mathtool/lib/tools/cuo_wei_xiang_jian.dart

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

class CuoWeiXiangJianPage extends StatefulWidget {
  @override
  _CuoWeiXiangJianPageState createState() => _CuoWeiXiangJianPageState();
}

class _CuoWeiXiangJianPageState extends State<CuoWeiXiangJianPage> {
  final TextEditingController aController = TextEditingController();
  final TextEditingController bController = TextEditingController();
  final TextEditingController qController = TextEditingController();
  final TextEditingController mController = TextEditingController();

  String result = '';

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(title: Text('错位相减法')),
      body: Padding(
        padding: EdgeInsets.all(16),
        child: Column(
          children: [
            Text(
              '通项为: aₙ = (a·n + b) · qⁿ⁺ᵐ',
              style: TextStyle(fontSize: 16, fontWeight: FontWeight.bold),
            ),
            SizedBox(height: 20),
            _buildInputField('a (系数)', aController),
            _buildInputField('b (常数)', bController),
            _buildInputField('q (公比)', qController),
            _buildInputField('m (指数偏移)', mController),
            SizedBox(height: 20),
            ElevatedButton(
              onPressed: _calculate,
              child: Text('计算'),
            ),
            SizedBox(height: 20),
            if (result.isNotEmpty)
              Card(
                child: Padding(
                  padding: EdgeInsets.all(16),
                  child: Text(
                    result,
                    style: TextStyle(fontSize: 16),
                  ),
                ),
              ),
          ],
        ),
      ),
    );
  }

  Widget _buildInputField(String label, TextEditingController controller) {
    return Padding(
      padding: EdgeInsets.symmetric(vertical: 8),
      child: 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 a = MathUtils.parseRational(aController.text);
      final b = MathUtils.parseRational(bController.text);
      final q = MathUtils.parseRational(qController.text);
      final m = int.parse(mController.text);

      // 将指数统一为n-1
      final aAdj = a * q.pow(m + 1);
      final bAdj = b * q.pow(m + 1);

      // 计算A,B
      final A = aAdj / (q - Rational.one);
      final B = (bAdj - A) / (q - Rational.one);

      setState(() {
        result = '结果: Sₙ = (A·n + B) · qⁿ - B\n'
      'A = ${MathUtils.rationalToString(A)}\n'
      'B = ${MathUtils.rationalToString(B)}';
      });
    } catch (e) {
      setState(() {
        result = '错误: $e';
      });
    }
  }

  @override
  void dispose() {
    aController.dispose();
    bController.dispose();
    qController.dispose();
    mController.dispose();
    super.dispose();
  }
}