W.02 Lineations, Central Rotations & Reflections in Lines — Code

For any non-null line l = <a : b : c> over a field F (char F != 2), the reflection sigma_l maps every point A = [x, y] and every line m = <a_2 : b_2 : c_2> to exact rational images whose denominators depend only on the quadratic norm a^2 + b^2, without radicals or angles.

Exact geometor.model SVG output of model.py for W.02 (Lineations, Central Rotations & Reflections in Lines).

Symbolic Construction & Verification Script (model.py)

"""GEOMETOR Wildberger symbolic model and proof script for W.02: Lineations, Central Rotations & Reflections in Lines.

        Enunciation: For any non-null line l = <a : b : c> over a field F (char F != 2), the reflection sigma_l maps every point A = [x, y] and every line m = <a_2 : b_2 : c_2> to exact rational images whose denominators depend only on the quadratic norm a^2 + b^2, without radicals or angles.
        """

        from __future__ import annotations

        import sys
        from pathlib import Path

        _ROOT_SRC = Path(__file__).resolve().parents[3] / "src"
        if str(_ROOT_SRC) not in sys.path:
            sys.path.insert(0, str(_ROOT_SRC))

        from geometor.wildberger.models import (  # noqa: E402
            TopicBuildResult,
            assert_zero_floats,
            build_principle_model,
        )
        from geometor.wildberger.render import render_svg  # noqa: E402


        def construct_w_02() -> TopicBuildResult:
            """Construct the exact symbolic model and verifications for W.02.

            Returns:
                Populated `TopicBuildResult` for W.02 (Lineations, Central Rotations & Reflections in Lines).
            """
            result = build_principle_model("W.02")
            assert_zero_floats(result.model)
            return result


        def main() -> None:
            """Execute W.02 symbolic construction, render `w-02.svg`, and print invariants."""
            here = Path(__file__).resolve().parent
            bundle = construct_w_02()
            svg_out = render_svg(
                bundle.model,
                here / "w-02.svg",
                extra_curves=bundle.extra_curves,
                annotations=bundle.annotations,
            )
            print("W.02: Lineations, Central Rotations & Reflections in Lines")
            print(f"  Elements in model: {len(bundle.model)}")
            print(f"  Rendered SVG:      {svg_out.name}")
            for label, val, status in bundle.verifications:
                print(f"  [OK] {label}: {val} ({status})")


        if __name__ == "__main__":
            main()