https://github.com/bollu/casette

Mixtape of computer algebra system (CAS) algorithms
https://github.com/bollu/casette

Last synced: 4 months ago
JSON representation

Mixtape of computer algebra system (CAS) algorithms

• Host: GitHub
• URL: https://github.com/bollu/casette
• Owner: bollu
• Created: 2021-06-02T14:41:52.000Z (over 4 years ago)
• Default Branch: master
• Last Pushed: 2025-03-31T16:08:27.000Z (7 months ago)
• Last Synced: 2025-06-03T23:55:59.913Z (5 months ago)
• Language: Lean
• Homepage:
• Size: 8.32 MB
• Stars: 8
• Watchers: 2
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

          
# CASette: Computer Algebra System algorithms

#### Algorithms

- [egg](./egg/egg.py), a minimal implementation of a e-graph and E-matching.

  We do not yet implement the bytecode interpreter as explained by the z3 e-matching paper.

- [Exists Forall solver for bitvector problems](./exists-forall-yices/solver.cpp)

- [A solver for the theory commutative semigroups](./little-engines-of-proof/commsemigroup.cpp),

  which has the key insight of bucchberger's algorithm, which is to build the rewrite that equates

  [critical pair](https://www.inf.ed.ac.uk/teaching/courses/ar/slides13.pdf) for terms,

  and to then order the equation to get a termnating rewrite system.

- [multivariate polynomial division](./division.py) to compute multivariate reminder term.

- [Bucchberger algorithm](./bucchberger.py) to computing grobner basis of ideal.

- [schrier sims algorithm](./schrier-sims.py) to compute a good representation of subgroups of the symmetric group. Formally,

  compute a [base and strong generating set](https://en.wikipedia.org/wiki/Schreier%E2%80%93Sims_algorithm).

- [todd coxeter algorithm](./todd-coxeter.py) to compute the permutation representation of the cosets of a subgroup. Formally,

  build the schrier graph and extract the coset table.

- [Fundamental theorem of symmetric polynomials](./ftsp.cpp) to write a given

  symmetric polynomial in terms of elementary symmetric polynomials.

- [Plucker coordinates](./plucker.py) implements common graphics operations via plucker coordinates, as a step to

  understand the grassmanian

#### Aspirational algorithms

- [Cutting to the chase](./cut-to-the-chase.py), a decision procedure for LIA that can show UNSATs of 

  large, complex systems of integer linear problems.

- [Hormander's algorithm](./hormander/solver.cpp), a quantifier elimination procedure for real closed fields

  that is fast enough to be proof producing 'in practice' for HOL light.

- [Shostak's algorithm](./shostak/solver.cpp) for combining theories in a way that is different from Nelson Oppen.

- [Schubert decomposition of the grassmanian](./grassman.py) to compute the cohomology of the grassmanian.

- [Algorithms on tableaux](./tableaux.cpp) in particular, implement RSK to show the RSK correspondence, and also implement the fourier transform

  on the symmetric group.

- [Monster](./monster.py) computing products of elements in the monster group.

#### Books

- Bijective combinatorics: Chapter on Tableaux.

- [SnoB: FFT for the symmetric group](http://people.cs.uchicago.edu/~risi/SnOB/index.html)

- FTSP: Fundamental theorem of symmetric polynomials

- Ideals, Varieties, Algorithms

- [Serees: Permutation group algorithms](https://doc.lagout.org/science/0_Computer%20Science/2_Algorithms/Permutation%20Group%20Algorithms%20%5BSeress%202003-03-17%5D.pdf)

- Decision Procedures: An algorithmic point of view

#### Notes

- [intuition for why symmetric polynomials are important](./reading/symmetric-polynomials.md)