diff --git a/README.md b/README.md index 06ad68f..7e1a1a5 100644 --- a/README.md +++ b/README.md @@ -5,10 +5,8 @@ [![Coverage Status](https://coveralls.io/repos/Jutho/WignerSymbols.jl/badge.svg?branch=master&service=github)](https://coveralls.io/github/Jutho/WignerSymbols.jl?branch=master) [![codecov.io](http://codecov.io/github/Jutho/WignerSymbols.jl/coverage.svg?branch=master)](http://codecov.io/github/Jutho/WignerSymbols.jl?branch=master) -Compute Wigner's 3j and 6j symbols, and related quantities such as Clebsch-Gordan coefficients and Racah's symbols. - -## Requirements -Latest version is compatible with Julia v0.7 only, but older versions can be installed on Julia v0.6. +Compute Wigner's 3j and 6j symbols, and related quantities such as Clebsch-Gordan +coefficients and Racah's symbols. ## Installation Install with the new package manager via `]add WignerSymbols` or @@ -18,7 +16,8 @@ Pkg.add("WignerSymbols") ``` ## Available functions -While the following function signatures are probably self-explanatory, you can query help for them in the Julia REPL to get further details. +While the following function signatures are probably self-explanatory, you can query help +for them in the Julia REPL to get further details. * `wigner3j(T::Type{<:AbstractFloat} = Float64, j₁, j₂, j₃, m₁, m₂, m₃ = -m₂-m₁) -> ::T` * `wigner6j(T::Type{<:AbstractFloat} = Float64, j₁, j₂, j₃, j₄, j₅, j₆) -> ::T` * `clebschgordan(T::Type{<:AbstractFloat} = Float64, j₁, m₁, j₂, m₂, j₃, m₃ = m₁+m₂) -> ::T` @@ -27,20 +26,31 @@ While the following function signatures are probably self-explanatory, you can q * `δ(j₁, j₂, j₃) -> ::Bool` * `Δ(T::Type{<:AbstractFloat} = Float64, j₁, j₂, j₃) -> ::T` -The package also defines the `HalfInteger` type that can be used to represent half-integer values. Construct if as `HalfInteger(a::Real)` or `HalfInteger(numerator::Integer, denominator::Integer)`. Furthermore, the range operator `a:b` can be used to create ranges of `HalfInteger` values (a `HalfIntegerRange`). +~~The package also defines the `HalfInteger` type that can be used to represent half- +integer values. Construct if as `HalfInteger(a::Real)` or `HalfInteger(numerator::Integer, +denominator::Integer)`. Furthermore, the range operator `a:b` can be used to create ranges +of `HalfInteger` values (a `HalfIntegerRange`).~~ + +The package now relies on [HalfIntegers.jl](https://github.com/sostock/HalfIntegers.jl) to +support and use arithmetic with half integer numbers. ## Implementation Largely based on reading the paper (but not the code): [1] [H. T. Johansson and C. Forssén, SIAM Journal on Scientific Compututing 38 (2016) 376-384](https://doi.org/10.1137/15M1021908) ([arXiv:1504.08329](https://arxiv.org/abs/1504.08329)) -with some additional modifications to further improve efficiency for large `j` (angular momenta quantum numbers). +with some additional modifications to further improve efficiency for large `j` (angular +momenta quantum numbers). -In particular, 3j and 6j symbols are computed exactly, in the format `√(r) * s` where `r` and `s` are exactly computed as `Rational{BigInt}`, -using an intermediate representation based on prime number factorization. As a consequence thereof, all of the above functions can be called -requesting `BigFloat` precision for the result. There is currently no convenient syntax for obtaining `r` and `s` directly (see TODO). +In particular, 3j and 6j symbols are computed exactly, in the format `√(r) * s` where `r` +and `s` are exactly computed as `Rational{BigInt}`, using an intermediate representation +based on prime number factorization. As a consequence thereof, all of the above functions +can be called requesting `BigFloat` precision for the result. There is currently no +convenient syntax for obtaining `r` and `s` directly (see TODO). -Most intermediate calculations (prime factorizations of numbers and their factorials, conversion between prime powers and `BigInt`s) are cached to improve the efficiency, but this can result in large use of memory when querying Wigner symbols for large values of `j`. +Most intermediate calculations (prime factorizations of numbers and their factorials, +conversion between prime powers and `BigInt`s) are cached to improve the efficiency, but +this can result in large use of memory when querying Wigner symbols for large values of `j`. Also uses ideas from @@ -53,5 +63,5 @@ for caching the computed 3j and 6j symbols. [3] [L. Wei, New formula for 9-j symbols and their direct calculation, Computers in Physics, 12 (1998), 632–634.](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.481.5946&rep=rep1&type=pdf) -* Convenient syntax to get the exact results in the `√(r) * s` format, but in such a way that it can be used by - the Julia type system and can be converted afterwards. +* Convenient syntax to get the exact results in the `√(r) * s` format, but in such a way + that it can be used by the Julia type system and can be converted afterwards.