ix-sedenion

name	ix-sedenion
description	Hypercomplex algebra — sedenion/octonion multiplication, Cayley-Dickson construction
disable-model-invocation	true

Hypercomplex Algebra

Operations on sedenions (16D), octonions (8D), and arbitrary Cayley-Dickson algebras.

When to Use

When the user needs hypercomplex number operations, wants to explore non-associative algebras, or needs Cayley-Dickson multiplication tables.

Capabilities

• Sedenion multiplication — 16-dimensional Cayley-Dickson product
• Octonion multiplication — 8-dimensional non-associative product
• Cayley-Dickson construction — Generic 2^n-dimensional algebra multiplication
• Conjugate and norm — For any Cayley-Dickson algebra element
• BSP tree — Binary space partition for nearest-neighbor queries

Key Concepts

• Complex → Quaternion → Octonion → Sedenion (each doubles dimension)
• Octonions lose associativity; sedenions also lose alternativity
• Zero divisors appear at dimension 16+

Programmatic Usage

use ix_sedenion::sedenion::Sedenion;
use ix_sedenion::octonion::Octonion;
use ix_sedenion::cayley_dickson::{double_multiply, double_conjugate, double_norm};

MCP Tool

Tool name: ix_sedenion Operations: multiply, conjugate, norm, cayley_dickson_multiply