Klasik olmayan polinomlar üzerine

The primary aim of this thesis is to develop classical computational tools that autom- atize and scale routine computations associated with key elements in higher-order Fourier analysis. For this aspect, it focuses on non-classical polynomials on finite abelian groups. The thesis aims to address several interconnected objectives. Most importantly, the thesis explores the classification of non-classical polynomials on arbitrary finite abelian groups and also aims at building software packages that are helpful in this theoretical sense. To do this, the study involves reviewing the literature on classical polynomials and non-classical polynomials defined on finite fields. Our work focuses on cyclic abelian groups with an aim to classify non-classical polynomials on more general finite abelian groups. The main computational method used in this thesis is benefiting from the Hermite normal form of polynomial matrices. By addressing these objectives, the research endeavors to advance the field of higher-order Fourier analysis, contribute valuable computational tools, and offer insights into fundamental theoretical inquiries.