From 0e056691cb7ac99c394f1f8ce240fb28ecc2bea7 Mon Sep 17 00:00:00 2001
From: "Thomas (Tom) C. Gorordo" <tcgorordo@gmail.com>
Date: Thu, 15 Aug 2024 09:34:47 -0700
Subject: [PATCH] remove added Combinatorics dep by hardcoding 9j arg
 permutations

---
 Project.toml         |  1 -
 src/WignerSymbols.jl | 22 ++++++++++++++++------
 2 files changed, 16 insertions(+), 7 deletions(-)

diff --git a/Project.toml b/Project.toml
index 02e6f6f..dedcec9 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,7 +4,6 @@ authors = ["Jutho Haegeman"]
 version = "2.1.0"
 
 [deps]
-Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
 HalfIntegers = "f0d1745a-41c9-11e9-1dd9-e5d34d218721"
 LRUCache = "8ac3fa9e-de4c-5943-b1dc-09c6b5f20637"
 Primes = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
diff --git a/src/WignerSymbols.jl b/src/WignerSymbols.jl
index 449e8fc..bec5de8 100644
--- a/src/WignerSymbols.jl
+++ b/src/WignerSymbols.jl
@@ -6,7 +6,6 @@ using RationalRoots
 using LRUCache
 const RRBig = RationalRoot{BigInt}
 import RationalRoots: _convert
-using Combinatorics: permutations
 
 include("growinglist.jl")
 include("bigint.jl") # additional GMP BigInt functionality not wrapped in Base.GMP.MPZ
@@ -270,8 +269,19 @@ function wigner9j(T::Type{<:Real}, j₁, j₂, j₃, j₄, j₅, j₆, j₇, j
     return _wigner9j(T, HalfInteger.((j₁, j₂, j₃, j₄, j₅, j₆, j₇, j₈, j₉))...)
 end
 
-const _perms9j = [(i, j) for i in permutations([1, 2, 3]), 
-                       j in permutations([1, 2, 3])]
+const _perms9j = [([1, 2, 3], [1, 2, 3]) ([1, 2, 3], [1, 3, 2]) ([1, 2, 3], [2, 1, 3]) ([1, 2, 3], [2, 3, 1]) ([1, 2, 3], [3, 1, 2]) ([1, 2, 3], [3, 2, 1]);
+                  ([1, 3, 2], [1, 2, 3]) ([1, 3, 2], [1, 3, 2]) ([1, 3, 2], [2, 1, 3]) ([1, 3, 2], [2, 3, 1]) ([1, 3, 2], [3, 1, 2]) ([1, 3, 2], [3, 2, 1]);
+                  ([2, 1, 3], [1, 2, 3]) ([2, 1, 3], [1, 3, 2]) ([2, 1, 3], [2, 1, 3]) ([2, 1, 3], [2, 3, 1]) ([2, 1, 3], [3, 1, 2]) ([2, 1, 3], [3, 2, 1]);
+                  ([2, 3, 1], [1, 2, 3]) ([2, 3, 1], [1, 3, 2]) ([2, 3, 1], [2, 1, 3]) ([2, 3, 1], [2, 3, 1]) ([2, 3, 1], [3, 1, 2]) ([2, 3, 1], [3, 2, 1]);
+                  ([3, 1, 2], [1, 2, 3]) ([3, 1, 2], [1, 3, 2]) ([3, 1, 2], [2, 1, 3]) ([3, 1, 2], [2, 3, 1]) ([3, 1, 2], [3, 1, 2]) ([3, 1, 2], [3, 2, 1]);
+                  ([3, 2, 1], [1, 2, 3]) ([3, 2, 1], [1, 3, 2]) ([3, 2, 1], [2, 1, 3]) ([3, 2, 1], [2, 3, 1]) ([3, 2, 1], [3, 1, 2]) ([3, 2, 1], [3, 2, 1])]
+
+const _signs9j = [1 -1 -1 1 1 -1;
+                  -1 1 1 -1 -1 1;
+                  -1 1 1 -1 -1 1;
+                  1 -1 -1 1 1 -1;
+                  1 -1 -1 1 1 -1;
+                  -1 1 1 -1 -1 1]
 
 function _wigner9j(T::Type{<:Real}, j₁::HalfInteger, j₂::HalfInteger, j₃::HalfInteger, 
                                     j₄::HalfInteger, j₅::HalfInteger, j₆::HalfInteger,
@@ -284,15 +294,15 @@ function _wigner9j(T::Type{<:Real}, j₁::HalfInteger, j₂::HalfInteger, j₃::
    
     # dictionary lookup, check all 72 permutations 
     k = [j₁ j₂ j₃; j₄ j₅ j₆; j₇ j₈ j₉]
-    for p in _perms9j
+    for (p, m) in zip(_perms9j, _signs9j)
         kk = Tuple(reshape(k[p...], 9))
         kkT = Tuple(reshape(transpose(k[p...]), 9))
         if haskey(Wigner9j, kk)
             r, s = Wigner9j[kk]
-            return _convert(T, s) * convert(T, signedroot(r))
+            return m * _convert(T, s) * convert(T, signedroot(r))
         elseif haskey(Wigner9j, kkT)
             r, s = Wigner9j[kkT]
-            return _convert(T, s) * convert(T, signedroot(r)) 
+            return m * _convert(T, s) * convert(T, signedroot(r)) 
         end
     end