duncanmazza/discrete-final

Animations for a presentation on discrete convex analysis.

Discrete Convex Analysis

A class project by Duncan Mazza and Colin Snow for MTH2110 Discrete Math at Olin College

Background

Our class project culminated in a presentation to the class on discrete convex analysis, the topic of our exploration. The presentation had an accompanying slide deck which contained various animations that were used to explain the technical definition of L-natural convexity of functions on the 2-dimensional integers and the Legendre-Fenchel transform. These animations were created using the Manim Community library.

Our primary technical reference:

K. Murota, “Main features of discrete convex analysis,” Jun 2018.[Online]. Available: https://www.comp.tmu.ac.jp/kzmurota/paper/rimsCOSS2018/COSS2018chap1.pdf

Directory

• convexity_1d.py: Animation showing the convexity definition for a discrete function on the 1-dimensional integers.
• convexity_2d.py: Animation showing L-natural convexity for a discrete function on the 2-dimensional integers.
• fruits_example.py: Brute-force search of optimal solution for the fruit-buying example described in the presentation. This example was designed to reflect the Gross Substitutes Property in Economics.
• legendre.py: Animations explaining the Legendre-Fenchel transform.

Usage

Documentation on installing the requisite libraries and generating the animations can be found at Manim Community documentation page.