Polynomial synthetic division: Difference between revisions

=={{header|Delphi}}==

{{libheader| System.SysUtils}}

{{libheader| Velthuis.BigRationals}}

{{Trans|Go}}

Thanks Rudy Velthuis for the [https://github.com/rvelthuis/DelphiBigNumbers Velthuis.BigRationals] library.<br>

<lang Delphi>

program Polynomial_synthetic_division;

{$APPTYPE CONSOLE}

uses

System.SysUtils,

Velthuis.BigRationals;

type

TPollynomy = record

public

Terms: TArray<BigRational>;

class operator Divide(a, b: TPollynomy): TArray<TPollynomy>;

constructor Create(Terms: TArray<BigRational>);

function ToString: string;

end;

{ TPollynomy }

constructor TPollynomy.Create(Terms: TArray<BigRational>);

begin

self.Terms := copy(Terms, 0, length(Terms));

end;

class operator TPollynomy.Divide(a, b: TPollynomy): TArray<TPollynomy>;

var

q, r: TPollynomy;

begin

var o: TArray<BigRational>;

SetLength(o, length(a.Terms));

for var i := 0 to High(a.Terms) do

o[i] := BigRational.Create(a.Terms[i]);

for var i := 0 to length(a.Terms) - length(b.Terms) do

begin

o[i] := BigRational.Create(o[i] div b.Terms[0]);

var coef := BigRational.Create(o[i]);

if coef.Sign <> 0 then

begin

var aa: BigRational := 0;

for var j := 1 to High(b.Terms) do

begin

aa := (-b.Terms[j]) * coef;

o[i + j] := o[i + j] + aa;

end;

end;

end;

var separator := length(o) - (length(b.Terms) - 1);

q := TPollynomy.Create(copy(o, 0, separator));

r := TPollynomy.Create(copy(o, separator, length(o)));

result := [q, r];

end;

function TPollynomy.ToString: string;

begin

Result := '[';

for var e in Terms do

Result := Result + e.ToString + ' ';

Result := Result + ']';

end;

var

p1, p2: TPollynomy;

begin

p1 := TPollynomy.Create([BigRational.Create(1, 1), BigRational.Create(-12, 1),

BigRational.Create(0, 1), BigRational.Create(-42, 1)]);

p2 := TPollynomy.Create([BigRational.Create(1, 1), BigRational.Create(-3, 1)]);

write(p1.ToString, ' / ', p2.ToString, ' = ');

var result := p1 / p2;

writeln(result[0].ToString, ' remainder ', result[1].ToString);

readln;

end.</lang>

{{out}}

<pre>[1 -12 0 -42 ] / [1 -3 ] = [1 -9 -27 ] remainder [-123 ]</pre>