CODEWITHSUNDEEP
pythonsympy
charpi
charpi

Reputation: 363

Sympy - comparing equivalent expressions with equal (=) sign

I understand that in Sympy, the == equivalence does not work for symbolic expressions and hence cannot be used to check for symbolic equivalence. From the documentations, it is recommended to use simplify (a-b) and check if the result is 0. E.g.,

>>> simplify((x + 1)**2 - (x**2 + 2*x + 1))

However, this does not seem to work for expressions with equals in them. E.g., I want to compare (2x=6 and x=3), which should be equal.

>>> a = Eq(2*x,6)
>>> b = Eq(x,3)
>>> simplify(a-b)
−x=3+(2x=6)

Or more complex equations which should be equivalent

>>> a = Eq(x*(y+1),6)
>>> b = Eq(2*x*y + 2*x, 12)
>>> simplify(a-b)
(x(y+1)=6)−(2x(y+1)=12)

Wondering if there is a good way or trick to do this in Sympy.

Thanks!

Upvotes: 2

Views: 2638

Answers (2)

Rdey
Rdey

Reputation: 468

Each expression has two useful methods equals() and compare():

x,y = symbols('x,y')
a = (9*x+30*x+21) / 3
b = x*(3+10)+7
a.equals(b)

Output:

True

Upvotes: 0

Zev
Zev

Reputation: 3491

What makes these equations equivalent is that they have the same solution set or that they are the same when solved for x. Have sympy solve them and compare the solutions:

from sympy import *
x, y = symbols('x y')

a = Eq(2*x,6)
b = Eq(x,3)
print(solve(a) == solve(b)) #True

The same works for your more complex example:

a = Eq(x*(y+1),6)
b = Eq(2*x*y + 2*x, 12)
print(solve(a)) # [{x: 6/(y + 1)}]
print(solve(b)) # [{x: 6/(y + 1)}]
print(solve(a) == solve(b)) # True

Upvotes: 2

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