pub const EUCLIDEAN3: &str = "# 3D Euclidean Geometric Algebra\n# Customized from auto-discovered entities\n\n[algebra]\ncomplete = false\nname = \"euclidean3\"\nmodule_path = \"euclidean::dim3\"\ndescription = \"3D Euclidean Geometric Algebra Cl(3,0,0)\"\n\n[signature]\npositive = [\"e1\", \"e2\", \"e3\"]\nnegative = []\nzero = []\n\n[norm]\n# Euclidean algebras use reverse for norm: x * reverse(x) = |x|^2\nprimary_involution = \"reverse\"\n\n# ============================================================\n# Types\n# ============================================================\n\n[types.Scalar]\ngrades = [0]\ndescription = \"Scalar (grade-0 element)\"\nfield_map = [\n { name = \"s\", blade = \"s\" }\n]\n\n[types.Vector]\ngrades = [1]\ndescription = \"3D vector\"\nfield_map = [\n { name = \"x\", blade = \"e1\" },\n { name = \"y\", blade = \"e2\" },\n { name = \"z\", blade = \"e3\" }\n]\n\n[types.Bivector]\ngrades = [2]\ndescription = \"3D bivector\"\n# Field names reflect what each component DOES (controls rotation around an axis):\n# - rz (e12): rotation around the z-axis (in the xy-plane)\n# - ry (e13): rotation around the y-axis (in the xz-plane)\n# - rx (e23): rotation around the x-axis (in the yz-plane)\nfield_map = [\n { name = \"rz\", blade = \"e12\" },\n { name = \"ry\", blade = \"e13\" },\n { name = \"rx\", blade = \"e23\" }\n]\n\n[types.Rotor]\ngrades = [0, 2]\ndescription = \"3D rotor (unit versor for rotations)\"\n# Rotors represent 3D rotations via the sandwich product: R * v * R^-1\n# - s: scalar part (cos(theta/2) for a rotation by angle theta)\n# - rz, ry, rx: rotation components (see Bivector docs)\nfield_map = [\n { name = \"s\", blade = \"s\" },\n { name = \"rz\", blade = \"e12\" },\n { name = \"ry\", blade = \"e13\" },\n { name = \"rx\", blade = \"e23\" }\n]\n\n[types.Trivector]\ngrades = [3]\ndescription = \"3D trivector (pseudoscalar)\"\nfield_map = [\n { name = \"ps\", blade = \"e123\" }\n]\n\n# Note: Entity_0_3 (scalar + pseudoscalar) is valid but rarely used\n# Note: Entity_1_3 (vector + trivector) is the odd subalgebra\n";Expand description
3D Euclidean algebra specification (TOML).