Variable in value in key-value pairs in dictionaries

Question

Let's say we have dictionary = ['a':x*2,'b':x*3] , and we set x to 2. When I print out the dictionary after this assignment, I get the one shown above, and not ['a':4,'b':6] . Why is that? I am currently trying to come up with a solution to Project Euler exercise 69 ( https://projecteuler.net/problem=69 ) for which I have made the following:

import math

from sympy import Symbol

magic_book={1:1,2:1}

maximum=0

for n in range(3,10**6+1):

    print(magic_book)
    print(n)
    if n in magic_book:
        if (n/magic_book[n])>maximum:
            maximum=n/magic_book[n]
        continue
        
    Phi=0
    x = Symbol('x')
    
    for m in range(1,n):
        if math.gcd(n,m)==1:
            magic_book[n*m]=x*magic_book[m]
            Phi+=1
    x=Phi
    if n/Phi>maximum:
        maximum=n/Phi
    
print(maximum)

When I set x equal Phi , magic_book does not update - why is this?

Answer 1

When you edit an object in Python, it does not go back and change what you previously stated using it. See for example:

x = 1
double_x = 2*x
x = 10

Your question is basically asking why double_x is not 20.

In order to substitute symbolic values with other values (like numeric values), .subs() is usually the best option if you are dealing with SymPy objects. However, a dictionary is not a SymPy object and it does not have a .subs() method. You must then loop through the dictionary and substitute its values like so:

for k, v in magic_book.items():
    maximum[k] = v.subs(x, Phi)  # assuming v is a SymPy object