---
name: gap-language
description: "GAP (Groups, Algorithms, Programming) system integration for computational discrete algebra. Generates group-theoretic structures, character tables, and algebraic objects for the Plurigrid ecosystem."
trit: 1
version: 1.0.0
---

# GAP Language Skill

**Trit**: +1 (PLUS) - GENERATOR

Generates algebraic structures (Groups, Rings, Fields) and computations (Character Tables, Orbit Stabilizers) for the Plurigrid ASI.

## Integration Schema

This skill connects to the **Plurigrid Lattice** via:

1.  **Group Theory -> Gay Colors**: Maps finite groups to color symmetries in `gay-mcp`.
2.  **Algebra -> Category Theory**: Provides concrete implementations for algebraic structures in `acsets`.

## Dynamic Sufficiency Triad

```
┌─────────────────────┐
│    gap-language     │
│    (Generator)      │
│      trit: +1       │
└──────────┬──────────┘
           │
           ▼
┌─────────────────────┐
│    gay-mcp          │
│   (Coordinator)     │
│     trit: 0         │
└──────────┬──────────┘
           │
           ▼
┌─────────────────────┐
│  narya-proofs       │
│   (Validator)       │
│     trit: -1        │
└─────────────────────┘
```

## Computational Capabilities

*   **Group Theory**: Permutation groups, Matrix groups, Finitely presented groups.
*   **Representation Theory**: Character tables, Representations.
*   **Combinatorics**: Combinatorial structures, Graph symmetries.

## Scientific Skill Interleaving

This skill interleaves with:
*   `acsets`: For categorical perspective on algebraic structures.
*   `gay-mcp`: For color-theoretic interpretation of group actions.
*   `python`: Via `gap-system` bindings or IPC.

## Usage

```bash
# Run a GAP computation
gap -c 'Print(Order(SymmetricGroup(5)), "\n");'
```

## Interleaving Log

See `INTERLEAVE_LOG.md` for the results of the subagent random walks integrating this skill.