Rosetta Stone

This section is the example corpus. Each page contains a human-readable description, generation code when available, the emitted serialized data, and links back to the relevant specification pages.

Table of Contents

Basics

Example Oscar.jl
Boolean X
Small Integer X
String X
UInt X
Int16 X
Float64 X
BigInt X

Containers

Example Oscar.jl
Vector of integers X
Mixed tuple X
Matrix of integers X
Dictionary (String to Int) X
Dictionary (String to polynomial variable) X
Set of integers X
Set of polynomial elements X

Rings

Example Oscar.jl
Integer in ZZ X
Rational number X
One in GF(5) X
Generator of GF(5^2) X
Multivariate polynomial X
Element of residue ring (ZZ(6)) X
Element of residue ring (6) X
Univariate polynomial X

Linear Algebra

Example Oscar.jl polymake
Rational matrix X X

Groups

Abelian Groups

Example Oscar.jl
Free abelian group X
Element of abelian group X
Homomorphism of free abelian groups X

Permutation Groups

Example Oscar.jl
Symmetric group X
Element of symmetric group X
Subgroup of symmetric group X
Element of subgroup of symmetric group X

Matrix Groups

Example Oscar.jl
Matrix group X
Element of matrix group X

Free Groups

Example Oscar.jl
Free group X
Element of free group X
Subgroup of free group X
Element of subgroup of free group X

Finitely Presented Groups

Example Oscar.jl
Finitely presented group X
Element of finitely presented group X
Subgroup of finitely presented group X
Element of subgroup of finitely presented group X

Pc Groups

Example Oscar.jl
Pc group X
Element of pc group X
Subgroup of pc group X
Element of subgroup of pc group X

Lie Theory

Root Data

Example Oscar.jl
Root system X
Positive root X
Positive coroot X
Positive roots X
Negative coroots X

Weight Lattice

Example Oscar.jl
Weight lattice X
Element of weight lattice X
Generators of weight lattice X

Weyl Group

Example Oscar.jl
Weyl group X
Element of Weyl group X
Generators of Weyl group X

Polyhedral Geometry

Polyhedra

Example Oscar.jl
Algebraic cube X
Dodecahedron dictionary X
Square polyhedron X

Fans

Example Oscar.jl
Normal fan of dodecahedron X
Normal fan of square X

Cones

Example Oscar.jl
Number-field cone X
Positive hull cone X

Matroids

Example Oscar.jl
Fano matroid X
Uniform matroid X

Optimization

Example CPLEX Oscar.jl cdd polymake
Linear program X X X X
Linear program X
Mixed-integer linear program X
Pair of linear programs X
Pair of mixed-integer linear programs X

Complexes and Subdivisions

Example Oscar.jl
Complex projective plane X
Number-field polyhedral complex X
Number-field subdivision X
Polyhedral complex X
Subdivision of points X

Phylogenetic

Example Oscar.jl
Phylogenetic tree (Float64) X
Phylogenetic tree (QQ) X

Combinatorics

Example Oscar.jl
Complete graph X