residue_integer_crt — RESIDUE theorem op

• Data kinds: signal × signal → table

• Call: import fullseye as fs; fs.ledger.residue_integer_crt(residues, moduli) -> 'dict' (to call the implementation directly, import residue; residue.residue_integer_crt(residues, moduli) -> 'dict'; from the registry, opsresidue.get("residue_integer_crt"))

Usage

Exact integer CRT (Garner's mixed-radix algorithm) -> dict.

residues and moduli are equal-length integer sequences; the moduli must be pairwise coprime and >= 2. Returns {"value": int, "modulus": int, "mixed_radix": [digits]} where value is the unique solution in [0, prod(moduli)). Arithmetic is Python's arbitrary-precision int — there is no rounding anywhere, which is why this op is the oracle for residue_crt.

The mixed-radix digits d_k satisfy value = d_0 + d_1 m_0 + d_2 m_0 m_1 + ...:

the *positional* (coarse-to-fine) reading of the same residues, i.e. the bridge between the residue view and the place-value view.

References (sample data, literature)

• 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.

Runnable examples (verified samples that actually call this op)

• poc_residue_crt — py -3.11 examples/poc_residue_crt.py

Ops the type connects to (they accept table as input)

—

Same category (theorem)

—

*Provenance: residue.py — RESIDUE 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.