braidpath op• Data kinds: signal × scalar → table
• Call: import fullseye as fs; fs.ledger.dynnikov_coordinates(word, n_strands) (to call the implementation directly, import braidpath; braidpath.dynnikov_coordinates(word, n_strands); from the registry, opsdrive.get("dynnikov_coordinates"))
• GPU: none (CPU reference implementation only)
Dynnikov coordinates of the braid acting on the standard curve diagram E = (0, …, 0; −1, …, −1) (integers, no overflow).
Taken on the disk with n + 1 punctures: the n strands plus one extra puncture at the right end (a and b both have length n − 1). This action is faithful, so coordinates equal ⇔ same braid. Each letter needs only a constant number of additions/subtractions and max / min, so the time is proportional to the word length (unlike handle reduction or free-group images, nothing swells —— the numbers only get larger, and Python integers do not overflow).
Returns: dict a, b (lists of int), key (tuple a + b, used as the class key), n_strands, n_punctures, max_abs (largest absolute value of the coordinates), bits.
Empty input (word with 0 elements) returns the coordinates of the standard curve diagram (reason: the empty word is the identity and does not move the curve diagram).
• 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_act · braid_equivalent · 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.