How to Compute Algebraic Functions in Python: Two Simple Methods Explained

Introduction

Hello, I’m a Python enthusiast. A fan from the Python Star Group asked how to implement an algebraic function in Python, so I’m sharing the solution here.

Solution 1: Basic Python

The power operator in Python is written as x ** n. Using this, we can define the required expression directly.

def calc(x, y):
    fenzi1 = x ** 2 + y ** 2
    fenmu1 = x ** 2 - y ** 2
    fenzi2 = x ** 3 - y ** 3
    fenmu2 = x ** 3 + y ** 3
    result = fenzi1 / fenmu1 + fenzi2 / fenmu2
    return result

if __name__ == '__main__':
    print(calc(7, 12))

The output is -2.700338000965717, a straightforward, textbook‑style result.

Solution 2: Using Sympy

By employing the third‑party library sympy, the same expression can be built symbolically and evaluated.

from sympy import symbols

x, y = symbols('x,y')  # define variables
f = ((x ** 2 + y ** 2) / (x ** 2 - y ** 2)) + ((x ** 3 - y ** 3) / (x ** 3 + y ** 3))
result = f.subs({x: 7, y: 12})
print(result)

This approach yields a clear symbolic representation, and f.subs() substitutes the numeric values to compute the result.

Conclusion

The fan’s question is answered with two methods: a direct implementation using basic Python operators and a more expressive solution using Sympy. Both are valid, and readers are encouraged to experiment with other approaches or ask further questions.