mathtool2/lib/tools/circle_equation.dart

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

import 'tool_kit.dart';

/// 圆的方程 —— 过三点的圆。
///
/// 设圆为 x² + y² + Dx + Ey + F = 0，把三个点代进去解 D、E、F。
/// 未知量在 Symja 侧用 dd/ee/ff 命名（D、E 是 Symja 的内置名）。
/// 三点共线时 Symja 的 Solve 返回空集，我们的表达式直接回一句中文说明。
class CircleEquationPage extends StatefulWidget {
  const CircleEquationPage({super.key});

  @override
  State<CircleEquationPage> createState() => _CircleEquationPageState();
}

class _CircleEquationPageState extends State<CircleEquationPage> {
  final _x1 = ToolField('点1 x', hint: '分数如 1/2，或小数');
  // 点的横纵坐标是一对，并排一行
  final _y1 = ToolField('点1 y', hint: '分数如 1/2，或小数', rowWithPrevious: true);
  final _x2 = ToolField('点2 x', hint: '分数如 1/2，或小数');
  // 点的横纵坐标是一对，并排一行
  final _y2 = ToolField('点2 y', hint: '分数如 1/2，或小数', rowWithPrevious: true);
  final _x3 = ToolField('点3 x', hint: '分数如 1/2，或小数');
  // 点的横纵坐标是一对，并排一行
  final _y3 = ToolField('点3 y', hint: '分数如 1/2，或小数', rowWithPrevious: true);

  @override
  Widget build(BuildContext context) => ToolScaffold(
    title: '圆的方程',
    fields: [_x1, _y1, _x2, _y2, _x3, _y3],
    compute: (session) async {
      final bind =
          'x1=${_need(_x1)},y1=${_need(_y1)},'
          'x2=${_need(_x2)},y2=${_need(_y2)},'
          'x3=${_need(_x3)},y3=${_need(_y3)}';
      final eqs =
          '{x1^2+y1^2+dd*x1+ee*y1+ff==0, '
          'x2^2+y2^2+dd*x2+ee*y2+ff==0, '
          'x3^2+y3^2+dd*x3+ee*y3+ff==0}';
      const noCircle = '"三点共线（没有外接圆）"';

      // 三个系数
      final defExpr =
          'With[{$bind}, Module[{s}, s=Solve[$eqs,{dd,ee,ff}]; '
          'If[s==={}, $noCircle, {dd,ee,ff} /. First[s]]]]';
      final defs = parseSymjaList((await session.compute(defExpr)).text);
      if (defs.length != 3) {
        // 共线：Symja 返回的就是那句中文，直接显示。
        return [ToolText('结果', '${defs.isEmpty ? '' : defs.first}')];
      }

      // 圆心 (-dd/2, -ee/2) 与半径平方 (dd²+ee²-4ff)/4
      final centerExpr =
          'With[{$bind}, Module[{s}, s=Solve[$eqs,{dd,ee,ff}]; '
          'If[s==={}, $noCircle, '
          '{-dd/2, -ee/2, (dd^2+ee^2-4*ff)/4} /. First[s]]]]';

      // 精确值 + 近似值都要：系数和圆心半径都是分数，小数形式有时更直观
      final defsN = parseSymjaList(
        (await session.compute('N[Rationalize[$defExpr], ${session.approximateDigits}]')).text,
      );
      final center = parseSymjaList((await session.compute(centerExpr)).text);
      final centerN = parseSymjaList(
        (await session.compute('N[Rationalize[$centerExpr], ${session.approximateDigits}]')).text,
      );

      String at(List<Object> l, int i) => i < l.length ? '${l[i]}' : '';

      final out = <ToolOutput>[
        ToolText('D', withApprox('${defs[0]}', at(defsN, 0))),
        ToolText('E', withApprox('${defs[1]}', at(defsN, 1))),
        ToolText('F', withApprox('${defs[2]}', at(defsN, 2))),
      ];
      if (center.length == 3) {
        // 圆心是坐标，两个分量各自配自己的近似值
        out.add(
          ToolText(
            '圆心',
            '(${withApprox('${center[0]}', at(centerN, 0))}, '
                '${withApprox('${center[1]}', at(centerN, 1))})',
          ),
        );
        out.add(ToolText('半径平方', withApprox('${center[2]}', at(centerN, 2))));
      }
      return out;
    },
  );

  /// 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;
  }
}