Rudimentary Exploration of the Concept of Action from Abstract Algebra and Basic Ring Theory aimed at Postulating Post-Quantum Computing Methods through Manipulation of Unknown Quantities as Applied to the Basic Concepts of Variables and Equations

In this research paper, we explore the possibilities associated with solving equations for variables, starting off at the most basic monomial expressions. However, analyzing the various definitions of the term ‘variable,’ it can be deduced that no single definition is sufficient to suffice the needs of compiling all possible solutions for a variable at one place, given that the equation in question is observed and operated using a combination of computational mathematics and abstract algebra. Although there is sufficient scientific literature available on applications of abstract algebra and ring theory in this field, solving for variables that logically represent unknown quantities has remained a relatively neglected area of study. Moreover, in this paper, the notions of mathematical operation and group action have been used almost interchangeably, which may not be agreed upon by the conventional academic system. The paper finally aims at developing postulates over the progress of computational mathematics, with special stress on machine learning, beyond the scope of quantum computing and related sciences.

Keywords: variables, abstract algebra, group action, unknown quantity, computation, quantum computing, digital computing