Simplify expressions given by sympy.sympify

Question

sp.simplify doesn’t seem to work when your expression is given by sp.sympify. How can I change that?

import sympy as sp

r = sp.Symbol('r', real = True)
f_str = 'sqrt(1/r**4)'

f1 = sp.sympify( f_str )
f2 = sp.sqrt(1/r**4)

for f in f1,f2:
    sp.pprint(sp.simplify(f))

which outputs

     ____
    ╱ 1  
   ╱  ──           # f1
  ╱    4 
╲╱    r  

1 
──                 # f2
 2
r

I was expecting that given a real value (r), a sympify expression could get simplified

Asked By: J.Pottiez

||

Source

Answer 1

The r in f1 isn’t the same as the r symbol you defined:

>>> f1.free_symbols == f2.free_symbols
False

In particular, this means that the assumption that r is real doesn’t carry through, which is necessary for the simplification you want.

You can remedy this postmortem by substituting the r in f1 with your r symbol:

>>> f1                # old r, no assumptions
sqrt(r**(-4))

>>> f1.subs("r", r)   # your r, with real assumption
r**(-2)

In general, you can specify assumptions for string inputs at construction time by passing a dictionary mapping string symbols to your desired SymPy Symbols:

>>> f3 = sp.sympify(f_str, {"r": r})

>>> f3
r**(-2)

>>> f3.free_symbols == f2.free_symbols
True

Answered By: Brian61354270

Answer 2

The other answer is correct but I want to note an alternative way that might be useful. The sympify function when given a string as input will pass that string to SymPy’s parse_expr function. Actually if you are parsing strings then it is better to call parse_expr directly rather than using sympify. If you do use parse_expr directly then you can pass other options to control how the expression gets parsed including specifying which symbol objects to use for each symbol name appearing in the string.

In [4]: import sympy as sp
   ...: 
   ...: r = sp.Symbol('r', real = True)

In [5]: sp.parse_expr('sqrt(1/r**4)', {'r': r})
Out[5]: 
1 
──
 2
r 

In [6]: sp.parse_expr('sqrt(1/r**4)')
Out[6]: 
     ____
    ╱ 1  
   ╱  ── 
  ╱    4 
╲╱    r

Answered By: Oscar Benjamin

Simplify expressions given by sympy.sympify

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