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

# 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.