Luis Antonio Vasquez Reina is a senior-year mathematics undergraduate student at Pontificia Universidad Católica del Perú. His main academic interests include modern algebra, computational mathematics and logic. In the future, he would like to do research and/or advanced mathematics in industry, in different locations of the world. Apart from that, he loves Star Wars, learning languages and history. He hopes to become a polyglot.
Project: A Calculus for Infinite Lists
Computer languages are usually constrained to lists of finite size subjected to operations. For example, one may join, partition, sum or nest them and get a finite list as a result. Even though explicit infinite lists cannot be implemented in a computer, in this project, I aim to provide the Wolfram Language with a symbolic calculus for lists of infinite length. That is, one would be able to treat expressions referring to infinite lists as arguments of operations, e.g. the infinite list of the roots of natural numbers. The implementation of this kind of operation to the Wolfram Language is the objective of my project.
Main Results in Detail
I have extended most of the basic Mathematica functions for lists to infinite lists through symbolic manipulation, though partial explicit numerical results can be obtained. Two nontrivial applications of these results are the capacity to define infinite graphs and to work with cellular automata with an infinite initial condition.
It is still pendant to extend other Mathematica functions for finite lists to work with this project’s approach for infinite lists in an optimal way. Also, an implementation could be explored for systems that, in principle, accept infinite initial conditions.