braidpath op• Data kinds: signal × signal × scalar → table
• Call: import fullseye as fs; fs.ledger.braid_equivalent(word_a, word_b, n_strands, method='dynnikov') (to call the implementation directly, import braidpath; braidpath.braid_equivalent(word_a, word_b, n_strands, method='dynnikov'); from the registry, opsdrive.get("braid_equivalent"))
• GPU: none (CPU reference implementation only)
Whether two braid words represent the same braid (are related by the relations alone).
method: "dynnikov" (compare coordinates, fast) / "handle" (handle-reduce a b⁻¹ and check whether it is empty) / "artin" (compare the free-group images) / "all" (compute all three; RuntimeError if they disagree —— an implementation check).
Returns: dict equal, method, key_a / key_b (Dynnikov keys), reduced_quotient (reduction of a b⁻¹, for handle / all).
Empty input (word_a with 0 elements) returns the answer of the comparison with the trivial braid (reason: the empty word is the identity, a valid braid).
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• poc_braid_homotopy_classes — py -3.11 examples/poc_braid_homotopy_classes.py
table as input)course_layout · course_occupancy · course_contains · world_build · world_camera · world_move · lidar_scan · rss_longitudinal_same
braidpath)braid_from_trajectories · braid_reduce · braid_artin_images · dynnikov_coordinates · dynnikov_act · homotopy_class_compare · pairwise_winding · homotopy_shortest_paths
*Provenance: braidpath.py — DRIVE operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.