╲
  ╲   ⎛          d          ⎞
   ╲  ⎜φ(i, x) + ──(φ(i, x))⎟
   ╱  ⎝          dx         ⎠
  ╱
 ╱
 ‾‾‾‾
i = 0

Does anyone have an idea why this might be, or what a workaround might be? TIA!

Upvotes: 0

Views: 159

Answers (1)

Yakov Dan
Yakov Dan

Reputation: 3372

I'm not sure why this doesn't work (as it should according to expression semantics), but here's a workaround:

from sympy import *

def substitution_in_sum(expr,old_sub_expr,new_sub_expr):
    if expr == old_sub_expr:
        return new_sub_expr
    elif expr.args==():
        return expr
    else:
        result_list = []
        for arg in expr.args:
            result_list.append(substitution_in_sum(arg,old_sub_expr,new_sub_expr))
        return expr.func(*tuple(result_list))

Upvotes: 1

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