public static void PolynomExamples()
{
// create by coefs
var pol = new Polynom(new double[] { 1, 2, 3, 4, 5 });
pol.Show(); // 5x^4 + 4x^3 + 3x^2 + 2x^1 + 1
// create by head coef and roots
pol = new Polynom(aN: 2, -1, 0, 1, 2);
pol.Show(); // 2x^4 + -4x^3 + -2x^2 + 4x^1 + -0
var points = new Point[] { new Point(1, 2), new Point(3, 4), new Point(5, 7) };
// interpolation polynom
pol = new Polynom(points);
pol.Show(); // 0,125x^2 + 0,5x^1 + 1,375
pol.Value(1).Show(); // 2
pol.Value(3).Show(); // 4
pol.Value(5).Show(); // 7
// interpolation polynom
pol = new Polynom(x => Math.Sin(x) + x, n: 6, a: -1, b: 1);
foreach (var val in new NetOnDouble(-1, 1, 12).Array)
{
$"pol = {pol.Value(val)} f = {Math.Sin(val)+val}".Show();
}
//pol = -1,841470984807902 f = -1,8414709848078965
//pol = -1,5480795026639842 f = -1,548086037891892
//pol = -1,230639272195443 f = -1,230638423911926
//pol = -0,8936010083785814 f = -0,8935994224990154
//pol = -0,5420855146782465 f = -0,5420861802628714
//pol = -0,18169222919395844 f = -0,1816930144179611
//pol = 0,18169222919395842 f = 0,1816930144179611
//pol = 0,5420855146782463 f = 0,5420861802628714
//pol = 0,8936010083785806 f = 0,8935994224990154
//pol = 1,2306392721954413 f = 1,230638423911926
//pol = 1,5480795026639818 f = 1,5480860378918924
//pol = 1,8414709848078967 f = 1,8414709848078965
// operations
var pol1 = new Polynom(new double[] { 1, 2, 3, 4, 5 });
var pol2 = new Polynom(new double[] { 2.2, 3 });
pol1.Show(); // 5x^4 + 4x^3 + 3x^2 + 2x^1 + 1
pol2.Show(); // 3x^1 + 2,2
pol2.ShowRational(); // (3x^1) + 11/5
(pol1 * pol2).Show(); // 15x^5 + 23x^4 + 17,8x^3 + 12,600000000000001x^2 + 7,4x^1 + 2,2
(pol1 / 2 + pol2 * 2.8 - 4.66).Show(); // 2,5x^4 + 2x^3 + 1,5x^2 + 9,399999999999999x^1 + 2
var a = pol1 / pol2;
var b = pol1 % pol2;
$"{pol1} == {a*pol2+b}".Show(); // 5x^4 + 4x^3 + 3x^2 + 2x^1 + 1 == 5x^4 + 4x^3 + 3x^2 + 2x^1 + 1
(a, b) = Polynom.Division(pol1 - 1.5, pol2);
$"{pol1-1.5} == {a * pol2 + b}".Show(); // 5x^4 + 4x^3 + 3x^2 + 2x^1 + -0,5 == 5x^4 + 4x^3 + 3x^2 + 2x^1 + -0,5
// derivative
(pol1 | 2).Show(); // 60x^2 + 24x^1 + 6
pol2.Value(pol1).Show(); //
pol2.Value(new SqMatrix(new double[, ] {
{ 1, 2 }, { 3, 4 }
})).PrintMatrix();
//5,2 6
//9 14,2
// integration
$"{pol1.S(-3,2)} == {FuncMethods.DefInteg.GaussKronrod.MySimpleGaussKronrod(pol1.Value,-3,2,n:15)}".Show();
// 245 == 244,99999999999997
}