A Robust Implementation of an Algorithm to Solve the $S$-Unit Equation

Abstract: The $S$-unit equation has vast applications in number theory. We will discuss an implementation of an algorithm to solve the $S$-unit equation in the mathematical software Sage. The mathematical foundation for this implementation and some applications will be outlined, including an asymptotic version of Fermat's Last Theorem for totally real cubic number fields with bounded discriminant in which 2 is totally ramified. We will conclude with a discussion on current and future work toward improving the existing Sage functionality.

number theory

Audience: researchers in the topic

Comments: pre-talk at 1:20

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.