Gandini's Emporeum of Stuff

GitHubs 🐱

1. Algorithms
2. Invariant Ring Implementation
3. Invariant Ring Master Repository
4. Seed Growth & Expansion - All Versions
5. Elementary Abelian Groups
6. Sam's Textbook
7. M2 Codespace Repo
8. Gordie's M2 Codespace Dev Repo
9. Gandini Textbook
10. M2 InvariantRing Package
11. M2 Master Repository
12. Lucas Repository
13. Madison Macaulay2 Repo
14. M2 Practice/Initial Development

Resources

1. PreTeXt Guide
2. Zotero
3. Invariant Ring Documentation
4. Gandini Thesis

Overleafs

1. Final Paper
2. Curi Poster
3. Intersection of Ideals
4. Invariant Ring 3.0
5. Skew Invariant Polynomials

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Algorithms

Stores the algorithms for all the gandini stuff.

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Current Algorithms

Key for reading:

• 📄 - $\text{ documentation}$
• 👁️‍🗨️ - $\text{ needs review}$
• 🔰 - $\text{ tested}$
• 🔻 - $\text{ untested}$
• 🚫 - $\text{ nonfunctional/incomplete algorithm}$
• ⚠️ - $\text{ undocumented}$
• ⏳ - $\text{ dated/redundant algorithm}$
• 🚛 - $\text{ ready for deployment}$

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ø/orbitSums/.

• actionDoc.m2 📄 Contains the documentation for the unimplemented action function.
• orbitSum.m2 🚛 Contains the package OrbitSum with all related functions:
  • $\text{listSpInd}(n, d)$
    Lists the special indicies that are related to a degree
  • $\text{listSpMon}(n, d)$
    Lists the special monomials that are related to a degree
  • $\text{orbSumList}(G, n, d)$
    Computes the orbit sums of a list of monomials
  • $\text{orbSum}(r, G, n)$
    Computes the orbit sum of a monomial
  • $\text{shuffMon}(r, n)$
    Permutes all the variables of a monomial and puts the permutations in a list.
• orbitSumDoc.m2 📄 👁️‍🗨️ Contains the documentation for the OrbitSum package.

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ø/p-invariants/.

• modVector.m2 (June 27th) 🔻 ⚠️ Utilizes a set of vectors in $\mathbb Z_2$ to find a set of seed generators in the Skew Commutative setting.
• invariantgens.m2 (July 7th) 🔰 Utilizes finding the submatricies of a weight matrix $W$ to find generating set of an invariant subring.
• spoiled_invariantgens.m2 (July 7th) 🔻 🚫 ⚠️ ⏳ Utilizes finding square submatricies of a weight matrix $W$ to find a set of generating seeds.
• demo.m2 (July 9th) Contains a demo for dq to understand how to use the algorithms in Macaulay2.

ø/p-invariants/invar_dependencies/.

• Contains helper functions for invariantgens.m2.
  • expandseeds.m2 (July 7th) 🔻 Contains the method $\text{expandseeds}$ for algorithmic seed expansion for a whole set.
  • gensDoc.m2 (July 7th) 📄 Contains the documentation for $\text{expandseeds}$, $\text{genseeds}$, and $\text{invariantgens}$.
  • genseeds.m2 (July 7th) 🔰 Contains the algorithm for seed generation with the submatrix method.
  • lucas-expandseeds.m2 (July 7th) 🚫 ⚠️ ⏳ Contains the old algorithm used by lucas to expand seed generators.

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ø/.devfiles/.

• Contains developer files for improving algorithms.

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Important Notes

Here is an image for your enjoyment.