mathtool/lib/utils/math_utils.dart

// utils/math_utils.dart
import 'package:rational/rational.dart';

class MathUtils {
  // 添加常量
  static final Rational zero = Rational.zero;
  static final Rational one = Rational.one;
  static final Rational two = Rational.fromInt(2);
  static final Rational half = Rational.fromInt(1) / Rational.fromInt(2);

  static Rational parseRational(String input) {
    try {
      // 去除空格
      input = input.trim();
      
      if (input.contains('/')) {
        List<String> parts = input.split('/');
        if (parts.length == 2) {
          String numerator = parts[0].trim();
          String denominator = parts[1].trim();
          
          // 修复：直接使用 Rational 构造函数而不是 parse
          BigInt num = BigInt.parse(numerator);
          BigInt den = BigInt.parse(denominator);
          
          if (den == BigInt.zero) {
            throw FormatException('分母不能为零');
          }
          
          return Rational(num, den);
        }
      }
      
      // 处理小数
      if (input.contains('.')) {
        return _decimalToRational(input);
      }
      
      // 处理整数
      return Rational.parse(input);
    } catch (e) {
      throw FormatException('无效的分数格式: $input');
    }
  }

  static Rational _decimalToRational(String decimalStr) {
    // 更精确的小数转分数实现
    if (!decimalStr.contains('.')) {
      return Rational.parse(decimalStr);
    }
    
    List<String> parts = decimalStr.split('.');
    String integerPart = parts[0];
    String decimalPart = parts[1];
    
    // 处理负号
    bool isNegative = integerPart.startsWith('-');
    if (isNegative) {
      integerPart = integerPart.substring(1);
    }
    
    // 如果整数部分是空的，设为0
    if (integerPart.isEmpty) {
      integerPart = '0';
    }
    
    // 计算分母：10的decimalPart长度次方
    BigInt denominator = BigInt.from(10).pow(decimalPart.length);
    // 计算分子：整数部分 * 分母 + 小数部分
    BigInt numerator = 
        BigInt.parse(integerPart) * denominator + BigInt.parse(decimalPart);
    
    if (isNegative) {
      numerator = -numerator;
    }
    
    return Rational(numerator, denominator);
  }

  static String rationalToString(Rational rational) {
    // 简化分数显示
    if (rational.denominator == BigInt.one) {
      return rational.numerator.toString();
    }
    
    // 尝试约分
    Rational simplified = rational;
    
    return '${simplified.numerator}/${simplified.denominator}';
  }

  static Rational det2(Rational a, Rational b, Rational c, Rational d) {
    return a * d - b * c;
  }

  static List<Rational> solveLinear2(
    Rational a1, Rational b1, Rational c1,
    Rational a2, Rational b2, Rational c2,
  ) {
    final det = det2(a1, b1, a2, b2);
    if (det == zero) {
      throw Exception('方程组无解或有无穷多解');
    }
    final x = det2(c1, b1, c2, b2) / det;
    final y = det2(a1, c1, a2, c2) / det;
    return [x, y];
  }

  // 创建 Rational 从 BigInt
  static Rational fromBigInt(BigInt value) {
    return Rational(value);
  }

  // 创建 Rational 从 int
  static Rational fromInt(int value) {
    return Rational.fromInt(value);
  }
  
  // 计算最大公约数
  static BigInt _gcd(BigInt a, BigInt b) {
    while (b != BigInt.zero) {
      final temp = b;
      b = a % b;
      a = temp;
    }
    return a;
  }
}