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Ingy döt Net 2026-02-01 16:33:20 -08:00
parent 5150844a7d
commit 4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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23
Task/Formal-power-series/Ada/formal-power-series-1.ada
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with Generic_Rational;
generic
with package Rational_Numbers is new Generic_Rational (<>);
package Generic_Taylor_Series is
use Rational_Numbers;
type Taylor_Series is array (Natural range <>) of Rational;
function "+" (A : Taylor_Series) return Taylor_Series;
function "-" (A : Taylor_Series) return Taylor_Series;
function "+" (A, B : Taylor_Series) return Taylor_Series;
function "-" (A, B : Taylor_Series) return Taylor_Series;
function "*" (A, B : Taylor_Series) return Taylor_Series;
function Integral (A : Taylor_Series) return Taylor_Series;
function Differential (A : Taylor_Series) return Taylor_Series;
function Value (A : Taylor_Series; X : Rational) return Rational;
Zero : constant Taylor_Series := (0 => Rational_Numbers.Zero);
One : constant Taylor_Series := (0 => Rational_Numbers.One);
end Generic_Taylor_Series;

103
Task/Formal-power-series/Ada/formal-power-series-2.ada
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package body Generic_Taylor_Series is
function Normalize (A : Taylor_Series) return Taylor_Series is
begin
for Power in reverse A'Range loop
if A (Power) /= 0 then
return A (0..Power);
end if;
end loop;
return Zero;
end Normalize;
function "+" (A : Taylor_Series) return Taylor_Series is
begin
return A;
end "+";
function "-" (A : Taylor_Series) return Taylor_Series is
Result : Taylor_Series (A'Range);
begin
for Power in A'Range loop
Result (Power) := -A (Power);
end loop;
return Result;
end "-";
function "+" (A, B : Taylor_Series) return Taylor_Series is
begin
if A'Last > B'Last then
return B + A;
else
declare
Result : Taylor_Series (0..B'Last);
begin
for Power in A'Range loop
Result (Power) := A (Power) + B (Power);
end loop;
for Power in A'Last + 1..B'Last loop
Result (Power) := B (Power);
end loop;
return Normalize (Result);
end;
end if;
end "+";
function "-" (A, B : Taylor_Series) return Taylor_Series is
begin
return A + (-B);
end "-";
function "*" (A, B : Taylor_Series) return Taylor_Series is
Result : Taylor_Series (0..A'Last + B'Last);
begin
for I in A'Range loop
for J in B'Range loop
Result (I + J) := A (I) * B (J);
end loop;
end loop;
return Normalize (Result);
end "*";
function Integral (A : Taylor_Series) return Taylor_Series is
begin
if A = Zero then
return Zero;
else
declare
Result : Taylor_Series (0..A'Last + 1);
begin
for Power in A'Range loop
Result (Power + 1) := A (Power) / Number (Power + 1);
end loop;
Result (0) := Rational_Numbers.Zero;
return Result;
end;
end if;
end Integral;
function Differential (A : Taylor_Series) return Taylor_Series is
begin
if A'Length = 1 then
return Zero;
else
declare
Result : Taylor_Series (0..A'Last - 1);
begin
for Power in Result'Range loop
Result (Power) := A (Power + 1) * Number (Power);
end loop;
return Result;
end;
end if;
end Differential;
function Value (A : Taylor_Series; X : Rational) return Rational is
Sum : Rational := A (A'Last);
begin
for Power in reverse 0..A'Last - 1 loop
Sum := Sum * X + A (Power);
end loop;
return Sum;
end Value;
end Generic_Taylor_Series;

53
Task/Formal-power-series/Ada/formal-power-series-3.ada
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with Ada.Text_IO; use Ada.Text_IO;
with Generic_Taylor_Series;
with Generic_Rational;
procedure Test_Taylor_Series is
package Integer_Rationals is new Generic_Rational (Integer);
package Integer_Taylor_Series is new Generic_Taylor_Series (Integer_Rationals);
use Integer_Taylor_Series;
-- Procedure to print a series
procedure Put (A : Taylor_Series) is
use Integer_Rationals;
procedure Put (A : Rational) is
begin
if Numerator (A) = 1 then
Put (" 1");
else
Put (Integer'Image (Numerator (A)));
end if;
if Denominator (A) /= 1 then
Put (" /");
Put (Integer'Image (Denominator (A)));
end if;
end Put;
begin
if A (0) /= 0 then
Put (A (0));
end if;
for Power in 1..A'Last loop
if A (Power) > 0 then
Put (" +");
Put (A (Power));
Put (" X **" & Integer'Image (Power));
elsif A (Power) < 0 then
Put (" -");
Put (abs A (Power));
Put (" X **" & Integer'Image (Power));
end if;
end loop;
end Put;
-- Cosine generator
function Cos (N : Natural) return Taylor_Series is
begin
if N = 0 then
return One;
else
return One - Integral (Integral (Cos (N - 1)));
end if;
end Cos;
begin
Put ("Cos ="); Put (Cos (5)); Put_Line (" ...");
Put ("Sin ="); Put (Integral (Cos (5))); Put_Line (" ...");
end Test_Taylor_Series;