MathALL/test-sqrt.html at main · xhc861/MathALL · GitHub

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<!DOCTYPE html>
<html>
<head>
  <meta charset="UTF-8">
  <title>测试根号功能</title>
  <style>
    body {
      font-family: Arial, sans-serif;
      padding: 20px;
      max-width: 800px;
      margin: 0 auto;
    }
    .test-case {
      margin: 20px 0;
      padding: 15px;
      border: 1px solid #ddd;
      border-radius: 8px;
      background: #f9f9f9;
    }
    .result {
      font-weight: bold;
      color: #10b981;
      font-size: 1.2em;
    }
    .expected {
      color: #666;
      font-style: italic;
    }
  </style>
</head>
<body>
  <h1>根号简化功能测试</h1>
  <div id="results"></div>

  <script type="module">
    // 简化根号函数
    function simplifySquareRoot(value) {
      if (value === 0) return { coefficient: 0, radicand: 1 };
      if (value < 0) return { coefficient: 0, radicand: 1 };

      let coefficient = 1;
      let radicand = Math.round(value);

      // 提取完全平方因子
      for (let i = 2; i * i <= radicand; i++) {
        while (radicand % (i * i) === 0) {
          coefficient *= i;
          radicand /= (i * i);
        }
      }

      return { coefficient, radicand };
    }

    // 格式化根号表达式
    function formatSquareRoot(coefficient, radicand) {
      if (coefficient === 0) return '0';
      if (radicand === 1) return coefficient.toString();
      if (coefficient === 1) return `√${radicand}`;
      return `${coefficient}√${radicand}`;
    }

    // 计算距离
    function calculateDistance(x1, y1, x2, y2) {
      const dx = x2 - x1;
      const dy = y2 - y1;
      const distanceSquared = dx * dx + dy * dy;
      const decimalDistance = Math.sqrt(distanceSquared);

      const distanceSquaredInt = Math.round(distanceSquared * 1000000) / 1000000;
      const distanceSquaredRounded = Math.round(distanceSquaredInt);

      let exact;
      if (Math.abs(distanceSquaredInt - distanceSquaredRounded) < 0.0001) {
        const { coefficient, radicand } = simplifySquareRoot(distanceSquaredRounded);
        exact = formatSquareRoot(coefficient, radicand);
      } else {
        exact = decimalDistance.toFixed(6);
      }

      return {
        decimal: decimalDistance,
        exact: exact,
        squared: distanceSquaredInt
      };
    }

    // 运行测试
    const tests = [
      { name: '√8', value: 8, expected: '2√2' },
      { name: '√12', value: 12, expected: '2√3' },
      { name: '√18', value: 18, expected: '3√2' },
      { name: '√50', value: 50, expected: '5√2' },
      { name: '√16', value: 16, expected: '4' },
      { name: '√5', value: 5, expected: '√5' },
      { name: '√32', value: 32, expected: '4√2' },
      { name: '√72', value: 72, expected: '6√2' },
    ];

    const distanceTests = [
      { name: '(0,0) → (3,4)', x1: 0, y1: 0, x2: 3, y2: 4, expected: '5' },
      { name: '(0,0) → (1,1)', x1: 0, y1: 0, x2: 1, y2: 1, expected: '√2' },
      { name: '(0,0) → (2,2)', x1: 0, y1: 0, x2: 2, y2: 2, expected: '2√2' },
      { name: '(1,2) → (4,6)', x1: 1, y1: 2, x2: 4, y2: 6, expected: '5' },
      { name: '(0,0) → (3,3)', x1: 0, y1: 0, x2: 3, y2: 3, expected: '3√2' },
    ];

    const resultsDiv = document.getElementById('results');

    // 测试根号简化
    resultsDiv.innerHTML += '<h2>根号简化测试</h2>';
    tests.forEach(test => {
      const result = simplifySquareRoot(test.value);
      const formatted = formatSquareRoot(result.coefficient, result.radicand);
      const passed = formatted === test.expected;

      resultsDiv.innerHTML += `
        <div class="test-case">
          <div><strong>${test.name}</strong></div>
          <div class="result">结果: ${formatted}</div>
          <div class="expected">预期: ${test.expected}</div>
          <div style="color: ${passed ? 'green' : 'red'}">
            ${passed ? '✓ 通过' : '✗ 失败'}
          </div>
        </div>
      `;
    });

    // 测试距离计算
    resultsDiv.innerHTML += '<h2>距离计算测试</h2>';
    distanceTests.forEach(test => {
      const result = calculateDistance(test.x1, test.y1, test.x2, test.y2);
      const passed = result.exact === test.expected;

      resultsDiv.innerHTML += `
        <div class="test-case">
          <div><strong>${test.name}</strong></div>
          <div class="result">精确值: ${result.exact}</div>
          <div>小数值: ${result.decimal.toFixed(6)}</div>
          <div>平方: ${result.squared}</div>
          <div class="expected">预期: ${test.expected}</div>
          <div style="color: ${passed ? 'green' : 'red'}">
            ${passed ? '✓ 通过' : '✗ 失败'}
          </div>
        </div>
      `;
    });
  </script>
</body>
</html>