# sagemath/sage architecture

> Architecture diagram of the GitHub repository sagemath/sage, generated by GitDiagram from its file tree, README and a sample of source files (last updated 2026-09-30). It is an AI-made overview: check details against the source.

- Interactive diagram: https://gitdiagram.com/sagemath/sage
- Repository: https://github.com/sagemath/sage

## Overview

SageMath is an interactive mathematical software system. A representative workflow is to request a combinatorial design or code, use construction and catalog modules to build it, and work with the resulting mathematical object; finite-field arithmetic supports several such constructions. The repository also includes a rich-output display manager for presenting results. The excerpts focus on designs, coding theory, runtime environment, and display, so this is a partial view of Sage’s much broader mathematical capabilities; relationships are included only where the README or source index supports them.

Main entry points: [`src/sage/combinat/designs/database.py`](https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/database.py) (Design Catalog), [`src/sage/combinat/designs/bibd.py`](https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/bibd.py) (BIBD Constructions), [`src/sage/coding/code_constructions.py`](https://github.com/sagemath/sage/blob/develop/src/sage/coding/code_constructions.py) (Code Constructions), [`src/sage/coding/linear_code.py`](https://github.com/sagemath/sage/blob/develop/src/sage/coding/linear_code.py) (Linear Codes)

## Diagram (Mermaid)

```mermaid
flowchart TD

subgraph group_designs["Combinatorial Designs"]
  node_bibd["BIBD Constructions<br/>[bibd.py]"]
  node_design_catalog["Design Catalog<br/>[database.py]"]
  node_block["Block Designs<br/>[block_design.py]"]
  node_difference["Difference Families"]
  node_orthogonal["Orthogonal Arrays"]
  node_incidence["Incidence Structures"]
end

subgraph group_coding["Coding Theory"]
  node_code_construct["Code Constructions"]
  node_linear_code["Linear Codes<br/>[linear_code.py]"]
  node_code_database["Code Database<br/>[databases.py]"]
end

subgraph group_algebra["Algebra Foundations"]
  node_finite_field["Finite Fields"]
  node_mod_ring["Integer Mod Rings"]
  node_polynomial_ring["Polynomial Rings"]
end

subgraph group_runtime["Runtime and Display"]
  node_sage["Sage Interface<br/>[all.py]"]
  node_environment["Runtime Environment<br/>[env.py]"]
  node_display["Rich Output Manager<br/>[display_manager.py]"]
  node_display_backend["Display Backend<br/>[backend_base.py]"]
end

node_user(("Mathematics User"))

node_user -->|"uses"| node_sage
node_bibd -->|"uses constructions"| node_design_catalog
node_bibd -->|"uses"| node_block
node_bibd -->|"uses"| node_difference
node_bibd -->|"uses"| node_orthogonal
node_design_catalog -->|"builds from"| node_orthogonal
node_design_catalog -->|"builds from"| node_bibd
node_design_catalog -->|"builds from"| node_difference
node_design_catalog -->|"builds from"| node_block
node_block -->|"uses"| node_incidence
node_design_catalog -->|"uses arithmetic"| node_mod_ring
node_design_catalog -->|"uses arithmetic"| node_finite_field
node_code_construct -->|"constructs"| node_linear_code
node_code_construct -->|"uses arithmetic"| node_finite_field
node_code_construct -->|"uses arithmetic"| node_mod_ring
node_code_construct -->|"uses arithmetic"| node_polynomial_ring
node_linear_code -->|"uses arithmetic"| node_finite_field
node_linear_code -->|"uses arithmetic"| node_polynomial_ring
node_code_database -->|"uses"| node_linear_code
node_code_database -->|"uses arithmetic"| node_finite_field
node_display -->|"selects backend"| node_display_backend
node_environment -->|"configures"| node_sage

click node_sage "https://github.com/sagemath/sage/blob/develop/src/sage/all.py"
click node_bibd "https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/bibd.py"
click node_design_catalog "https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/database.py"
click node_block "https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/block_design.py"
click node_difference "https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/difference_family.py"
click node_orthogonal "https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/orthogonal_arrays.py"
click node_incidence "https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/incidence_structures.py"
click node_code_construct "https://github.com/sagemath/sage/blob/develop/src/sage/coding/code_constructions.py"
click node_linear_code "https://github.com/sagemath/sage/blob/develop/src/sage/coding/linear_code.py"
click node_code_database "https://github.com/sagemath/sage/blob/develop/src/sage/coding/databases.py"
click node_finite_field "https://github.com/sagemath/sage/blob/develop/src/sage/rings/finite_rings/finite_field_constructor.py"
click node_mod_ring "https://github.com/sagemath/sage/blob/develop/src/sage/rings/finite_rings/integer_mod_ring.py"
click node_polynomial_ring "https://github.com/sagemath/sage/blob/develop/src/sage/rings/polynomial/polynomial_ring_constructor.py"
click node_environment "https://github.com/sagemath/sage/blob/develop/src/sage/env.py"
click node_display "https://github.com/sagemath/sage/blob/develop/src/sage/repl/rich_output/display_manager.py"
click node_display_backend "https://github.com/sagemath/sage/blob/develop/src/sage/repl/rich_output/backend_base.py"

classDef toneNeutral fill:#f8fafc,stroke:#334155,stroke-width:1.5px,color:#0f172a
classDef toneBlue fill:#dbeafe,stroke:#2563eb,stroke-width:1.5px,color:#172554
classDef toneAmber fill:#fef3c7,stroke:#d97706,stroke-width:1.5px,color:#78350f
classDef toneMint fill:#dcfce7,stroke:#16a34a,stroke-width:1.5px,color:#14532d
classDef toneRose fill:#ffe4e6,stroke:#e11d48,stroke-width:1.5px,color:#881337
classDef toneIndigo fill:#e0e7ff,stroke:#4f46e5,stroke-width:1.5px,color:#312e81
classDef toneTeal fill:#ccfbf1,stroke:#0f766e,stroke-width:1.5px,color:#134e4a
class node_bibd,node_design_catalog,node_block,node_difference,node_orthogonal,node_incidence,node_user toneBlue
class node_code_construct,node_linear_code,node_code_database toneAmber
class node_finite_field,node_mod_ring,node_polynomial_ring toneMint
class node_sage,node_environment,node_display,node_display_backend toneRose
```

## Components

### Combinatorial Designs

- [BIBD Constructions](https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/bibd.py): `src/sage/combinat/designs/bibd.py`
- [Design Catalog](https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/database.py): `src/sage/combinat/designs/database.py`
- [Block Designs](https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/block_design.py): `src/sage/combinat/designs/block_design.py`
- [Difference Families](https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/difference_family.py): `src/sage/combinat/designs/difference_family.py`
- [Orthogonal Arrays](https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/orthogonal_arrays.py): `src/sage/combinat/designs/orthogonal_arrays.py`
- [Incidence Structures](https://github.com/sagemath/sage/blob/develop/src/sage/combinat/designs/incidence_structures.py): `src/sage/combinat/designs/incidence_structures.py`

### Coding Theory

- [Code Constructions](https://github.com/sagemath/sage/blob/develop/src/sage/coding/code_constructions.py): `src/sage/coding/code_constructions.py`
- [Linear Codes](https://github.com/sagemath/sage/blob/develop/src/sage/coding/linear_code.py): `src/sage/coding/linear_code.py`
- [Code Database](https://github.com/sagemath/sage/blob/develop/src/sage/coding/databases.py): `src/sage/coding/databases.py`

### Algebra Foundations

- [Finite Fields](https://github.com/sagemath/sage/blob/develop/src/sage/rings/finite_rings/finite_field_constructor.py): `src/sage/rings/finite_rings/finite_field_constructor.py`
- [Integer Mod Rings](https://github.com/sagemath/sage/blob/develop/src/sage/rings/finite_rings/integer_mod_ring.py): `src/sage/rings/finite_rings/integer_mod_ring.py`
- [Polynomial Rings](https://github.com/sagemath/sage/blob/develop/src/sage/rings/polynomial/polynomial_ring_constructor.py): `src/sage/rings/polynomial/polynomial_ring_constructor.py`

### Runtime and Display

- [Sage Interface](https://github.com/sagemath/sage/blob/develop/src/sage/all.py): `src/sage/all.py`
- [Runtime Environment](https://github.com/sagemath/sage/blob/develop/src/sage/env.py): `src/sage/env.py`
- [Rich Output Manager](https://github.com/sagemath/sage/blob/develop/src/sage/repl/rich_output/display_manager.py): `src/sage/repl/rich_output/display_manager.py`
- [Display Backend](https://github.com/sagemath/sage/blob/develop/src/sage/repl/rich_output/backend_base.py): `src/sage/repl/rich_output/backend_base.py`

### Other components

- **Mathematics User**

## Connections

- Mathematics User → Sage Interface: uses
- BIBD Constructions → Design Catalog: uses constructions (evidence: `src/sage/combinat/designs/bibd.py`)
- BIBD Constructions → Block Designs: uses (evidence: `src/sage/combinat/designs/bibd.py`)
- BIBD Constructions → Difference Families: uses (evidence: `src/sage/combinat/designs/bibd.py`)
- BIBD Constructions → Orthogonal Arrays: uses (evidence: `src/sage/combinat/designs/bibd.py`)
- Design Catalog → Orthogonal Arrays: builds from (evidence: `src/sage/combinat/designs/database.py`)
- Design Catalog → BIBD Constructions: builds from (evidence: `src/sage/combinat/designs/database.py`)
- Design Catalog → Difference Families: builds from (evidence: `src/sage/combinat/designs/database.py`)
- Design Catalog → Block Designs: builds from (evidence: `src/sage/combinat/designs/database.py`)
- Block Designs → Incidence Structures: uses (evidence: `src/sage/combinat/designs/block_design.py`)
- Design Catalog → Integer Mod Rings: uses arithmetic (evidence: `src/sage/combinat/designs/database.py`)
- Design Catalog → Finite Fields: uses arithmetic (evidence: `src/sage/combinat/designs/database.py`)
- Code Constructions → Linear Codes: constructs (evidence: `src/sage/coding/code_constructions.py`)
- Code Constructions → Finite Fields: uses arithmetic (evidence: `src/sage/coding/code_constructions.py`)
- Code Constructions → Integer Mod Rings: uses arithmetic (evidence: `src/sage/coding/code_constructions.py`)
- Code Constructions → Polynomial Rings: uses arithmetic (evidence: `src/sage/coding/code_constructions.py`)
- Linear Codes → Finite Fields: uses arithmetic (evidence: `src/sage/coding/linear_code.py`)
- Linear Codes → Polynomial Rings: uses arithmetic (evidence: `src/sage/coding/linear_code.py`)
- Code Database → Linear Codes: uses (evidence: `src/sage/coding/databases.py`)
- Code Database → Finite Fields: uses arithmetic (evidence: `src/sage/coding/databases.py`)
- Rich Output Manager → Display Backend: selects backend (evidence: `src/sage/repl/rich_output/display_manager.py`)
- Runtime Environment → Sage Interface: configures (evidence: `src/sage/all.py`)