mathtool2/lib/tools/circle_equation.dart

// tools/circle_equation.dart
import 'package:flutter/material.dart';
import 'package:rational/rational.dart';
import '../utils/math_utils.dart';

class CircleEquationPage extends StatefulWidget {
  @override
  _CircleEquationPageState createState() => _CircleEquationPageState();
}

class _CircleEquationPageState extends State<CircleEquationPage> {
  final TextEditingController x1Controller = TextEditingController();
  final TextEditingController y1Controller = TextEditingController();
  final TextEditingController x2Controller = TextEditingController();
  final TextEditingController y2Controller = TextEditingController();
  final TextEditingController x3Controller = TextEditingController();
  final TextEditingController y3Controller = TextEditingController();

  String result = '';

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(title: Text('圆的方程')),
      body: Padding(
        padding: EdgeInsets.all(16),
        child: Column(
          children: [
            Text('请输入三个点的坐标:'),
            SizedBox(height: 10),
            Row(
              children: [
                Expanded(child: _buildInputField('点1 x', x1Controller)),
                SizedBox(width: 10),
                Expanded(child: _buildInputField('点1 y', y1Controller)),
              ],
            ),
            Row(
              children: [
                Expanded(child: _buildInputField('点2 x', x2Controller)),
                SizedBox(width: 10),
                Expanded(child: _buildInputField('点2 y', y2Controller)),
              ],
            ),
            Row(
              children: [
                Expanded(child: _buildInputField('点3 x', x3Controller)),
                SizedBox(width: 10),
                Expanded(child: _buildInputField('点3 y', y3Controller)),
              ],
            ),
            SizedBox(height: 20),
            ElevatedButton(
              onPressed: _calculate,
              child: Text('计算圆的方程'),
            ),
            SizedBox(height: 20),
            if (result.isNotEmpty)
              Card(
                child: Padding(
                  padding: EdgeInsets.all(16),
                  child: Text(
                    result,
                    style: TextStyle(fontSize: 14, fontFamily: 'Monospace'),
                  ),
                ),
              ),
          ],
        ),
      ),
    );
  }

  Widget _buildInputField(String label, TextEditingController controller) {
    return TextField(
      controller: controller,
      keyboardType: TextInputType.numberWithOptions(signed: true, decimal: true),
      decoration: InputDecoration(
        labelText: label,
        border: OutlineInputBorder(),
        hintText: '输入分数如: 1/2 或小数',
      ),
    );
  }

  void _calculate() {
    try {
      final x1 = MathUtils.parseRational(x1Controller.text);
      final y1 = MathUtils.parseRational(y1Controller.text);
      final x2 = MathUtils.parseRational(x2Controller.text);
      final y2 = MathUtils.parseRational(y2Controller.text);
      final x3 = MathUtils.parseRational(x3Controller.text);
      final y3 = MathUtils.parseRational(y3Controller.text);

      final z1 = x1 * x1 + y1 * y1;
      final z2 = x2 * x2 + y2 * y2;
      final z3 = x3 * x3 + y3 * y3;

      final solutions = MathUtils.solveLinear2(
        x1 - x2, y1 - y2, z2 - z1,
        x1 - x3, y1 - y3, z3 - z1,
      );

      final D = solutions[0];
      final E = solutions[1];
      final F = -z1 - D * x1 - E * y1;
      final r2 = (D * D + E * E - Rational.fromInt(4) * F)/Rational.fromInt(4);

      setState(() {
        result = '''
      圆的方程: x² + y² + Dx + Ey + F = 0
      D = ${MathUtils.rationalToString(D)}
      E = ${MathUtils.rationalToString(E)}
      F = ${MathUtils.rationalToString(F)}
      圆心: (${MathUtils.rationalToString(-D / Rational.fromInt(2))},
      ${MathUtils.rationalToString(-E / Rational.fromInt(2))})
      半径平方: ${MathUtils.rationalToString(r2)}
      ''';
      });
    } catch (e) {
      setState(() {
        result = '错误: $e\n注意: 三个点不能共线';
      });
    }
  }

  @override
  void dispose() {
    x1Controller.dispose();
    y1Controller.dispose();
    x2Controller.dispose();
    y2Controller.dispose();
    x3Controller.dispose();
    y3Controller.dispose();
    super.dispose();
  }
}