将 sympy 中命名表达式的字符串转换为表达式本身

Question

Description of the practical problem :
I have defined many expression using sympy , as in

import sympy as sp
a, b = sp.symbols('a,b', real=True, positive=True)
Xcharles_YclassA_Zregion1 = 1.01 * a**1.01 * b**0.99
Xbob_YclassA_Zregion1 = 1.009999 * a**1.01 * b**0.99
Xbob_YclassA_Zregion2 = 1.009999 * a**1.01 * b**0.99000000001
...

So I have used the names of the expressions to describe options (eg, charles , bob ) within categories (eg, X ).

Now I want a function that takes two strings (eg, 'Xcharles_YclassA_Zregion1' and 'Xbob_YclassA_Zregion1' ) and returns its simplified ratio (in this example, 1.00000099009999 ), so I can quickly check "how different" they are, in terms of result, not in terms of how they are written. Eg, 2*a and a*2 are the same for my objective.

How can I achieve this?

Notes :

1. The expressions in the example are hardcoded for the sake of simplicity. But in my actual case they come from a sequence of many other expressions and operations.
2. Not all combinations of options for all categories would exist. Eg, Xcharles_YclassA_Zregion2 may not exist. Actually, if I were to write a table for existing expression names, it would be sparsely filled.
3. I guess rewriting my code using dict to store the table might solve my problem. But I would have to modify a lot of code for that.
4. Besides the practical aspects of my objective, I don't know if there is any formal difference between Symbol (which is a specific class) and expression . From the sources I read (eg, this ) I did not arrive to a conclusion. This understanding may help in solving the question.

---

TL;DR - What I tried

I aimed at something like

def verify_ratio(vstr1, vstr2):
    """Compare the result of two different computations of the same quantity"""
    ratio = sp.N(sp.parsing.sympy_parser.parse_expr(vstr1)) / sp.parsing.sympy_parser.parse_expr(vstr2)
    print(vstr1 + ' / ' + vstr2, '=', sp.N(ratio))
    return

This did not work. Code below shows why

import sympy as sp
a, b = sp.symbols('a,b', real=True, positive=True)
expr2 = 1.01 * a**1.01 * b**0.99
print(type(expr2), '->', expr2)
    
expr2b = sp.parsing.sympy_parser.parse_expr('expr2')
print(type(expr2b), '->', expr2b)

expr2c = sp.N(sp.parsing.sympy_parser.parse_expr('expr2'))
print(type(expr2c), '->', expr2c)
#print(sp.N(sp.parsing.sympy_parser.parse_expr('expr2')))

expr2d = sp.sympify('expr2')
print(type(expr2d), '->', expr2d)

with output

<class 'sympy.core.mul.Mul'> -> 1.01*a**1.01*b**0.99
<class 'sympy.core.symbol.Symbol'> -> expr2
<class 'sympy.core.symbol.Symbol'> -> expr2
<class 'sympy.core.symbol.Symbol'> -> expr2

I need something that takes the string 'expr2' and returns the expression 1.01 * a**1.01 * b**0.99 .

---

None of my attempts achieved the objective. Questions or links which did not help (at least for me):

1. From string to sympy expression
2. https://docs.sympy.org/latest/tutorials/intro-tutorial/basic_operations.html
3. https://docs.sympy.org/latest/modules/parsing.html
4. https://docs.sympy.org/latest/modules/core.html#sympy.core.sympify.sympify
5. https://docs.sympy.org/latest/tutorials/intro-tutorial/manipulation.html

Answer 1

If, when parsing, you want to use the expression that has been mapped to a variable you have to pass the dictionary that python uses to keep track of those mappings, ie locals()

>>> from sympy.abc import x
>>> from sympy import sympify, parse_expr
>>> y = x + 2
>>> sympify('y')
y
>>> sympify('y', locals=locals())
x + 2
>>> parse_expr('y', local_dict=locals())
x + 2

Answer 2

As suggested by Oscar Benjamin from the Sympy Google group, eval does the job

def verify_ratio(vstr1, vstr2):
    """Compare the result of two different computations of the same quantity"""
    print(vstr1 + ' / ' + vstr2, '=', eval(vstr1 + ' / ' + vstr2))
    return

What shows this would work is

>>> import sys
>>> import sympy as sp
>>> a, b = sp.symbols('a,b', real=True, positive=True)
>>> a is eval('a')
True

In my case, all expressions and symbols I am using in vstr1 and vstr2 are global. If nesting within other functions, I might need to pass further parameters to verify_ratio , as in the solution by smichr.