racah-py

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Python bindings (PyO3 + maturin) for the racah crate's SU(N) surface: irreps from Dynkin labels, fusion with outer multiplicities, dense m-basis Clebsch–Gordan tensors, F/R symbols with their multiplicity axes, the verification gates, and the gauge fingerprint. racah is the coefficient authority behind TeNeT-py's SU(N) symmetry provider; this package is how that consumer (and any other Python code) reaches it.

Import name is racah; the distribution is racah-py. Wheels are always built with the crate's cgc-gen feature on, so the generated coefficients are available out of the box. CGC/F/R arrays come back as NumPy float64 arrays.

Installation

From PyPI (Python ≥ 3.12; prebuilt abi3 wheels for linux-x86_64 and macos-arm64):

pip install racah-py

Or from a checkout (needs a Rust stable toolchain):

git clone https://github.com/Ryo-wtnb11/racah
cd racah/racah-py
python -m venv .venv && . .venv/bin/activate
pip install maturin
maturin develop --release          # builds the extension into the active venv

or build a wheel and install it anywhere:

maturin build --release --manifest-path racah-py/Cargo.toml --out dist
pip install --no-index --find-links dist racah-py

CI (wheels.yml) builds abi3-py312 wheels for linux-x86_64 and macos-arm64; py-v* tags/releases publish them to PyPI. One wheel per platform covers CPython ≥ 3.12.

Quick start

Verified against the built extension; every call below is the actual API (see racah.pyi for the full typed surface).

import racah

three = racah.Irrep([1, 0])            # SU(3) fundamental, from its Dynkin label
assert three.dim() == 3                # exact integer, arbitrary precision
eight = racah.Irrep([1, 1])            # the adjoint

# Fusion: 3 x 3bar = 1 + 8, and the adjoint appears twice in 8 x 8.
assert racah.fusion(three, three.dual()) == [
    (racah.Irrep([0, 0]), 1),
    (eight, 1),
]
assert racah.fusion_multiplicity(eight, eight, eight) == 2  # N^8_88

# m-basis Clebsch-Gordan tensor: [dim(s1), dim(s2), dim(s3), N^{s3}_{s1 s2}].
cgc = racah.clebsch_gordan(three, three.dual(), eight)
assert cgc.shape == (3, 3, 8, 1)

# F-symbol block over the four multiplicity indices [mu, nu, kappa, lambda].
f = racah.f_symbol(eight, eight, eight, eight, eight, eight)
assert f.shape == (2, 2, 2, 2)

# R-symbol multiplicity matrix, N^c_ab x N^c_ba.
r = racah.r_symbol(three, three.dual(), eight)
assert r.shape == (1, 1)

# The verification gates raise RuntimeError on violation.
racah.check_pentagon(three, three.dual(), three, three.dual())

# The gauge fingerprint a consumer pins next to persisted coefficients.
print(racah.sun_authority_fingerprint())

The rest of the surface: Irrep.from_weight / Irrep.trivial constructors, the dynkin / weight / rank properties, check_f_unitarity and check_hexagon alongside check_pentagon, and su2_frobenius_schur(two_j).

Ill-posed input (bad label, mixed rank, empty fusion vertex) raises ValueError; a tripped numerical gate (orthonormality, F-unitarity, pentagon, hexagon, factorization failure) raises RuntimeError.

Versioning and the gauge fingerprint

F/R/CGC values depend on the CGC gauge; racah publishes them in one frozen canonical gauge. racah.sun_authority_fingerprint() returns the opaque authority string identifying that convention, generation pipeline, and tolerance policy — TeNeT-py pins it next to persisted coefficients and refuses a mismatch on load. Compare it by equality only; a breaking coefficient change bumps the fingerprint epoch and is recorded in the CHANGELOG. Same fingerprint means same convention and value agreement within the oracle tolerance, not cross-process bit-identity (docs.rs: sun_authority_fingerprint).

Documentation

The semantics are the crate's; the bindings add nothing:

User Guide — task-oriented chapters; shapes and axis conventions match the arrays returned here.
docs/theory.pdf — the mathematics behind the objects.
docs/gauge.md — the frozen SU(N) gauge specification the fingerprint names.
docs.rs/racah — exact per-item semantics and errors.
docs/README.md — the full documentation index.

Development

uv venv && uv pip install maturin pytest numpy
cd racah-py && maturin develop --release
pytest tests

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0.1.2

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racah-py 0.1.1

racah-py

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