How to Compute Algebraic Functions in Python: Two Practical Methods

Preface

A fan in a Python community asked how to implement algebraic functions in Python; this article shares two solutions to help learners.

Solution Process

Wei Ge's solution

The logic is straightforward: use Python's exponent operator (**). The following code computes the expression using basic arithmetic.

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, illustrating a textbook‑style approach.

Moon God's solution

This method employs the third‑party library sympy for symbolic computation.

from sympy import symbols

x, y = symbols('x,y')  # define variables
# define the algebraic expression
f = ((x ** 2 + y ** 2) / (x ** 2 - y ** 2)) + ((x ** 3 - y ** 3) / (x ** 3 + y ** 3))
# substitute concrete values and evaluate
result = f.subs({x: 7, y: 12})

The symbolic expression and substitution are shown in the accompanying images.

Conclusion

The article demonstrates two viable ways to compute algebraic functions in Python: a direct arithmetic method and a symbolic approach using sympy. Readers are encouraged to experiment further and share alternative solutions.