Complex roots of polynomial with real coefficients (dynamic)
Have also a look at "Complex roots of polynomial with real coefficients".
Compute *all* complex roots of a polynomial with real coefficients and display them in the complex plane. JSXGraph has its own variant of the Aberth, Ehrlich, Weierstraß algorithm implemented.
Coefficients $a_7$ and $a_8$ of polynomial can be manipulated by dragging the sliders.
// Define the id of your board in BOARDID
const board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-9, 9, 9, -9],
axis: true
});
// Coefficients [a_o, ..., a_n] of a polynomial,
// starting with a_0, a_1, ...
var coefficients = [-1, 3, -9, 1, 0, 0, -8, 9, -9, 1];
// Manipulate coefficients a_7 and a_8
var a8 = board.create('slider', [
[0, 7],
[6, 7],
[-10, -9, 10]
], {
name: 'a_8',
snapWidth: 0.1,
snapValues: [0],
snapValueDistance: 0.4
});
var a7 = board.create('slider', [
[0, 6],
[6, 6],
[-10, 9, 10]
], {
name: 'a_7',
snapWidth: 0.1,
snapValues: [0],
snapValueDistance: 0.4
});
var i;
for (i = 0; i < 9; i++) {
board.create('point', [
(function(ii) {
return function() {
coefficients[7] = a7.Value();
coefficients[8] = a8.Value();
let roots = JXG.Math.Numerics.polzeros(coefficients);
return [roots[ii].real, roots[ii].imaginary];
}
})(i)
], {
withLabel: false
});
}
board.create('text', [-8, -4.5, () => JXG.Math.Numerics.generatePolynomialTerm(coefficients, coefficients.length - 1, 'x', 1)]);
This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note that you have to mention The Center of Mobile Learning with Digital Technology in the credits.