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RootsFormula
We computed the real solution of the polynomial equation in real time.
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RootsFormula
"解の公式"を用いて、１～４次方程式の実数解をリアルタイムに計算しました。
Using the formula of solution, We computed the real solution of the linear/quadratic/cubic/quartic equation in real time.
###MOVIE
###▼ １次方程式 (linear equation)
Ks1[2] * X + Ks1[1] = 0var
Ks :TDouble2D; //多項式の係数
X1 :Double; //解
XsN :Byte; //解の個数 = 0～1
Ks[1] := 1; // 1
Ks[2] := 2; // X
XsN := PolySolveReal( Ks, X1 );###▼ ２次方程式 (Quadratic equation)
Ks1[3] * X^2 + Ks1[2] * X + Ks1[1] = 0var
Ks :TDouble2D; //多項式の係数
Xs :Double; //解の配列
XsN :Byte; //解の個数 = 0～2
Ks[1] := 1; // 1
Ks[2] := 2; // X
Ks[3] := 3; // X^2
XsN := PolySolveReal( Ks, Xs );###▼ ３次方程式 (Cubic equation)
Ks1[4] * X^3 + Ks1[3] * X^2 + Ks1[2] * X + Ks1[1] = 0function PolySolveReal( const Ks_:TSingle4D; out Xs_:TSingle3D ) :Byte;
function PolySolveReal( const Ks_:TDouble4D; out Xs_:TDouble3D ) :Byte;
var
Ks :TDouble2D; //多項式の係数
Xs :Double; //解の配列
XsN :Byte; //解の個数 = 1 or 3
Ks[1] := 1; // 1
Ks[2] := 2; // X
Ks[3] := 3; // X^2
Ks[4] := 4; // X^3
XsN := PolySolveReal( Ks, Xs );###▼ ４次方程式 (Quartic equation)
Ks1[5] * X^4 + Ks1[4] * X^3 + Ks1[3] * X^2 + Ks1[2] * X + Ks1[1] = 0function PolySolveReal( const Ks_:TSingle5D; out Xs_:TSingle4D ) :Byte;
function PolySolveReal( const Ks_:TDouble5D; out Xs_:TDouble4D ) :Byte;
var
Ks :TDouble2D; //多項式の係数
Xs :Double; //解の配列
XsN :Byte; //解の個数 = 0～4
Ks[1] := 1; // 1
Ks[2] := 2; // X
Ks[3] := 3; // X^2
Ks[4] := 4; // X^3
Ks[5] := 5; // X^4
XsN := PolySolveReal( Ks, Xs );