interp_poly op• Data kinds: signal → roots
• Call: import mathops; mathops.poly_roots(coeffs, real_only=False, imag_tol=1e-09) (or opsmath.get("poly_roots"))
All roots of a polynomial (coefficients highest-power-first) — complex included.
Roots are the eigenvalues of the companion matrix (`np.roots`); the
polynomial must have degree ≥ 1 and a non-zero leading coefficient
(fail-closed: a zero leading coefficient means the stated degree is a lie —
trim it explicitly rather than have it silently dropped).
Returns complex128, sorted by real part then imaginary part
(deterministic). Complex answers are honest answers: `x² + 1` really does
have roots `±i`, and hiding them would misreport the polynomial. Pass
`real_only=True` to keep only roots whose imaginary part is negligible
(`|imag| <= imag_tol * max(1, |root|)`) and get them back as a sorted
float64 array — possibly empty, which is the correct answer for
`x² + 1`.
Numerical note: root-finding conditioning degrades with degree and with
clustered roots (a double root moves ~`sqrt(eps)` under coefficient
noise — Wilkinson's classic analysis); treat high-degree roots as
approximate. HALCON: no root-finding tuple operator.
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.
• math_metrology — py -3.11 examples/math_metrology.py
roots as input)—
interp_poly)interp_linear · interp_cubic · poly_fit · poly_eval
*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.