braidpath op• Data kinds: signal × scalar → table
• Call: import fullseye as fs; fs.ledger.braid_artin_images(word, n_strands) (to call the implementation directly, import braidpath; braidpath.braid_artin_images(word, n_strands); from the registry, opsdrive.get("braid_artin_images"))
• GPU: none (CPU reference implementation only)
Artin representation of a braid: images (freely reduced words) of the generators x₁..xₙ of the free group F_n.
σᵢ: xᵢ ↦ xᵢ xᵢ₊₁ xᵢ⁻¹, xᵢ₊₁ ↦ xᵢ, all others fixed. The image of a word w = σ_{i1} σ_{i2} … is built by substituting from left to right. This representation is faithful (Artin 1925), so all images agree ⇔ same braid. It is an exact test using only free reduction, a second implementation that confirms “equal” independently of Dynnikov coordinates. The image length can grow exponentially with the word length, so it stops at MAX_WORD letters (RuntimeError). ★The limit is not an argument: a cutoff that does not change the answer becomes a “knob with no effect” (2026-10-23). Empty input (word with 0 elements) returns the images of the identity map (reason: the empty word is the identity, and each image is xₖ itself).
Returns: dict images (list of length n; each element is a list of signed integers, where ±k = x_k^(±1)), lengths, identity (whether every image is xₖ itself).
• 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.
• (none yet)
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 · dynnikov_coordinates · 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.