mirror of
https://github.com/blackboxprogramming/BlackRoad-Operating-System.git
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0108860bff
Create comprehensive research-lab pack structure with mathematical and quantum computing modules from blackroad-prism-console: Math Modules: - hilbert_core.py: Hilbert space symbolic reasoning - collatz/: Distributed Collatz conjecture verification - linmath/: Linear mathematics C library - lucidia_math_forge/: Symbolic proof engine - lucidia_math_lab/: Experimental mathematics Quantum Modules: - lucidia_quantum/: Quantum core - quantum_engine/: Circuit simulation Experiments: - br_math/: Gödel gap, quantum experiments Includes pack.yaml manifest and comprehensive README. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude <noreply@anthropic.com>
52 lines
1.3 KiB
Python
52 lines
1.3 KiB
Python
"""Quaternion‑Ternary token algebra utilities."""
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from __future__ import annotations
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from dataclasses import dataclass
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import numpy as np
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TERNARY = (-1, 0, 1)
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def ternary_mul(a: int, b: int) -> int:
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"""Balanced‑ternary multiplication with 0 absorbing."""
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if a == 0 or b == 0:
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return 0
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return 1 if a == b else -1
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@dataclass
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class QT3:
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"""Quaternion‑Ternary statement."""
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v: int
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q: np.ndarray # (4,) quaternion [w,x,y,z]
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def __post_init__(self) -> None:
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if self.v not in TERNARY:
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raise ValueError("v must be -1,0,+1")
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self.q = np.asarray(self.q, dtype=float)
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self.q = self.q / np.linalg.norm(self.q)
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def star(self, other: "QT3") -> "QT3":
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"""Compose with another statement."""
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v = ternary_mul(self.v, other.v)
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q = quat_mul(self.q, other.q)
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return QT3(v=v, q=q)
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def quat_mul(a: np.ndarray, b: np.ndarray) -> np.ndarray:
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"""Quaternion multiplication."""
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w1, x1, y1, z1 = a
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w2, x2, y2, z2 = b
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return np.array(
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[
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w1 * w2 - x1 * x2 - y1 * y2 - z1 * z2,
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w1 * x2 + x1 * w2 + y1 * z2 - z1 * y2,
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w1 * y2 - x1 * z2 + y1 * w2 + z1 * x2,
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w1 * z2 + x1 * y2 - y1 * x2 + z1 * w2,
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]
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)
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__all__ = ["QT3", "ternary_mul", "quat_mul"]
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