Polynomial derivative: Difference between revisions
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-x^4 - x^3 + x + 1 -> -4x^3 - 3x^2 + 1
</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
const Poly1: array [0..1-1] of double = (5); {5}
const Poly2: array [0..2-1] of double = (4,-3); {-3x+4}
const Poly3: array [0..3-1] of double = (-1,6,5); {5x^2+6x-1}
const Poly4: array [0..4-1] of double = (-4,3,-2,1); {x^3-2x^2+3x-4}
const Poly5: array [0..5-1] of double = (1,1,0,-1,-1); {-x^4-x^3+x+1}
function GetDerivative(P: array of double): TDoubleDynArray;
var I,N: integer;
begin
SetLength(Result,Length(P)-1);
if Length(P)<1 then exit;
for I:=0 to High(Result) do
Result[I]:= (I+1)*P[I+1];
end;
function GetPolyStr(D: array of double): string;
{Get polynomial in standard math format string}
var I: integer;
var S: string;
function GetSignStr(Lead: boolean; D: double): string;
{Get the sign of coefficient}
begin
Result:='';
if D>0 then
begin
if not Lead then Result:=' + ';
end
else
begin
Result:='-';
if not Lead then Result:=' - ';
end;
end;
begin
Result:='';
{Get each coefficient}
for I:=High(D) downto 0 do
begin
{Ignore zero values}
if D[I]=0 then continue;
{Get sign and coefficient}
S:=GetSignStr(Result='',D[I]);
S:=S+FloatToStrF(abs(D[I]),ffFixed,18,0);
{Combine with exponents }
if I>1 then Result:=Result+Format('%SX^%d',[S,I])
else if I=1 then Result:=Result+Format('%SX',[S,I])
else Result:=Result+Format('%S',[S]);
end;
end;
procedure ShowDerivative(Memo: TMemo; Poly: array of double);
{Show polynomial and and derivative}
var D: TDoubleDynArray;
begin
D:=GetDerivative(Poly);
Memo.Lines.Add('Polynomial: '+GetPolyStr(Poly));
Memo.Lines.Add('Derivative: '+'['+GetPolyStr(D)+']');
Memo.Lines.Add('');
end;
procedure ShowPolyDerivative(Memo: TMemo);
var D: TDoubleDynArray;
begin
ShowDerivative(Memo,Poly1);
ShowDerivative(Memo,Poly2);
ShowDerivative(Memo,Poly3);
ShowDerivative(Memo,Poly4);
ShowDerivative(Memo,Poly5);
end;
</syntaxhighlight>
{{out}}
<pre>
Polynomial: 5
Derivative: []
Polynomial: -3X + 4
Derivative: [-3]
Polynomial: 5X^2 + 6X - 1
Derivative: [10X + 6]
Polynomial: 1X^3 - 2X^2 + 3X - 4
Derivative: [3X^2 - 4X + 3]
Polynomial: -1X^4 - 1X^3 + 1X + 1
Derivative: [-4X^3 - 3X^2 + 1]
Elapsed Time: 17.842 ms.
</pre>
=={{header|F_Sharp|F#}}==
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