Here is information on loading a package in Mathematica.
The documentation notebook for each package contains examples for each function.
Major packages:
| package | description | documentation |
| IntegerSequences | IntegerSequences is a package for identifying and computing with integer sequences from a variety of classes. | notebook cloud |
| ListTricks | ListTricks is a collection of about 50 structure manipulation, classification, and searching tools that can be thought of as extending the core Wolfram Language. | notebook cloud |
| SymbolicWords | SymbolicWords is a collection of tools for manipulating run-length encodings of words and morphisms with symbolic exponents.
I used this package to establish the structure of many extremal a/b-power-free words for explicit and symbolic rational numbers a/b.
| notebook cloud |
Packages related to binary trees:
| package | description | documentation |
| BinaryTrees | BinaryTrees is a package for generating, visualizing, and manipulating binary trees.
papers:
| notebook cloud |
| ParseWords
(requires BinaryTrees) | ParseWords is a package for studying parse words of pairs of binary trees under a certain grammar related to the four color theorem.
paper: Toward a language theoretic proof of the four color theorem | notebook cloud |
| TreePatterns
(requires BinaryTrees) | TreePatterns is a package for studying trees that avoid a given tree pattern.
If Singular and the interface package by Manuel Kauers and Viktor Levandovskyy are suitably installed, TreePatterns uses Singular to compute Gröbner bases, which is faster than in Mathematica.
| notebook cloud |
Packages related to cellular automata:
| package | description | documentation |
| AdditiveRules | AdditiveRules is a package for studying additive cellular automaton rules over a commutative monoid. | |
| BijectiveRules | BijectiveRules is a package for studying right bijective and left bijective cellular automaton rules. | notebook cloud |
| CellularAutomatonBoundaries | CellularAutomatonBoundaries is a collection of tools for studying boundaries of one-dimensional cellular automata. | notebook cloud |
| CellularAutomatonData | CellularAutomatonData is a source of data on boundaries of one-dimensional cellular automata. | notebook cloud |
Other packages:
| package | description | documentation |
| BinomialCoefficients | BinomialCoefficients is a package containing implementations of several theorems on the residues and divisibility properties of binomial coefficients.
paper: The number of nonzero binomial coefficients modulo pα | notebook cloud |
| EquivalentWords | EquivalentWords is a package for studying automorphic conjugacy in the free group on 2 generators.
I used this package to compute all automorphic conjugacy classes for words of length at most 20.
| notebook cloud |
| PocketChange | PocketChange is a package for analyzing the long-term behavior of the set of coins in one's pocket.
paper: What's in YOUR wallet? | notebook cloud |
| SinkhornPolynomials | SinkhornPolynomials is a package for computing the polynomial equation satisfied by an entry of the Sinkhorn limit of a matrix.
This package is large, so it is only available as an ancillary file from this arXiv submission.
| notebook cloud |
| StringTricks | StringTricks is a collection of string manipulation and analysis tools. | notebook cloud |
| TeXTools | TeXTools automates some common tasks involved in writing papers in LaTeX. | notebook cloud |