Merge pull request #409 from marvin-hansen/main

feat(deep_causality_multivector): Added new normalize_l2

Author: marvin-hansen

Cargo.lock

@@ -40,9 +40,13 @@ path = "../deep_causality_tensor"
 version = "0.1"
 
 
-[dev-dependencies]
-criterion = {version = "0.8"}
+[dependencies.deep_causality_core]
+path = "../deep_causality_core"
+version = "0.0.1"
+
 
+[dev-dependencies]
+criterion = { version = "0.8" }
 
 [[bench]]
 name = "multivector_bench"
@@ -84,7 +88,3 @@ path = "examples/maxwell_multivector.rs"
 [[example]]
 name = "pga3d_multivector_example"
 path = "examples/pga3d_multivector.rs"
-
-
-
-[dependencies]

deep_causality_multivector/Cargo.toml

@@ -0,0 +1,19 @@
+# CausalMultiVector Examples
+
+This directory contains examples demonstrating the capabilities of the `CausalMultiVector` and its related abstractions.
+Each example is designed to highlight a specific engineering or scientific use case where Geometric Algebra provides a
+more robust, intuitive, or performant solution compared to traditional linear algebra.
+
+| File                                                           | Description                                                                                                                                                                                    | Key Concepts                                                                  |
+|----------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------|
+| [basic_multivector.rs](basic_multivector.rs)                   | Demonstrates the fundamental operations of Geometric Algebra, such as the geometric, outer, and inner products.                                                                                | Geometric Algebra, Geometric Product, Outer Product, Inner Product            |
+| [clifford_mhd_mulitvector.rs](clifford_mhd_mulitvector.rs)     | Showcases "Metric Agnosticism" by calculating the Lorentz force in both classical (Euclidean) and relativistic (Minkowski) regimes using the same code, essential for plasma physics.          | Metric Agnosticism, Plasma Physics, Lorentz Force, Euclidean vs. Minkowski    |
+| [dixon_multivector.rs](dixon_multivector.rs)                   | Implements Dixon Algebra (Cl_C(6)), a structure used in high-energy particle physics to naturally encode the complex symmetries of the Standard Model.                                         | Dixon Algebra, Particle Physics, Standard Model, Octonions                    |
+| [geometric_tilt_estimator.rs](geometric_tilt_estimator.rs)     | An adaptive gravity observer that uses a Causal Monad to estimate a gravity vector, eliminating Gimbal Lock and providing a hardware-independent kernel for state estimation in robotics.      | Tilt Estimation, Gimbal Lock, Causal Monad, Adaptive Observer, Robotics       |
+| [grmhd_integration.rs](grmhd_integration.rs)                   | A "Multi-Physics Monad" that couples a General Relativity (GR) solver with a Magnetohydrodynamics (MHD) solver, allowing simulations to adapt their mathematical basis to physical conditions. | GRMHD, Multi-Physics, General Relativity, MHD, Causal Coupling                |
+| [hilbert_multivector.rs](hilbert_multivector.rs)               | Simulates Quantum Gates and States using `HilbertState`, leveraging the natural isomorphism between Geometric Algebra and Quantum Mechanics for verifying quantum algorithms.                  | Quantum Computing, Hilbert Space, Geometric Algebra, Quantum Gates            |
+| [hkt_multivector.rs](hkt_multivector.rs)                       | Demonstrates how `CausalMultiVector` implements Higher-Kinded Types (Functor, Applicative, Monad) for building composable and reusable physics pipelines with "Algebraic Programming".         | Higher-Kinded Types (HKT), Functor, Applicative, Monad, Algebraic Programming |
+| [hopf_fibration_multivector.rs](hopf_fibration_multivector.rs) | Uses the Hopf Fibration to project high-dimensional quantum states (Spinors) onto a visible 2-sphere (Bloch Sphere), aiding in Topological Data Analysis and quantum system debugging.         | Hopf Fibration, Quantum Mechanics, Spinors, Topological Data Analysis         |
+| [maxwell_multivector.rs](maxwell_multivector.rs)               | Unifies Electric and Magnetic fields into a single Electromagnetic Field Bivector derived from a 4-Vector Potential, crucial for high-fidelity antenna and radar design.                       | Maxwell's Equations, Electromagnetism, Geometric Algebra, Vector Potential    |
+| [pga3d_multivector.rs](pga3d_multivector.rs)                   | Implements Projective Geometric Algebra (PGA) to represent points, lines, and planes uniformly and uses "Motors" to handle rigid body motions in computer graphics and robotics.               | Projective Geometric Algebra (PGA), Robotics, Computer Graphics, Motors       |
+

deep_causality_multivector/examples/README.md

@@ -5,6 +5,20 @@
 
 use deep_causality_multivector::{CausalMultiVector, Metric, MultiVector};
 
+// -----------------------------------------------------------------------------------------
+// ENGINEERING VALUE:
+// Geometric Algebra (GA) unifies multiple mathematical systems (Complex Numbers, Quaternions,
+// Vector Algebra) into a single, consistent framework.
+//
+// This example demonstrates the core operations:
+// - Geometric Product: Combines rotation and scaling.
+// - Outer Product (Wedge): Represents spanned areas/volumes (subspaces).
+// - Inner Product (Dot): Represents projection and metric contraction.
+//
+// By using GA, engineers can write code that is more geometric, intuitive, and less prone
+// to coordinate-system errors common in linear algebra.
+// -----------------------------------------------------------------------------------------
+
 fn main() -> Result<(), Box<dyn std::error::Error>> {
     println!("--- CausalMultiVector Basic Usage ---");
 

deep_causality_multivector/examples/basic_multivector.rs

@@ -5,6 +5,18 @@
 
 use deep_causality_multivector::{CausalMultiVector, Metric, MultiVector};
 
+// -----------------------------------------------------------------------------------------
+// ENGINEERING VALUE:
+// Plasma Physics and Fusion research often involve switching between Classical (Euclidean)
+// and Relativistic (Minkowski) regimes. Errors in metric signatures can lead to
+// catastrophic simulation failures (e.g., calculating force in the wrong direction).
+//
+// This example demonstrates "Metric Agnosticism":
+// The same code `F = J . B` correctly calculates the Lorentz Force in BOTH regimes.
+// The `CausalMultiVector` type handles the underlying metric algebra (spacetime signature),
+// ensuring physical correctness and safety at the type level.
+// -----------------------------------------------------------------------------------------
+
 fn main() {
     println!("--- PLASMA FUSION SIMULATION: Reactor Confinement Check ---");
     println!("Context: A Stationary Tokamak Reactor (e.g., ITER).");

deep_causality_multivector/examples/clifford_mhd_mulitvector.rs

@@ -6,6 +6,18 @@
 use deep_causality_multivector::{DixonAlgebra, MultiVector};
 use deep_causality_num::Complex;
 
+// -----------------------------------------------------------------------------------------
+// ENGINEERING VALUE:
+// High-energy particle physics (Standard Model) relies on complex symmetries (SU(3)xSU(2)xU(1)).
+// Dixon Algebra (Cl_C(6)) provides a mathematical structure that naturally encodes these
+// symmetries using Octonions and Complex numbers.
+//
+// This example demonstrates how to construct and manipulate these high-dimensional
+// algebraic structures. This capability is essential for researchers modeling
+// Quantum Field Theory (QFT) or exploring Beyond Standard Model (BSM) physics
+// within a computational framework.
+// -----------------------------------------------------------------------------------------
+
 fn main() {
     println!("=== Dixon Algebra (Cl_C(6)) Example ===");
     println!("This algebra operates on Octonions in particle physics models (e.g. C. Furey).");