chore: complete update

tests/Domain/QrCode/ValueObject/PolynomialTest.php

@@ -0,0 +1,75 @@
+<?php
+
+declare(strict_types=1);
+
+use App\Domain\QrCode\ValueObject\GaloisField;
+use App\Domain\QrCode\ValueObject\Polynomial;
+
+test('Polynomial kann erstellt werden', function () {
+    $field = new GaloisField();
+    $poly = new Polynomial($field, [1, 2, 3]); // x^2 + 2x + 3
+
+    expect($poly->getCoefficients())->toBe([1, 2, 3]);
+    expect($poly->getDegree())->toBe(2);
+});
+
+test('Polynomial entfernt führende Nullen', function () {
+    $field = new GaloisField();
+    $poly = new Polynomial($field, [0, 0, 1, 2]); // x + 2
+
+    expect($poly->getCoefficients())->toBe([1, 2]);
+    expect($poly->getDegree())->toBe(1);
+});
+
+test('Polynomial kann an Stelle x ausgewertet werden', function () {
+    $field = new GaloisField();
+    $poly = new Polynomial($field, [1, 0, 1]); // x^2 + 1
+
+    expect($poly->evaluateAt(0))->toBe(1);
+    expect($poly->evaluateAt(1))->toBe(0); // 1^2 + 1 = 2 = 0 in GF(2)
+    expect($poly->evaluateAt(2))->toBe(5); // 2^2 + 1 = 5
+});
+
+test('Polynomial Addition funktioniert', function () {
+    $field = new GaloisField();
+    $poly1 = new Polynomial($field, [1, 2]); // x + 2
+    $poly2 = new Polynomial($field, [3, 4]); // 3x + 4
+
+    $sum = $poly1->add($poly2);
+
+    // In GF(2^8) ist Addition = XOR, daher 1⊕3=2, 2⊕4=6
+    expect($sum->getCoefficients())->toBe([2, 6]);
+});
+
+test('Polynomial Multiplikation funktioniert', function () {
+    $field = new GaloisField();
+    $poly1 = new Polynomial($field, [1, 1]); // x + 1
+    $poly2 = new Polynomial($field, [1, 0, 1]); // x^2 + 1
+
+    $product = $poly1->multiply($poly2);
+
+    // (x + 1)(x^2 + 1) = x^3 + x^2 + x + 1
+    expect($product->getCoefficients())->toBe([1, 1, 1, 1]);
+});
+
+test('Polynomial Division funktioniert', function () {
+    $field = new GaloisField();
+    $poly1 = new Polynomial($field, [1, 0, 1]); // x^2 + 1
+    $poly2 = new Polynomial($field, [1, 1]); // x + 1
+
+    $result = $poly1->divideAndRemainder($poly2);
+
+    // (x^2 + 1) ÷ (x + 1) = x - 1 + 2/(x+1)
+    // In GF(2^8): Quotient = x - 1 = x + 1, Rest = 2
+    expect($result['quotient']->getCoefficients())->toEqual([1, 1]);
+    expect($result['remainder']->getCoefficients())->toEqual([0]);
+});
+
+test('Generator Polynom kann korrekt erstellt werden', function () {
+    $field = new GaloisField();
+    $generator = Polynomial::buildGenerator($field, 3);
+
+    // Erwartetes Ergebnis für Grad 3
+    expect($generator->getDegree())->toBe(3);
+    expect(count($generator->getCoefficients()))->toBe(4);
+});