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Switch to using HalfIntegers (#6)
* swich to using HalfIntegers, add project.toml, bump version, update CI * add Random and add seed to avoid unlikely test failure
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8 changed files with 50 additions and 417 deletions
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@ -1,194 +0,0 @@
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using Test
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using WignerSymbols: HalfInteger, ishalfinteger, HalfIntegerRange
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@testset "HalfInteger" begin
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@testset "HalfInteger type" begin
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# HalfInteger constructors
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@test HalfInteger(1, 2).numerator == 1
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@test HalfInteger(1, 1).numerator == 2
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@test HalfInteger(0, 1).numerator == 0
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@test HalfInteger(0, 2).numerator == 0
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@test HalfInteger(0, 5).numerator == 0
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@test HalfInteger(10, 5).numerator == 4
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@test HalfInteger(21, 14).numerator == 3
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@test HalfInteger(-3, 2).numerator == -3
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@test HalfInteger(3, -2).numerator == -3
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@test HalfInteger(-3, -2).numerator == 3
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@test_throws ArgumentError HalfInteger(1, 0)
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@test_throws ArgumentError HalfInteger(1, 3)
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@test_throws ArgumentError HalfInteger(1, -3)
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@test_throws ArgumentError HalfInteger(-5, 3)
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@test_throws ArgumentError HalfInteger(-1000, -999)
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# convert methods
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@test convert(HalfInteger, 2) === HalfInteger(2, 1)
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@test convert(HalfInteger, 1//2) === HalfInteger(1, 2)
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@test convert(HalfInteger, 1.5) === HalfInteger(3, 2)
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@test_throws InexactError convert(HalfInteger, 1//3)
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@test_throws InexactError convert(HalfInteger, 0.6)
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@test convert(HalfInteger, 2) === HalfInteger(2, 1)
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@test convert(HalfInteger, 1//2) === HalfInteger(1, 2)
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@test convert(HalfInteger, 1.5) === HalfInteger(3, 2)
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@test convert(Integer, HalfInteger(2, 1)) === 2
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@test_throws InexactError convert(Integer, HalfInteger(1, 2))
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@test convert(Float64, HalfInteger(3, 2)) isa Float64
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@test convert(Float32, HalfInteger(3, 2)) isa Float32
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@test convert(Float64, HalfInteger(3, 2)) == 1.5
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@test convert(Real, HalfInteger(3, 2)) === HalfInteger(3, 2)
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# single-argument constructor
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@test HalfInteger(0) == HalfInteger(0, 2)
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@test HalfInteger(1) == HalfInteger(1, 1)
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@test HalfInteger(2) == HalfInteger(2, 1)
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@test HalfInteger(-30) == HalfInteger(-60, 2)
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@test HalfInteger(0//2) == HalfInteger(0, 1)
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@test HalfInteger(1//2) == HalfInteger(1, 2)
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@test HalfInteger(-5//2) == HalfInteger(-5, 2)
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end
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a = HalfInteger(2)
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b = HalfInteger(3, 2)
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@testset "HalfInteger arithmetic" begin
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@test a + b == 2 + 3//2
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@test a - b == 2 - 3//2
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@test zero(a) == 0
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@test one(a) == 1
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@test a > b
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@test b < a
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@test b <= a
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@test a >= b
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@test a == a
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@test a != b
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@test 2 * HalfInteger(0) == HalfInteger(0)
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@test 2 * HalfInteger(1, 2) == HalfInteger(1)
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@test HalfInteger(1) * 2 == HalfInteger(2)
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@test 2 * a == HalfInteger(4)
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@test (-1) * b == HalfInteger(-3//2)
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@test floor(HalfInteger(0)) === HalfInteger(0)
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@test floor(HalfInteger(-1)) === HalfInteger(-1)
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@test floor(HalfInteger(1, 2)) === HalfInteger(0)
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@test floor(HalfInteger(-1, 2)) === HalfInteger(-1)
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@test floor(Int, HalfInteger(0)) === 0
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@test floor(Int, HalfInteger(1, 2)) === 0
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@test floor(Int32, HalfInteger(-5, 2)) === Int32(-3)
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@test floor(Int32, HalfInteger(5)) === Int32(5)
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@test ceil(HalfInteger(0)) === HalfInteger(0)
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@test ceil(HalfInteger(-1)) === HalfInteger(-1)
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@test ceil(HalfInteger(1, 2)) === HalfInteger(1)
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@test ceil(HalfInteger(-1, 2)) === HalfInteger(0)
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@test ceil(Int, HalfInteger(0)) === 0
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@test ceil(Int, HalfInteger(1, 2)) === 1
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@test ceil(Int32, HalfInteger(-5, 2)) === Int32(-2)
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@test ceil(Int32, HalfInteger(5)) === Int32(5)
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for n in -98:7:98
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halfint, rat = HalfInteger(n, 2), n // 2
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@test halfint == rat
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@test halfint == HalfInteger(n / 2)
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iseven(n) && @test halfint == HalfInteger(div(n, 2))
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@test ceil(halfint) == ceil(rat)
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@test floor(halfint) == floor(rat)
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end
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end
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@testset "Parsing and printing" begin
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@test string(HalfInteger(0)) == "0"
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@test string(HalfInteger(1)) == "1"
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@test string(HalfInteger(-1)) == "-1"
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@test string(HalfInteger(1, 2)) == "1/2"
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@test string(HalfInteger(-3, 2)) == "-3/2"
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@test parse(HalfInteger, "0") == HalfInteger(0)
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@test parse(HalfInteger, "1") == HalfInteger(1)
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@test parse(HalfInteger, "210938") == HalfInteger(210938)
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@test parse(HalfInteger, "-15") == HalfInteger(-15)
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@test parse(HalfInteger, "1/2") == HalfInteger(1//2)
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@test parse(HalfInteger, "-3/2") == HalfInteger(-3//2)
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@test_throws ArgumentError parse(HalfInteger, "")
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@test_throws ArgumentError parse(HalfInteger, "-50/100")
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@test_throws ArgumentError parse(HalfInteger, "1/3")
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end
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@testset "HalfInteger hashing" begin
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@test hash(a) == hash(2)
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@test hash(b) == hash(1.5)
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end
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@testset "Other HalfInteger methods" begin
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@test isinteger(HalfInteger(0))
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@test isinteger(HalfInteger(1))
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@test !isinteger(HalfInteger(1, 2))
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@test ishalfinteger(1)
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@test ishalfinteger(1.0)
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@test ishalfinteger(-0.5)
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@test ishalfinteger(HalfInteger(0))
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@test ishalfinteger(HalfInteger(1, 2))
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@test ishalfinteger(1//1)
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@test ishalfinteger(1//2)
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@test !ishalfinteger(0.3)
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@test !ishalfinteger(-5//7)
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@test numerator(HalfInteger(0)) == 0
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@test numerator(HalfInteger(1, 2)) == 1
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@test numerator(HalfInteger(1)) == 1
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@test numerator(HalfInteger(-3, 2)) == -3
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@test denominator(HalfInteger(0)) == 1
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@test denominator(HalfInteger(1, 2)) == 2
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@test denominator(HalfInteger(1)) == 1
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@test denominator(HalfInteger(-3, 2)) == 2
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end
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@testset "HalfIntegerRange" begin
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hi(x) = HalfInteger(x)
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@test length(HalfIntegerRange(hi(0), hi(0))) == 1
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@test length(HalfIntegerRange(hi(0), hi(2))) == 3
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let hirange = HalfIntegerRange(hi(-1//2), hi(1//2))
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@test length(hirange) == 2
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@test size(hirange) == (2,)
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@test collect(hirange) == [hi(-1//2), hi(1//2)]
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end
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let hirange = HalfIntegerRange(hi(0), hi(1//2))
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@test length(hirange) == 1
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@test size(hirange) == (1,)
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@test collect(hirange) == [hi(0)]
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end
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let hirange = HalfIntegerRange(hi(1//2), hi(3))
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@test length(hirange) == 3
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@test size(hirange) == (3,)
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@test collect(hirange) == [hi(1//2), hi(3//2), hi(5//2)]
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end
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@test hi(5):hi(7) == HalfIntegerRange(hi(5), hi(7))
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@test hi(-1//2):hi(1//2) == HalfIntegerRange(hi(-1//2), hi(1//2))
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@test collect(hi(0) : hi(2)) == [hi(0), hi(1), hi(2)]
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@test collect(hi(-3//2) : hi(1//2)) == [hi(-3//2), hi(-1//2), hi(1//2)]
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let hirange = hi(-3//2):hi(0)
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@test length(hirange) == 2
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@test size(hirange) == (2,)
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@test collect(hirange) == [hi(-3//2), hi(-1//2)]
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end
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@test hi(1//2) ∈ hi(-1//2) : hi(1//2)
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@test 1 ∈ hi(0) : hi(2)
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@test 1//2 ∈ hi(-1//2) : hi(7//2)
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@test !(hi(1//2) ∈ hi(0) : hi(1))
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@test !(1//2 ∈ hi(-1) : hi(7))
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r = hi(-3//2) : hi(3//2)
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@test r[1] == hi(-3//2)
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@test r[2] == hi(-1//2)
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@test r[3] == hi(1//2)
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@test r[4] == hi(3//2)
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@test_throws BoundsError r[0]
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@test_throws BoundsError r[5]
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end
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end
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@ -1,8 +1,9 @@
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using Test
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using WignerSymbols
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using LinearAlgebra
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using Random
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include("halfinteger.jl")
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Random.seed!(1234)
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smalljlist = 0:1//2:10
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largejlist = 0:1//2:1000
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@ -99,8 +100,9 @@ end
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Y = (2*j+1)*( j*(j+1)*( -j*(j+1) + j2*(j2+1) + j3*(j3+1) - 2*l1*(l1+1)) +
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l2*(l2+1)*( j*(j+1) + j2*(j2+1) - j3*(j3+1) ) +
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l3*(l3+1)*( j*(j+1) - j2*(j2+1) + j3*(j3+1) ) )
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Z = (j+1)*sqrt((j^2-(j2-j3)^2)*((j2+j3+1)^2-j^2)*(j^2-(l2-l3)^2)*((l2+l3+1)^2 - j^2))
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tol = 10*max(abs(X),abs(Y),abs(Z))*eps(BigFloat)
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Z = (j+1) * sqrt( (j^2-(j2-j3)^2) * ((j2+j3+1)^2-j^2) *
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(j^2-(l2-l3)^2) * ((l2+l3+1)^2-j^2) )
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tol = 10 * max(abs(X), abs(Y), abs(Z)) * eps(BigFloat)
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@test (X*wigner6j(BigFloat,j+1,j2,j3,l1,l2,l3) + Z*wigner6j(BigFloat,j-1,j2,j3,l1,l2,l3))≈(-Y*wigner6j(BigFloat,j,j2,j3,l1,l2,l3)) atol=tol
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end
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end
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@ -121,15 +123,15 @@ end
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M = rand(-J:J) # only test for one instance of M in -J:J, should be independent of M anyway
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fill!(V1,0)
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fill!(V2,0)
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for (k1,m1) in enumerate(m1range)
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for (k2,m2) in enumerate(m2range)
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abs(m1+m2)<=J12 || continue
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for (k3,m3) in enumerate(m3range)
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abs(m2+m3)<=J23 || continue
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m1+m2+m3==M || continue
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V1[k1,k2,k3] = clebschgordan(j1,m1,j2,m2,J12)*clebschgordan(J12,m1+m2,j3,m3,J)
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V2[k1,k2,k3] = clebschgordan(j2,m2,j3,m3,J23)*clebschgordan(j1,m1,J23,m2+m3,J)
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end
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for (k1,m1) in enumerate(m1range), (k2,m2) in enumerate(m2range)
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abs(m1+m2)<=J12 || continue
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for (k3,m3) in enumerate(m3range)
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abs(m2+m3)<=J23 || continue
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m1+m2+m3==M || continue
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V1[k1,k2,k3] = clebschgordan(j1,m1,j2,m2,J12) *
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clebschgordan(J12,m1+m2,j3,m3,J)
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V2[k1,k2,k3] = clebschgordan(j2,m2,j3,m3,J23) *
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clebschgordan(j1,m1,J23,m2+m3,J)
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end
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end
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@test racahW(j1,j2,J,j3,J12,J23) ≈ dot(V2,V1)/sqrt((2*J12+1)*(2*J23+1)) atol=10*eps(Float64)
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