dynsys op• Data kinds: table → pairs
• Call: import fullseye as fs; fs.ledger.dynsys_poincare_section(states, axis=2, value=None, direction=1) (to call the implementation directly, import mathops; mathops.dynsys_poincare_section(states, axis=2, value=None, direction=1); from the registry, opsmath.get("dynsys_poincare_section"))
Where a trajectory crosses a plane — with the crossing point interpolated.
Takes the `x block of :func:ode_flow_states` and returns the points where
coordinate *axis* crosses *value* in the given *direction* (+1 upward, -1
downward, 0 either). The crossing is found by **linear interpolation between
the two straddling samples**, not by taking the nearer sample — otherwise the
section is quantised by the step size and a periodic orbit looks like a cloud.
★Why this earns its place: a periodic orbit must give one point (to
within the interpolation error), a period-2 orbit two, and a chaotic one a
fractal set. That is a check with a number in it, unlike "the picture looks
like a strange attractor".
Returns a `pairs` array of the remaining coordinates at each crossing.
Raises `ValueError`: states not (S, n) with S >= 2; axis out of range;
direction not in (-1, 0, 1); non-finite input; no crossing found (reported,
not returned as an empty array that a caller may read as "no orbit").
Every mathops op validates its input before computing (nothing slips through silently):
• **complex input raises ValueError** — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• **masked arrays with masked elements raise ValueError** — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• **NaN/Inf raises ValueError on every input** (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• 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_what_a_picture_cannot_check — py -3.11 examples/poc_what_a_picture_cannot_check.py
pairs as input)neighbour_index_gaps · curve_locality
dynsys)ode_flow_states · ode_vector_field_grid · dynsys_lyapunov_spectrum · dynsys_bifurcation_map · dynsys_correlation_dimension
*Provenance: mathops.py — MATH 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.