diff --git a/lib/solver.dart b/lib/solver.dart index eb3b7a7..a2f25dc 100644 --- a/lib/solver.dart +++ b/lib/solver.dart @@ -401,25 +401,6 @@ class SolverService { final eqParts = input.split('='); if (eqParts.length != 2) throw Exception("方程格式错误，应包含一个 '='。"); - // Keep original equation for display - final originalEquation = _formatOriginalEquation(input); - - // Parse coefficients symbolically (kept for potential future use) - // final leftCoeffsSymbolic = _parsePolynomialSymbolic(eqParts[0]); - // final rightCoeffsSymbolic = _parsePolynomialSymbolic(eqParts[1]); - // final aSymbolic = _subtractCoefficients( - // leftCoeffsSymbolic[2] ?? '0', - // rightCoeffsSymbolic[2] ?? '0', - // ); - // final bSymbolic = _subtractCoefficients( - // leftCoeffsSymbolic[1] ?? '0', - // rightCoeffsSymbolic[1] ?? '0', - // ); - // final cSymbolic = _subtractCoefficients( - // leftCoeffsSymbolic[0] ?? '0', - // rightCoeffsSymbolic[0] ?? '0', - // ); - // Also get numeric values for calculations final leftCoeffs = _parsePolynomial(eqParts[0], variable); final rightCoeffs = _parsePolynomial(eqParts[1], variable); @@ -431,12 +412,15 @@ class SolverService { return _solveLinearEquation('${b}x+$c=0'); } + // Create expanded equation display + final expandedEquation = _formatExpandedEquation(input); + steps.add( CalculationStep( stepNumber: 1, title: '整理方程', explanation: r'将方程整理成标准形式 $ax^2+bx+c=0$。', - formula: originalEquation, + formula: expandedEquation, ), ); @@ -1406,136 +1390,59 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} int gcd(int a, int b) => b == 0 ? a : gcd(b, a % b); - /// 格式化原始方程，保持符号形式 - String _formatOriginalEquation(String input) { - // Parse the equation and convert to LaTeX + /// 格式化展开后的方程 + String _formatExpandedEquation(String input) { + // The input is already expanded, so we just need to format it for LaTeX display String result = input.replaceAll(' ', ''); - // 确保方程格式正确 + // Ensure equation format is correct if (!result.contains('=')) { result = '$result=0'; } final parts = result.split('='); if (parts.length == 2) { - // Check if the equation is already in standard polynomial form - // If it doesn't contain parentheses and looks like a standard polynomial, - // return it as-is to avoid unnecessary parsing - final leftSide = parts[0]; - final rightSide = parts[1]; + // Clean up the expanded expression directly without re-parsing + // to avoid adding unnecessary parentheses + String leftStr = _cleanExpandedExpressionForDisplay(parts[0]); + String rightStr = _cleanExpandedExpressionForDisplay(parts[1]); - // If left side is a standard polynomial (no parentheses, only x^2, x, and constants) - // and right side is 0, return the original - if (_isStandardPolynomial(leftSide) && - (rightSide == '0' || rightSide.isEmpty)) { - result = '$leftSide=0'; - return '\$\$$result\$\$'; - } - - try { - final leftParser = Parser(parts[0]); - final leftExpr = leftParser.parse(); - final rightParser = Parser(parts[1]); - final rightExpr = rightParser.parse(); - - // Get the string representation and clean it up - String leftStr = leftExpr.toString().replaceAll('*', '\\cdot'); - String rightStr = rightExpr.toString().replaceAll('*', '\\cdot'); - - // Clean up unnecessary parentheses - leftStr = _cleanParentheses(leftStr); - rightStr = _cleanParentheses(rightStr); - - result = '$leftStr=$rightStr'; - } catch (e) { - // Fallback to original if parsing fails - result = result.replaceAll('sqrt(', '\\sqrt{'); - result = result.replaceAll(')', '}'); - } - } else { - try { - final parser = Parser(result.split('=')[0]); - final expr = parser.parse(); - - // Get the string representation and clean it up - String exprStr = expr.toString().replaceAll('*', '\\cdot'); - exprStr = _cleanParentheses(exprStr); - - result = '$exprStr=0'; - } catch (e) { - // Fallback - result = result.replaceAll('sqrt(', '\\sqrt{'); - result = result.replaceAll(')', '}'); - } + result = '$leftStr=$rightStr'; } return '\$\$$result\$\$'; } - /// 检查字符串是否为标准多项式形式（不含括号，只有x^2、x和常数项） - bool _isStandardPolynomial(String expr) { - // Remove spaces - final cleanExpr = expr.replaceAll(' ', ''); + /// 清理展开后的表达式用于显示，去除不必要的括号 + String _cleanExpandedExpressionForDisplay(String expr) { + String result = expr; - // If it contains parentheses, it's not standard - if (cleanExpr.contains('(') || cleanExpr.contains(')')) { - return false; - } - - // Check if it matches the pattern of a standard polynomial - // Should only contain: digits, x, ^, +, -, and spaces (already removed) - final validChars = RegExp(r'^[0-9x\^\+\-\.]*$'); - if (!validChars.hasMatch(cleanExpr)) { - return false; - } - - // Should not have complex expressions like x*x or 2x*3 - if (cleanExpr.contains('*') || cleanExpr.contains('/')) { - return false; - } - - // Should have proper x^2 format (not xx or x2) - if (cleanExpr.contains('x^2') || - cleanExpr.contains('x^3') || - cleanExpr.contains('x^4')) { - // This is likely a polynomial - return true; - } - - // Check for simple terms like x, 2x, x+1, etc. - final termPattern = RegExp( - r'^[+-]?(?:\d*\.?\d*)?x?(?:\^\d+)?(?:[+-][+-]?(?:\d*\.?\d*)?x?(?:\^\d+)?)*$', - ); - return termPattern.hasMatch(cleanExpr); - } - - /// 清理不必要的括号 - String _cleanParentheses(String expr) { - // 移除最外层的括号，如果它们不影响运算顺序 - if (expr.startsWith('(') && expr.endsWith(')')) { - String inner = expr.substring(1, expr.length - 1); - - // 检查移除括号是否会改变含义 - // 简单检查：如果内部没有运算符，或者只有加减号，可以移除 - if (!inner.contains('+') && - !inner.contains('-') && - !inner.contains('*') && - !inner.contains('/')) { - return inner; - } - - // 如果内部表达式是简单的，可以移除括号 - // 例如：(x+1) 可以变成 x+1, 但 (x+1)*(x-1) 不能移除 - final operators = RegExp(r'[+\-*/]'); - final matches = operators.allMatches(inner).toList(); - - // 如果只有一个运算符且是加减号，可以移除 - if (matches.length == 1 && (inner.contains('+') || inner.contains('-'))) { - return inner; + // 移除最外层的括号，如果它们包围整个表达式 + if (result.startsWith('(') && result.endsWith(')')) { + String inner = result.substring(1, result.length - 1); + // 检查内部是否包含运算符，如果不包含或只包含加减号，可以移除括号 + if (!inner.contains('*') && !inner.contains('/')) { + // 对于加减号，检查是否只有一个运算符 + final plusMinusCount = + '+'.allMatches(inner).length + '-'.allMatches(inner).length; + if (plusMinusCount <= 1) { + result = inner; + } } } - return expr; + // 移除内部不必要的括号 + result = result.replaceAll('(+', '('); + result = result.replaceAll('(-', '('); + + // 格式化乘法符号 + result = result.replaceAll('*', '\\cdot'); + + // 处理根号 + result = result.replaceAll('sqrt(', '\\sqrt{'); + result = result.replaceAll(')', '}'); + + return result; } /// 清理展开后的表达式格式