Sympy - 比较表达式

Question

Is there a way to check if two expressions are mathematically equal? I expected tg(x)cos(x) == sin(x) to output True , but it outputs False . Is there a way to make such comparisons with sympy? Another example is (a+b)**2 == a**2 + 2*a*b + b**2 which surprisingly also outputs False .

I found some similar questions, but none covered this exact problem.

Answer 1

Is there a way to check if two expressions are mathematically equal? I expected tg(x)cos(x) == sin(x) to output True , but it outputs False . Is there a way to make such comparisons with sympy? Another example is (a+b)**2 == a**2 + 2*a*b + b**2 which surprisingly also outputs False .

I found some similar questions, but none covered this exact problem.

Answer 2

Is there a way to check if two expressions are mathematically equal? I expected tg(x)cos(x) == sin(x) to output True , but it outputs False . Is there a way to make such comparisons with sympy? Another example is (a+b)**2 == a**2 + 2*a*b + b**2 which surprisingly also outputs False .

I found some similar questions, but none covered this exact problem.

Answer 3

Is there a way to check if two expressions are mathematically equal? I expected tg(x)cos(x) == sin(x) to output True , but it outputs False . Is there a way to make such comparisons with sympy? Another example is (a+b)**2 == a**2 + 2*a*b + b**2 which surprisingly also outputs False .

I found some similar questions, but none covered this exact problem.

Answer 4

As previously stated, (expr1 - expr2).simplify() or expr1.equals(expr2) will sometimes fail to recognize equality for expressions that are complex to simplify. To deal with this, a numerical evaluation of the expressions with random numbers may constitute a relatively safe "brute force" test. I've adapted the excellent solution by @Okapi575 to:

1. Test the numerical equality N-times with different random numbers each time for a more confident diagnostic
2. Warn the user when a pair of expressions only passes the numeric test but not the symbolic equality test.

For example:

Hope it can prove useful:

import sympy as sp
import numpy as np

def check_equal(Expr1, Expr2, n=10):
    
    # Minimal tests
    if Expr1==None or Expr2==None:
        return(False)
    if Expr1.free_symbols!=Expr2.free_symbols:
        return(False)
    vars = Expr1.free_symbols
    
    # Numeric (brute force) equality testing n-times
    for i in range(n):
        your_values=np.random.random(len(vars))
        Expr1_num=Expr1
        Expr2_num=Expr2
        for symbol,number in zip(vars, your_values):
            Expr1_num=Expr1_num.subs(symbol, sp.Float(number))
            Expr2_num=Expr2_num.subs(symbol, sp.Float(number))
        Expr1_num=float(Expr2_num)
        Expr2_num=float(Expr2_num)
        if not np.allclose(Expr1_num, Expr2_num):
            print("Fails numerical test")
            return(False)
        
    # If all goes well so far, check symbolic equality
    if (Expr1.equals(Expr2)):
        return(True)

    else:
        print("Passes the numerical test but not the symbolic test")
        # Still returns true though
        return(True)

Answer 5

Is there a way to check if two expressions are mathematically equal? I expected tg(x)cos(x) == sin(x) to output True , but it outputs False . Is there a way to make such comparisons with sympy? Another example is (a+b)**2 == a**2 + 2*a*b + b**2 which surprisingly also outputs False .

I found some similar questions, but none covered this exact problem.