Coding in Mathematica and more

Project Description: Creating code in Mathematica, and perhaps another software package, that allows the computation of specific mathematical invariants, given the algorithm for determining the associated inequalities. To be specific, while I know how to calculate by hand the inequalities of any particular example and can enter those into Mathematica for a quick calculation of volume, I am seeking the creation of code that will allow one to simply enter two positive integers and let Mathematica do all the work. Moreover, I am seeking the creation of a website that Algebraists can use to access the code and calculations. The relevance of this project is that, in general, the invariants being calculated are very difficult to compute. This project considers a specific family of examples where it is algorithmically possible to calculate the invariants, which are realized as volumes of polytopes. International researchers would find it valuable to have a web interface where they can generate many examples and test their theories of the relationship between the invariants. We would aim to publish our work in the Mathematics Journal Involve, specifically designed for faculty and student collaboration.

Desired Student Qualifications: Facility with Mathematica and computer software in general. This project is probably best suited for a student majoring or minoring in Computer Science, or has a strong knowledge of programming and web design.

Project Timeline: One year to eighteen months, depending upon the student.

Duties of Student Researcher: The student would be responsible for determining how to code Mathematica so that it can determine the inequalities involved and then compute the volumes. The student would need to learn the software Macaulay 2 for supplemental calculations. Thirdly, the student would be tasked with creating a webpage for researchers to use.

Last Updated on 2017-10-18 14:05:00