Add comprehensive test suite and fix noteboo

.github/copilot-instructions.md

@@ -0,0 +1,197 @@
+# Copilot Instructions for Linear_Algebra
+
+## Project Architecture
+
+This is a **Julia linear algebra computing project** using DrWatson for reproducibility, focused on geometric transformations and linear algebra operations with visualization capabilities. The codebase follows a **modular mathematical library pattern** with comprehensive testing and documentation.
+
+### Core Components
+
+- **`src/Linear_Algebra.jl`**: Main module with exports for basic operations and transformation matrices
+- **`src/linear_algebra_basic.jl`**: Core linear algebra functions (distances, projections, line operations, intersections)
+- **`src/linear_algebra_transform.jl`**: Matrix transformations (projection, rotation, stretch, reflection matrices)
+- **`test/`**: Comprehensive test suite with CI-compatible plotting tests (49 total tests)
+- **`docs/`**: Documenter.jl setup with cross-repository deployment to math_tech_study
+
+## Critical Development Patterns
+
+### Module Structure
+```julia
+# Main module uses @reexport for clean interface
+@reexport using GeometryBasics, Plots, LinearAlgebra, RationalRoots, Symbolics
+# Comprehensive exports for all functions
+export distance_2_points, center_of_gravity, barycentric_coord, plot_param_line
+# ... matrix functions, line functions, etc.
+```
+
+### Test Setup (Uses @quickactivate)
+```julia
+# Tests use DrWatson @quickactivate pattern
+using DrWatson, Test
+@quickactivate "Linear_Algebra"
+using Linear_Algebra
+using GeometryBasics, LinearAlgebra
+```
+
+### CI-Compatible Plotting Pattern
+```julia
+# Environment detection for plotting tests
+if get(ENV, "CI", "false") == "true" || get(ENV, "GITHUB_ACTIONS", "false") == "true"
+    # In CI, just test that the function exists
+    @test hasmethod(plot_param_line, (typeof(p), typeof(q), Int64))
+else
+    # Local testing - allow plotting but capture any display issues
+    try
+        points = plot_param_line(p, q, 3)
+        # ... test plotting results
+    catch e
+        # Graceful fallback for plotting failures
+        @test hasmethod(plot_param_line, (typeof(p), typeof(q), Int64))
+    end
+end
+```
+
+## Julia Coding Standards
+
+### Linear Algebra Functions
+1. Use GeometryBasics.Point2f for 2D points consistently
+2. Use regular Arrays ([Float64]) for vectors in calculations
+3. Handle both symbolic and numeric matrix operations
+4. Degrees vs radians: `rotation_matrix(d)` takes degrees, `rotation_matrix_ns(θ)` takes radians
+5. Matrix functions return 2x2 matrices for 2D transformations
+6. Always export new functions in main module
+7. Use clear parameter naming (θ for angles, v/w for vectors, p/q for points)
+
+### Function Categories
+8. **Basic Operations**: Distance, center of gravity, barycentric coordinates
+9. **Vector Operations**: Angle calculations, orthogonality, projections, reflections
+10. **Line Geometry**: Parametric/implicit conversions, distance calculations, intersections
+11. **Matrix Transformations**: Projection, rotation, stretch, reflection matrices
+12. **Symbolic Functions**: Provide both symbolic and numeric versions
+
+### Documentation & Comments
+13. Include detailed comments explaining geometric concepts
+14. Use clear variable names (e.g., `p1`, `p2` for points, `v`, `w` for vectors)
+15. Document angle conventions (degrees vs radians) in function comments
+16. Explain mathematical formulas in comments
+17. Maintain consistency with mathematical notation
+
+### Testing Patterns
+18. **Comprehensive Coverage**: 49 tests covering ~100% of functions
+19. **CI-Safe**: Plotting tests skip in headless environments
+20. **Edge Cases**: Test mathematical edge cases (orthogonal vectors, zero angles, etc.)
+21. **Type Testing**: Verify return types (Point2f, AbstractVector, matrices)
+22. **Numerical Precision**: Use `atol=1e-10` for floating-point comparisons
+23. **Error Handling**: Use try-catch for functions that might fail in CI
+
+### Code Organization
+24. **Two-File Structure**: Basic operations in `linear_algebra_basic.jl`, matrices in `linear_algebra_transform.jl`
+25. **Consistent Naming**: Functions end with descriptive suffixes (`_matrix`, `_line`, `_coord`)
+26. **Symbolic Variants**: Provide `_symbolic` versions for algebraic manipulation
+27. **Export Everything**: All public functions exported from main module
+
+## Dependencies & Performance
+
+**Main Dependencies**: GeometryBasics, Plots, LinearAlgebra, RationalRoots, Symbolics
+**Test Dependencies**: DrWatson, Test, GeometryBasics, LinearAlgebra
+
+### Mathematical Libraries Used
+- **GeometryBasics.jl**: For Point2f types and geometric primitives
+- **LinearAlgebra.jl**: For `norm()`, `dot()`, matrix operations
+- **Symbolics.jl**: For `@variables` in symbolic matrix functions
+  - Pattern: `@variables θ`, `@variables λ₁` for symbolic parameters
+  - Use `Symbolics.value.(substitute.(expr, var => value))` for evaluation
+- **Plots.jl**: For visualization functions (`scatter!`, `plot!`, `display`)
+- **RationalRoots.jl**: For rational approximations
+
+## Key Workflows
+
+### Running Tests Locally
+```bash
+julia --project=. test/runtests.jl
+```
+
+### Running Tests in CI Mode
+```bash
+CI=true julia --project=. test/runtests.jl
+```
+
+### Building Documentation
+```bash
+julia --project=. docs/make.jl
+```
+
+### CI Considerations
+- Tests automatically detect CI environment via ENV variables
+- Plotting tests skip gracefully in headless mode
+- 49 tests in local mode, 47 tests in CI mode (plotting tests reduced)
+- Test execution time: ~15-16 seconds
+
+## Git Best Practices
+
+- **Never use `git add .`** - Always stage files explicitly by name to avoid accidentally committing development files, notebooks, or temporary files
+- Use `git add <specific-file-path>` to stage only the intended files for commit
+- Feature branch naming: Use descriptive names like `add-tests-fix-notebook`
+
+### Pull Request Creation
+- **ALWAYS push changes first**: Use `git push origin BRANCH_NAME` before creating PR
+- **Do NOT use `gh pr create`** - The GitHub CLI command doesn't work properly in this environment
+- **Use GitHub web interface instead**: Create PR links manually with detailed descriptions
+- **PR Link Format**: `https://github.com/FourMInfo/Linear_Algebra/compare/main...BRANCH_NAME`
+- **Include comprehensive descriptions**: Detail all changes, test coverage, and architectural improvements
+- **Reference issue numbers**: Link to related issues when applicable
+
+## Azure Integration
+
+- Use Azure Best Practices: When generating code for Azure, running terminal commands for Azure, or performing operations related to Azure, invoke your `azure_development-get_best_practices` tool if available
+
+## Project-Specific Conventions
+
+### Mathematical Operations
+- **Point Types**: Use `Point2f(x, y)` for 2D points consistently
+- **Vector Types**: Use `[Float64]` arrays for vector calculations
+- **Angle Conventions**: Document whether functions expect degrees or radians
+- **Matrix Size**: All 2D transformation matrices are 2x2
+- **Coordinate Systems**: Standard mathematical coordinate system (not screen coordinates)
+
+### Function Naming Patterns
+- **Distance Functions**: `distance_*` (e.g., `distance_2_points`, `distance_to_implicit_line`)
+- **Matrix Functions**: `*_matrix` (e.g., `rotation_matrix`, `projection_matrix`)
+- **Line Functions**: `*_line` (e.g., `explicit_line`, `parametric_to_implicit_line`)
+- **Coordinate Functions**: `*_coord` (e.g., `barycentric_coord`)
+
+### Test Organization
+- **Grouped by Category**: Basic functions, transformation matrices, line geometry, advanced functions
+- **CI Compatibility**: Plotting tests with environment detection
+- **Comprehensive Coverage**: Test both happy path and edge cases
+- **Type Validation**: Verify return types match expectations
+
+### Documentation Structure
+- **Cross-Repository Deployment**: Deploys to math_tech_study repository
+- **Subdirectory Pattern**: Available at study.fourm.info/linear_algebra/
+- **Auto-docs Integration**: Uses `@autodocs` for automatic function documentation
+- **Mathematical Notation**: Supports LaTeX rendering in documentation
+
+## Function Signature Patterns
+
+### Basic Linear Algebra
+```julia
+distance_2_points(p::Point, q::Point) -> Float64
+center_of_gravity(p::Point, q::Point, t) -> Point
+vector_angle_cos(p::Vector, q::Vector) -> Float64
+orthproj(v::Vector, w::Vector) -> Vector
+```
+
+### Matrix Transformations
+```julia
+rotation_matrix(d::Number) -> Matrix      # Takes degrees
+rotation_matrix_ns(θ::Number) -> Matrix   # Takes radians
+projection_matrix(x::Vector) -> Matrix
+reflection_matrix(U::Vector) -> Matrix
+```
+
+### Line Operations
+```julia
+parametric_to_implicit_line(p::Point, v::Vector) -> (Float64, Float64, Float64)
+distance_to_implicit_line(a::Number, b::Number, c::Number, r::Point) -> Float64
+foot_of_line(P::Point, v::Vector, R::Point) -> Tuple(Point, Float64)
+```

notebooks/Linear_Algebra.ipynb

@@ -430,7 +430,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -440,7 +440,7 @@
     "using DrWatson\n",
     "\n",
     "# Activate the project\n",
-    "quickactivate(@__DIR__, \"Math_Foundations\")\n",
+    "quickactivate(@__DIR__, \"Linear_Algebra\")\n",
     "\n",
     "# Load the package \n",
     "using Linear_Algebra"
@@ -923,6 +923,13 @@
     "println(\"P ==P*P: \",P ≈ P*P)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -932,7 +939,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -942,7 +949,7 @@
     "using DrWatson\n",
     "\n",
     "# Activate the project\n",
-    "quickactivate(@__DIR__, \"Math_Foundations\")\n",
+    "quickactivate(@__DIR__, \"Linear_Algebra\")\n",
     "\n",
     "# Load the package \n",
     "using Linear_Algebra"