On symbolic computation of C.P. Okeke functional equations using Python programming language

This present paper is inspired by one of the questions posed by Okeke (Results Math 78(96):1-30, 2023, see Remark 2.10b). In particular, we aim to develop a robust computer code based on the theoretical results obtained in Okeke (2023), which determines the polynomial solutions of the following func...

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Bibliographic Details
Published in:Aequationes mathematicae Vol. 98; no. 2; pp. 483 - 502
Main Authors: Okeke, Chisom Prince, Ogala, Wisdom I., Nadhomi, Timothy
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.04.2024
Springer Nature B.V
Subjects:
Analysis
Combinatorics
Exact solutions
Functional equations
Mathematics
Mathematics and Statistics
Numerical methods
Polynomials
Programming languages
Python
Robustness (mathematics)
Polynomial functions
Functional equations
Secondary: 39A70 39-04
Sagemath
Python
Primary: 39B52
ISSN:0001-9054, 1420-8903
Online Access:Get full text
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Summary:This present paper is inspired by one of the questions posed by Okeke (Results Math 78(96):1-30, 2023, see Remark 2.10b). In particular, we aim to develop a robust computer code based on the theoretical results obtained in Okeke (2023), which determines the polynomial solutions of the following functional equation, 0.1 ∑ i = 1 n γ i F ( a i x + b i y ) = ∑ j = 1 m ( α j x + β j y ) f ( c j x + d j y ) , for all x , y ∈ R , γ i , α j , β j ∈ R , and a i , b i , c j , d j ∈ Q , and their special forms. The primary motivation for writing such a computer code is that solving even simple equations belonging to class (0.1) needs long and tiresome calculations. Therefore, one of the advantages of such a computer code is that it allows us to solve complicated problems quickly, easily, and efficiently. Additionally, the computer code will significantly improve the level of accuracy in calculations. Along with that, there is also the factor of speed. We point out that the computer code will operate with symbolic calculations provided by the programming language Python, which means that it does not contain any numerical or approximate methods, and it yields the exact solutions of the equations considered.
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ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-023-01008-2