Use subs to replace subexpression with symbol

[arne-ws]

I'm trying to replace a nested function with a symbol by applying subs.

However, this doesn't seem to work for every case:

For Equation (2) my code below prints what I expect:

D_star = 

C_vss⋅D_th
──────────
  C_vth  

But for Equation (3) subs doesn't seem to work and f_v is printed rather longish as:

f_v = 

      ⎛                                       3/2               ⎞
      ⎜         ⎛         ⎛    _________    ⎞⎞                  ⎟
      ⎜         ⎜         ⎜   ╱  φ          ⎟⎟                  ⎟
      ⎜         ⎜C_t⋅D_th⋅⎜  ╱  ─── + 1  - 1⎟⎟               3/2⎟
      ⎜         ⎜         ⎝╲╱   φ_t         ⎠⎟    ⎛      ___⎞   ⎟
      ⎜     -k₁⋅⎜────────────────────────────⎟   ⋅⎝1 + ╲╱ 2 ⎠   ⎟
      ⎜         ⎝          C_vth⋅φ           ⎠                  ⎟
f_max⋅⎝1 - ℯ                                                    ⎠

Any idea why subs is not working for Equation (3)?

Thanks!

Arne

Code example:

import sympy as sp

s = sp.Symbol 

print 'sympy version ' + sp.__version__ + '\n'

def s_print(func_str, repl_str=None):

    '''Print function and replace subexpression'''

    print func_str + ' = \n'

    if repl_str != None:

        sp.pprint(eval(func_str).subs(eval(repl_str), s(repl_str)))

    else:

        sp.pprint(eval(func_str))

    print '\n'

# (1) C_vss

phi, phi_t, C_t = sp.symbols('phi phi_t C_t')

C_vss = (sp.sqrt(2) + 1)*C_t*(sp.sqrt(1 + phi/phi_t) - 1)

s_print('C_vss')

# (2) D_star

C_vth, D_th = sp.symbols('C_vth D_th')

D_star = C_vss/C_vth * D_th

s_print('D_star', 'C_vss')

# (3) f_v

f_max, k_1, Phi = sp.symbols('f_max k_1, Phi')

f_v = f_max * (1 - sp.exp(-k_1 * (D_star/phi)**(sp.Rational(3,2))))

s_print('f_v', 'D_star')

[Chris Smith]

Let's see where the problem is:

>>> arg=(1+sqrt(2))*x

>>> arg.subs(arg,1)

1

That was ok (and easy). Now let's wrap it in sqrt

>>> sqrt(arg).subs(arg,1)

sqrt(x)*sqrt(1 + sqrt(2))

That time there was no change -- it doesn't see a single "arg" when the powers are split.

>>> (sqrt(arg)**3).subs(arg,1)

sqrt(x)*sqrt(1 + sqrt(2))

Hmmm...but this time it got 1 of the 3/2 replaced

>>> (sqrt(arg/y)**3).subs(arg/y,1)

(x/y)**(3/2)*(1 + sqrt(2))**(3/2)

But none of a more complicated arg is replaced.

>>> (sqrt(arg/y)**3).subs(sqrt(arg/y),2)

8

If you match the fractional part of the power it looks like it can do it. But if I try s_print('f_v','sqrt(D_star)') this doesn't work.

Looks like a bug.