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Ingy döt Net 2023-07-01 11:58:00 -04:00
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commit f23f22d71c
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Task/Quaternion-type/F-Sharp/quaternion-type.fs Normal file
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open System
[<Struct; StructuralEquality; NoComparison>]
type Quaternion(r : float, i : float, j : float, k : float) =
member this.A = r
member this.B = i
member this.C = j
member this.D = k
new (f : float) = Quaternion(f, 0., 0., 0.)
static member (~-) (q : Quaternion) = Quaternion(-q.A, -q.B, -q.C, -q.D)
static member (+) (q1 : Quaternion, q2 : Quaternion) =
Quaternion(q1.A + q2.A, q1.B + q2.B, q1.C + q2.C, q1.D + q2.D)
static member (+) (q : Quaternion, r : float) = q + Quaternion(r)
static member (+) (r : float, q: Quaternion) = Quaternion(r) + q
static member (*) (q1 : Quaternion, q2 : Quaternion) =
Quaternion(
q1.A * q2.A - q1.B * q2.B - q1.C * q2.C - q1.D * q2.D,
q1.A * q2.B + q1.B * q2.A + q1.C * q2.D - q1.D * q2.C,
q1.A * q2.C - q1.B * q2.D + q1.C * q2.A + q1.D * q2.B,
q1.A * q2.D + q1.B * q2.C - q1.C * q2.B + q1.D * q2.A)
static member (*) (q : Quaternion, r : float) = q * Quaternion(r)
static member (*) (r : float, q: Quaternion) = Quaternion(r) * q
member this.Norm = Math.Sqrt(r * r + i * i + j * j + k * k)
member this.Conjugate = Quaternion(r, -i, -j, -k)
override this.ToString() = sprintf "Q(%f, %f, %f, %f)" r i j k
[<EntryPoint>]
let main argv =
let q = Quaternion(1., 2., 3., 4.)
let q1 = Quaternion(2., 3., 4., 5.)
let q2 = Quaternion(3., 4., 5., 6.)
let r = 7.
printfn "q = %A" q
printfn "q1 = %A" q1
printfn "q2 = %A" q2
printfn "r = %A" r
printfn "q.Norm = %A" q.Norm
printfn "q1.Norm = %A" q1.Norm
printfn "q2.Norm = %A" q2.Norm
printfn "-q = %A" -q
printfn "q.Conjugate = %A" q.Conjugate
printfn "q + r = %A" (q + (Quaternion r))
printfn "q1 + q2 = %A" (q1 + q2)
printfn "q2 + q1 = %A" (q2 + q1)
printfn "q * r = %A" (q * r)
printfn "q1 * q2 = %A" (q1 * q2)
printfn "q2 * q1 = %A" (q2 * q1)
printfn "q1*q2 %s q2*q1" (if (q1 * q2) = (q2 * q1) then "=" else "<>")
printfn "q %s Q(1.,2.,3.,4.)" (if q = Quaternion(1., 2., 3., 4.) then "=" else "<>")
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