Solving Irreducible Polynomials over Zp and GCD, LCM of Two Polynomials over Fn Using Python
DOI:
https://doi.org/10.29303/semeton.v1i2.227Keywords:
Reducible Polynomial, GCD, LCM, PythonAbstract
This research aims to solve the irreducible polynomial problem over finite field Zp and determine the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two polynomials over finite field Fn using Python programming language. In the digital age, programming plays an important role in various disciplines. Python, with its simple syntax and computational libraries like SymPy, has become a top choice among the various programming languages available. Polynomials appear frequently in the computer field, especially in cryptographic algorithms, data compression, and error coding. This research utilizes Euclid's Algorithm to determine the GCD and LCM of two polynomials over a finite field Fn, as well as evaluate the irreducibility of polynomials over a finite field Zp. Determining irreducibility is very important in polynomial theory and is a challenging task if done manually. With the help of Python, this research produces a script or syntax that is able to automate the process, thus saving time and reducing complexity. The final result of this research is an effective Python script or syntax to determine the GCD and LCM of two polynomials over Fn, as well as evaluate whether a polynomial is reducible or irreducible over Zp.References
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