Support Lorentz spinors as complex quaternions

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Pull request overview

Adds support for treating complexified quaternions as Lorentz-group spinors (STA rotors) by switching complex-quaternion normalization/“norm” behavior to the spinor norm, and documents the geometric-algebra foundations. Also restructures test/docs environments and extends test coverage for the new Lorentz behavior.

Changes:

• Implement spinor-norm behavior for abs, abs2, absvec, abs2vec on Complex-component quaternions (and add _hypot support).
• Add a dedicated Lorentz/STA normalization test suite and update existing math tests accordingly.
• Expand documentation with new Geometric Algebra and Spacetime Algebra pages; introduce workspace-style test/docs projects and a more capable test runner CLI.

Reviewed changes

Copilot reviewed 16 out of 18 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
src/quaternion.jl	Adds _hypot and new vector normalize methods used by rotor normalization.
src/math.jl	Changes abs/abs2/absvec/abs2vec semantics for Complex components to use spinor norm.
test/runtests.jl	Reworks test runner with CLI filtering (--file, --tags, etc.) and adds lorentz.jl to the suite.
test/math.jl	Updates expected values for complex norms to match the new spinor-norm definitions.
test/lorentz.jl	New tests validating STA/Lorentz normalization and _hypot behavior for boosts/rotations/phases.
test/basis.jl	Skips selected basis/normalization tests for Symbolics.Num due to simplification limitations.
test/base.jl	Adjusts Symbolics rotor test and LaTeX rendering expectations.
test/Project.toml	Introduces a dedicated test environment with explicit deps/compat.
test.jl	Removes the old top-level test/coverage runner script.
docs/src/geometric_algebra.md	New documentation page deriving quaternion conventions from GA.
docs/src/spacetime_algebra.md	New documentation page explaining complexified quaternions and the spinor norm in STA.
docs/src/references.bib	Adds citations used by the new GA/STA docs.
docs/make.jl	Adds the new docs pages and conditional inclusion of local notes/remotes.
docs/local_notes.jl	Optional “local notes” integration for docs builds (detects and wires extra pages/remotes).
docs/serve.jl	Adds a simple LiveServer-based doc serving script.
docs/Project.toml	Adds workspace-style sources entry for local package development.
Project.toml	Adds [workspace] and removes test-only extras/targets in favor of test/Project.toml.
.gitignore	Ignores optional local docs notes and some tool configuration files.

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[Copilot]

Defining normalize(v::AbstractVector{Complex{T}}) and especially normalize(v::AbstractVector) here adds/overrides methods for LinearAlgebra.normalize globally (since using LinearAlgebra is in scope). This changes normalization semantics for all vectors in user code once Quaternionic is loaded (e.g. normalize([1,2,3]) will now call hypot(v...), and Complex vectors will use the spinor norm), which is a breaking/unsafe side effect unrelated to quaternions.

Consider restricting these methods to quaternion-component types only (e.g. SVector{4,...}), or using an internal helper (e.g. _normalize_components) that rotor calls, while leaving LinearAlgebra.normalize behavior unchanged for general vectors.

Suggested change

	# We need that helper to normalize complex quaternions
	normalize(v::AbstractVector{Complex{T}}) where T = v ./ _hypot(v)
	# We simplify for real-valued quaternions, falling back on the default `hypot`
	normalize(v::AbstractVector) = v ./ hypot(v...)
	# Internal helper to normalize quaternion component vectors without extending
	# LinearAlgebra.normalize for all AbstractVector values.
	_normalize_components(v::AbstractVector{Complex{T}}) where T = v ./ _hypot(v)
	# Real-valued quaternion components can use the default hypot-based magnitude.
	_normalize_components(v::AbstractVector) = v ./ hypot(v...)