m2invariants

Authors: Mallory Dolorfino, Francesca Gandini, Daniel Qin, Sam Ratliff, and Lucas Rizzolo

Created for distribution after the Youth Math Conference at Ohio State University (2021)

License: GNU General Public License v3.0 as described in the LICENSE.md

Copyright 2021, Mallory Dolorfino, Francesca Gandini, Daniel Qin, Sam Ratliff, and Lucas Rizzolo. You may redistribute this file under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or any later version.

The project explores Invariant Theory using Macaulay2. The following files and folders are provided:

1. Generating Random Systems
   • primeList.m2 ---> Holds a list of large primes, used to pseudo-generate random primes
   • rMat.m2 ---> Original code from creating random systems to test, considered unstable
   • sam_rMat.m2 ---> Testing and benchmarking for the Derksen-Gandini algorithm and modifications of it
   • testInv.m2 ---> Tests the generation of invariants using a seed monomial
   • testInv_rMat.m2 ---> Uses rMat and testInv to test a potential hash table algorithm
   • README.md ---> README
2. M2 Object Testing
   • LinkedList2.m2 ---> Establishes a LinkedList object similar to Java.util.LinkedList
   • Node2.m2 ---> Required to make the LinkedList
   • README.md ---> README
3. Non-Packaged Algorithms
   • generator_algorithm.m2 ---> The Ratliff-Rizzolo-Gandini Algorithm that uses seed invariants. Makes comparison to Derksen-Gandini
   • README.md ---> README
4. Other testing code
   • DFS_Invariants.java ---> Searches for invariants using a depth-first search
   • Invariants.java ---> Used with DFS_Invariants.java
   • exampleForPres.java ---> An example of the Derksen-Gandini algorithm as inmplemented in Macaulay2
   • invariantsLinearSpace.m2 ---> Other explorations
   • invariants_exploration.m2 ---> Other explorations
   • README.md ---> README
5. InvariantCalculator v1.1
   • dat
     • test.dat ---> location for stored data
     • vals.dat ---> sample save data
   • gensAlg.m2 ---> contains the two algorithms for use
   • inputParser.m2 ---> parses the inputs taken from files or users
   • inputs.m2 ---> takes inputs from the user
   • invarDriver_2.m2 ---> driver for the code
   • men
     • credits.txt ---> Credits menu, not finished
     • kSymb.txt ---> K College symbol at first print
     • man.txt ---> manual, not finished
     • menu.txt ---> main menu
     • opts.txt ---> options menu
     • pref.txt ---> preferences menu
   • printSig.m2 ---> print beginning signature
   • README.txt ---> Extrememly valuable README
   • vals.dat ---> Result of buggy code. Please ignore :)
6. LICENSE.md ---> GNU General Public License v3.0
7. README.md ---> This file

Please read the README files in each folder for a better explanation of the separation of the code

For more information regarding this repository, please contact:

• Lucas Rizzolo:
  • email: lucasrizzolo (at) icloud (dot) com
  • github: @lrizzolo