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
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 |