Polynomial evaluation: what changed

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Title: Polynomial evaluation

New		Line
1	+	# Introduction
2	+
3	+	It is often useful to evaluate a polynomial at a given point. The method shown below allows to calculate it by using only multiplication and addition, without any power.
4	+
5	+	# Horner's method
6	+
7	+	Only 1-degree polynomial are evaluated, e.g. 3.x^2 + 2.x + 1, can be written, by means of an astute factorization, ((3.x +2).x + 1).
8	+
9	+	``` pascal
10	+	program PolyTest;
11	+
12	+	type
13	+	// coef's rank = it's degree
14	+	TDegres = 0..10;
15	+	TPolynome = record
16	+	Deg: TDegres;
17	+	Coefs: array[TDegres] of Double;
18	+	end;
19	+
20	+	function PolyEval(const aPoly: TPolynome; X: Double): Double;
21	+	var
22	+	i: TDegres;
23	+	begin
24	+	with aPoly do
25	+	begin
26	+	Result := 0;
27	+	for i := Deg downto Low(Coefs) do
28	+	Result := Result * X + Coefs[i];
29	+	end;
30	+	End;
31	+
32	+	(* Exemples *)
33	+	var
34	+	P: TPolynome;
35	+	begin
36	+	P.Deg := 2;
37	+	P.Coefs[2] := 3;
38	+	P.Coefs[1] := 2;
39	+	P.Coefs[0] := 1;
40	+	WriteLn('P(',7,') = ', PolyEval(7):10:2);
41	+
42	+	P.Deg := 0;
43	+	P.Coefs[2] := 0;
44	+	P.Coefs[1] := 0;
45	+	P.Coefs[0] := 1;
46	+	WriteLn('P(',7,') = ', PolyEval(7):10:2);
47	+	End
48	+	```
49	+
50	+	# See also
51	+
52	+	\[<https://en.wikipedia.org/wiki/Horner%27s_method>\\| Horner's method (wiki)\]
53	+
54	+	---
55	+	From the Free Pascal wiki, page "Polynomial evaluation", as it stood on 2020-02-23 after a change by Trev, out of the wiki's dump of 2024-05-26. Copyright stays with the author who wrote it, according to the old wiki's [[Licensing]] page. If you have concerns about this material, [message the admin](/wiki-contact).