mathtool2/lib/tools/symmetry.dart

// tools/symmetry.dart
import 'package:flutter/material.dart';

import '../symja.dart';
import 'tool_kit.dart';

/// 对称变换 —— 三种模式共用一个页面，靠下拉框切换。
///
/// 输入框按模式分别建好、缓存在 [_fields] 里：切回来时原来填的数还在，
/// 而外壳看到的是不同的 list 实例，会自动把上一次的结果清掉。
class SymmetryPage extends StatefulWidget {
  const SymmetryPage({super.key});

  @override
  State<SymmetryPage> createState() => _SymmetryPageState();
}

class _SymmetryPageState extends State<SymmetryPage> {
  static const _modes = ['点关于直线对称', '直线关于点对称', '直线关于直线对称'];

  int _mode = 0;

  // 每种模式一套输入框，建一次、一直留着重用。
  final Map<int, List<ToolField>> _fields = {
    0: [
      ToolField('点 x', hint: '分数如 1/2，或小数'),
      // 点的横纵坐标是一对，并排一行
      ToolField('点 y', hint: '分数如 1/2，或小数', rowWithPrevious: true),
      ToolField('直线 A', hint: 'Ax + By + C = 0 的 A'),
      ToolField('直线 B', hint: 'Ax + By + C = 0 的 B'),
      ToolField('直线 C', hint: 'Ax + By + C = 0 的 C'),
    ],
    1: [
      ToolField('直线 A', hint: 'Ax + By + C = 0 的 A'),
      ToolField('直线 B', hint: 'Ax + By + C = 0 的 B'),
      ToolField('直线 C', hint: 'Ax + By + C = 0 的 C'),
      ToolField('点 x', hint: '分数如 1/2，或小数'),
      ToolField('点 y', hint: '分数如 1/2，或小数', rowWithPrevious: true),
    ],
    2: [
      ToolField('原直线 A', hint: 'Px + Qy + R = 0 的 P'),
      ToolField('原直线 B', hint: 'Px + Qy + R = 0 的 Q'),
      ToolField('原直线 C', hint: 'Px + Qy + R = 0 的 R'),
      ToolField('对称轴 A', hint: 'Ax + By + C = 0 的 A'),
      ToolField('对称轴 B', hint: 'Ax + By + C = 0 的 B'),
      ToolField('对称轴 C', hint: 'Ax + By + C = 0 的 C'),
    ],
  };

  @override
  Widget build(BuildContext context) {
    final fields = _fields[_mode]!;
    return ToolScaffold(
      title: '对称变换',
      fields: fields,
      intro: Column(
        crossAxisAlignment: CrossAxisAlignment.start,
        children: [
          DropdownButton<int>(
            value: _mode,
            isExpanded: true,
            items: [
              for (var i = 0; i < _modes.length; i++)
                DropdownMenuItem(value: i, child: Text(_modes[i])),
            ],
            onChanged: (v) {
              if (v != null) setState(() => _mode = v);
            },
          ),
        ],
      ),
      compute: (session) async {
        final f = _fields[_mode]!;

        if (_mode == 0) {
          // 点 (x, y) 关于直线 Ax + By + C = 0 的对称点
          final x = _need(f[0]);
          final y = _need(f[1]);
          final a = _need(f[2]);
          final b = _need(f[3]);
          final c = _need(f[4]);
          final expr =
              'With[{A=$a,B=$b,C=$c,x=$x,y=$y}, '
              'Module[{t=(A*x+B*y+C)/(A^2+B^2)}, {x-2*A*t, y-2*B*t}]]';
          final r = parseSymjaList((await session.compute(expr)).text);
          final rN = parseSymjaList(
            (await session.compute(
              approxExpr('Rationalize[$expr]', session.approximateDigits),
            )).text,
          );
          return [ToolText('对称点', '(${_pair(r, rN, 0)}, ${_pair(r, rN, 1)})')];
        }

        if (_mode == 1) {
          // 直线 Ax + By + C = 0 关于点 (x, y)：A、B 不变，C' = -2Ax - 2By - C
          final a = _need(f[0]);
          final b = _need(f[1]);
          final c = _need(f[2]);
          final x = _need(f[3]);
          final y = _need(f[4]);
          final expr =
              'With[{A=$a,B=$b,C=$c,x=$x,y=$y}, '
              '{A, B, -2*A*x-2*B*y-C}]';
          return [_line(await _withApprox(session, expr))];
        }

        // 原直线 Px + Qy + R = 0 关于对称轴 Ax + By + C = 0
        final p = _need(f[0]);
        final q = _need(f[1]);
        final rr = _need(f[2]);
        final a = _need(f[3]);
        final b = _need(f[4]);
        final c = _need(f[5]);
        final expr =
            'With[{P=$p,Q=$q,R=$rr,A=$a,B=$b,C=$c}, '
            'Module[{k=2*(P*A+Q*B)/(A^2+B^2)}, {P-A*k, Q-B*k, R-C*k}]]';
        return [_line(await _withApprox(session, expr))];
      },
    );
  }

  /// 精确值 + 近似值：每个分量各自配上自己的小数。
  Future<List<Object>> _withApprox(SymjaSession session, String expr) async {
    final r = parseSymjaList((await session.compute(expr)).text);
    final n = parseSymjaList(
      (await session.compute(
        approxExpr('Rationalize[$expr]', session.approximateDigits),
      )).text,
    );
    return [
      for (var i = 0; i < r.length; i++)
        withApprox('${r[i]}', i < n.length ? '${n[i]}' : ''),
    ];
  }

  String _pair(List<Object> r, List<Object> n, int i) =>
      withApprox('${r[i]}', i < n.length ? '${n[i]}' : '');

  /// 把 Symja 回来的一串 {A, B, C} 拼成直线方程文本。
  ToolOutput _line(List<Object> r) =>
      ToolText('对称直线方程', '${r[0]}·x + ${r[1]}·y + ${r[2]} = 0');

  /// 取一个标量输入框：空着或填了多个值都直接报中文错。
  String _need(ToolField f) {
    if (f.count == 0) throw Exception('请填写「${f.label}」');
    if (f.count > 1) throw Exception('「${f.label}」只能填一个数');
    return f.text;
  }
}