The wigner-symbols package

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Clebsch-Gordan coefficients and Wigner 3-j, 6-j, and 9-j symbols.

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Versions 1.0.0
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Dependencies base (==4.*) [details]
License MIT
Copyright (c) 2015 Phil Ruffwind
Author Phil Ruffwind
Category Math
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Source repo head: git clone
Uploaded Fri Oct 2 07:21:08 UTC 2015 by Rufflewind
Distributions NixOS:1.0.0
Downloads 272 total (10 in the last 30 days)
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Status Docs available [build log]
Last success reported on 2015-10-04 [all 1 reports]
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Readme for wigner-symbols-1.0.0

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wigner-symbols Build status

Quick links: changelog, documentation.

This library calculates:

  • Clebsch-Gordan coefficients
  • Wigner 3-j symbols
  • Wigner 6-j symbols
  • Wigner 9-j symbols

These sets of numbers are commonly used in physics to couple, uncouple, and recouple eigenstates of angular momentum and similar operators. Mathematically, they describe the relationship between the bases of irreducible representations of SU(2) or SO(3) and those of their tensor products.

The library uses the Condon-Shortley phase convention as typical in physics.

Each function has a …Sq variant that returns the exact value as a SignedSqrtRational, which represents a mathematical expression of the form:

s √(n / d)


  • s is a sign (either +, -, or 0),
  • n is a nonnegative numerator, and
  • d is a positive denominator.


The package is available on Hackage:

cabal install wigner-symbols