Mirror Matrix on the Wall: coding and vector notation as tools for introspection

TL;DR

This paper explores how GNU Octave's use of vector notation enhances mathematical expressiveness and problem-solving efficiency, aligning programming practices with mathematical reasoning to improve introspection and code clarity.

Contribution

It analyzes operators and functions in GNU Octave, demonstrating how vector notation improves alignment with mathematical notation and code effectiveness.

Findings

Vector notation enhances code expressiveness and efficiency.

Case studies illustrate improved problem-solving with vector notation.

GNU Octave becomes more intuitive for mathematical and scientific users.

Abstract

The vector notation adopted by GNU Octave plays a significant role as a tool for introspection, aligning itself with the vision of Kenneth E. Iverson. He believed that, just like mathematics, a programming language should be an effective thinking tool for representing and reasoning about problems we wish to address. This work aims to explore the use of vector notation in GNU Octave through the analysis of operators and functions, providing a closer alignment with mathematical notation and enhancing code efficiency. We will delve into fundamental concepts such as indexing, broadcasting, and function handles, and present case studies for a deeper understanding of these concepts. By adopting vector notation, GNU Octave becomes a powerful tool for mathematicians, scientists and engineers, enabling them to express and solve complex problems more effectively and intuitively.