bisquare

module BiSquare
open System
open System.Diagnostics



type SquareRootResult =
    | NoRoots
    | OneSemiRoot of double
    | TwoSemiRoots of double * double

type BiSquareRootResult =
    | FullComplexRoots
    | Zero
    | TwoRoots of double * double
    | FourRoots of double * double * double * double
    | FourRootsWithComplex of double * double


let CalculateSemiRoots(a: double, b: double, c: double):SquareRootResult =
    let D = b*b - 4.0*a*c;
    if D < 0.0 then NoRoots
    else if D = 0.0 then
        let rt = -b / (2.0 * a)
        OneSemiRoot rt
    else
        let sqrtD = Math.Sqrt(D)
        let rt1 = (-b + sqrtD) / (2.0 * a)
        let rt2 = (-b - sqrtD) / (2.0 * a)
        TwoSemiRoots (rt1, rt2)

let CalculateBiSquareRoots(semiroot: SquareRootResult): BiSquareRootResult =
    match semiroot with
    | NoRoots -> FullComplexRoots
    | OneSemiRoot(rt) when rt = 0.0 -> Zero
    | OneSemiRoot(rt) when rt > 0.0 -> TwoRoots(sqrt(rt),-sqrt(rt))
    | OneSemiRoot(rt) -> FullComplexRoots
    | TwoSemiRoots(rt1, rt2) when rt1 < 0.0 && rt2 < 0.0 -> FullComplexRoots
    | TwoSemiRoots(rt1, rt2) when rt1 < 0.0 || rt2 < 0.0 -> if rt1>0.0 then FourRootsWithComplex(sqrt(rt1), -sqrt(rt1)) else FourRootsWithComplex(sqrt(rt2), -sqrt(rt2))
    | TwoSemiRoots(rt1, rt2) -> FourRoots(sqrt(rt1), -sqrt(rt1), sqrt(rt2), -sqrt(rt2))


let PrintRoots(a: double, b: double, c: double):unit =
    printf "Коэффициенты: a=%A, b=%A, c=%A. " a b c
    let root = CalculateBiSquareRoots(CalculateSemiRoots(a,b,c))
    let textResult =
        match root with
        | FullComplexRoots -> "Корни лежат в комплексной плоскости"
        | Zero -> "Просто " + "0"
        | TwoRoots(rt1, rt2) -> "Два корня " + rt1.ToString() + " и " + rt2.ToString()
        | FourRootsWithComplex(rt1, rt2) -> "Два корня " + rt1.ToString() + " и " + rt2.ToString() + " и еще два корня лежащие в комплексной плоскости"
        | FourRoots(rt1, rt2, rt3, rt4) -> "Четыре корня " + rt1.ToString() + " и " + rt2.ToString() + rt3.ToString() + " и " + rt4.ToString()
    printfn "%s" textResult