From 1455c0b98c88dcae0026ca14252cbc0d867130ce Mon Sep 17 00:00:00 2001 From: LittleSheep Date: Tue, 16 Sep 2025 22:47:48 +0800 Subject: [PATCH] :sparkles: Support multi variables --- lib/solver.dart | 197 +++++++++++++++++++++++++++++++----------------- 1 file changed, 126 insertions(+), 71 deletions(-) diff --git a/lib/solver.dart b/lib/solver.dart index cd1e06c..ec850e2 100644 --- a/lib/solver.dart +++ b/lib/solver.dart @@ -37,8 +37,8 @@ class SolverService { for (int m = -100; m <= 100; m++) { for (int n = -100; n <= 100; n++) { if (m + n == -bb && m * n == cc) { - String factor1 = _formatFactorTerm(1, -m); - String factor2 = _formatFactorTerm(1, -n); + String factor1 = _formatFactorTerm(1, -m, 'x'); + String factor2 = _formatFactorTerm(1, -n, 'x'); return '($factor1)($factor2)'; } } @@ -65,15 +65,15 @@ class SolverService { } /// 格式化因式中的项 - String _formatFactorTerm(int coeff, int constTerm) { + String _formatFactorTerm(int coeff, int constTerm, [String variable = 'x']) { String result = ''; if (coeff != 0) { if (coeff == 1) - result += 'x'; + result += variable; else if (coeff == -1) - result += '-x'; + result += '-$variable'; else - result += '${coeff}x'; + result += '${coeff}$variable'; } if (constTerm != 0) { if (result.isNotEmpty) { @@ -89,15 +89,36 @@ class SolverService { return result; } + /// 检测方程中的变量 + Set _detectVariables(String input) { + final variablePattern = RegExp(r'\b([a-zA-Z])\b'); + final matches = variablePattern.allMatches(input); + return matches.map((match) => match.group(1)!).toSet(); + } + /// 主入口方法，识别并分发任务 CalculationResult solve(String input) { // 预处理输入字符串 final cleanInput = input.replaceAll(' ', '').toLowerCase(); - // 对包含x的方程进行预处理，展开表达式 + // 检测方程中的变量 + final variables = _detectVariables(cleanInput); + if (variables.isEmpty) { + // 如果没有变量，当作简单表达式处理 + try { + return _solveSimpleExpression(input); + } catch (e) { + throw Exception('无法识别的格式。请检查您的方程或表达式。'); + } + } + + // 获取主变量（第一个检测到的变量） + final mainVariable = variables.first; + + // 对包含变量的方程进行预处理，展开表达式 String processedInput = cleanInput; - if (processedInput.contains('x') && processedInput.contains('(')) { - processedInput = _expandExpressions(processedInput); + if (processedInput.contains(mainVariable) && processedInput.contains('(')) { + processedInput = _expandExpressions(processedInput, mainVariable); } // 0. 检查是否是 (expr)^n = constant 的形式（任意次幂） @@ -113,13 +134,19 @@ class SolverService { final rightValue = double.tryParse(rightStr); if (rightValue != null) { - return _solveGeneralPowerEquation(exprStr, n, rightValue, cleanInput); + return _solveGeneralPowerEquation( + exprStr, + n, + rightValue, + cleanInput, + mainVariable, + ); } } // 0.5. 检查是否是 a(expr)^2 = b 的形式（向后兼容） final squareEqMatch = RegExp( - r'^(\d*\.?\d*)\(([^)]+)\)\^2\s*=\s*(.+)$', + r'^(\d*\.?\d*)?\(([^)]+)\)\^2\s*=\s*(.+)$', ).firstMatch(cleanInput); if (squareEqMatch != null) { final coeffStr = squareEqMatch.group(1)!; @@ -132,14 +159,16 @@ class SolverService { // 解析右边 double right = double.parse(rightStr); - // 解析 expr 为 x ± h - final exprMatch = RegExp(r'x\s*([+-]\s*\d*\.?\d*)?').firstMatch(exprStr); + // 解析 expr 为 variable ± h + final exprMatch = RegExp( + r'$mainVariable\s*([+-]\s*\d*\.?\d*)?', + ).firstMatch(exprStr); if (exprMatch != null) { final hStr = exprMatch.group(1) ?? ''; double constant = hStr.isEmpty ? 0.0 : double.parse(hStr.replaceAll(' ', '')); - double h = -constant; // For (x - h)^2, h is the center + double h = -constant; // For (var - h)^2, h is the center // 使用有理数计算 final coeffRat = _rationalFromDouble(coeff); @@ -173,44 +202,49 @@ class SolverService { title: '开方', explanation: '对方程两边同时开平方。', formula: - '\$\$x ${h >= 0 ? '+' : ''}$h = \\pm \\sqrt{\\frac{${innerRat.numerator}}{${innerRat.denominator}}}\$\$', + '\$\$${mainVariable} ${h >= 0 ? '+' : ''}$h = \\pm \\sqrt{\\frac{${innerRat.numerator}}{${innerRat.denominator}}}\$\$', ), CalculationStep( stepNumber: 4, - title: '解出 x', - explanation: '分别取正负号，解出 x 的值。', - formula: '\$\$x_1 = $x1Str, \\quad x_2 = $x2Str\$\$', + title: '解出 ${mainVariable}', + explanation: '分别取正负号，解出 ${mainVariable} 的值。', + formula: + '\$\$${mainVariable}_1 = $x1Str, \\quad ${mainVariable}_2 = $x2Str\$\$', ), ], - finalAnswer: '\$\$x_1 = $x1Str, \\quad x_2 = $x2Str\$\$', + finalAnswer: + '\$\$${mainVariable}_1 = $x1Str, \\quad ${mainVariable}_2 = $x2Str\$\$', ); } } } - // 1. 检查是否为二元一次方程组 (格式: ...;...) - if (processedInput.contains(';') && - processedInput.contains('x') && - processedInput.contains('y')) { - return _solveSystemOfLinearEquations(processedInput); + // 1. 检查是否为多元一次方程组 (格式: ...;...) + if (processedInput.contains(';') && variables.length > 1) { + return _solveSystemOfLinearEquations(processedInput, variables); } - // 2. 检查是否为一元二次方程 (包含 x^2 或 x²) - if (processedInput.contains('x^2') || processedInput.contains('x²')) { - return _solveQuadraticEquation(processedInput.replaceAll('x²', 'x^2')); + // 2. 检查是否为一元二次方程 (包含 variable^2 或 variable²) + if (processedInput.contains('${mainVariable}^2') || + processedInput.contains('${mainVariable}²')) { + return _solveQuadraticEquation( + processedInput.replaceAll('${mainVariable}²', '${mainVariable}^2'), + mainVariable, + ); } - // 3. 检查是否为幂次方程 (x^n = a 的形式) - if (processedInput.contains('x^') && processedInput.contains('=')) { - return _solvePowerEquation(processedInput); + // 3. 检查是否为幂次方程 (variable^n = a 的形式) + if (processedInput.contains('${mainVariable}^') && + processedInput.contains('=')) { + return _solvePowerEquation(processedInput, mainVariable); } - // 4. 检查是否为一元一次方程 (包含 x 但不包含 y 或 x^2) - if (processedInput.contains('x') && !processedInput.contains('y')) { - return _solveLinearEquation(processedInput); + // 4. 检查是否为一元一次方程 (包含主变量) + if (processedInput.contains(mainVariable)) { + return _solveLinearEquation(processedInput, mainVariable); } - // 4. 如果都不是，则作为简单表达式计算 + // 如果都不是，则作为简单表达式计算 try { return _solveSimpleExpression(input); // 使用原始输入以保留运算符 } catch (e) { @@ -287,7 +321,10 @@ class SolverService { } /// 2. 求解一元一次方程 - CalculationResult _solveLinearEquation(String input) { + CalculationResult _solveLinearEquation( + String input, [ + String variable = 'x', + ]) { final steps = []; // Parse the input to get LaTeX-formatted version final parser = Parser(input); @@ -303,7 +340,7 @@ class SolverService { ), ); - final parts = _parseLinearEquation(input); + final parts = _parseLinearEquation(input, variable); final a = parts.a, b = parts.b, c = parts.c, d = parts.d; final newA = _rationalFromDouble(a) - _rationalFromDouble(c); @@ -313,9 +350,9 @@ class SolverService { CalculationStep( stepNumber: 1, title: '移项', - explanation: '将所有含 x 的项移到等式左边，常数项移到右边。', + explanation: '将所有含 ${variable} 的项移到等式左边，常数项移到右边。', formula: - '\$\$${a}x ${c >= 0 ? '-' : '+'} ${c.abs()}x = $d ${b >= 0 ? '-' : '+'} ${b.abs()}\$\$', + '\$\$${a}${variable} ${c >= 0 ? '-' : '+'} ${c.abs()}${variable} = $d ${b >= 0 ? '-' : '+'} ${b.abs()}\$\$', ), ); @@ -325,7 +362,7 @@ class SolverService { title: '合并同类项', explanation: '合并等式两边的项。', formula: - '\$\$${_formatNumber(newA.toDouble())}x = ${_formatNumber(newD.toDouble())}\$\$', + '\$\$${_formatNumber(newA.toDouble())}${variable} = ${_formatNumber(newD.toDouble())}\$\$', ), ); @@ -340,17 +377,23 @@ class SolverService { steps.add( CalculationStep( stepNumber: 3, - title: '求解 x', - explanation: '两边同时除以 x 的系数 ($newA)。', - formula: '\$\$x = \\frac{$newD}{$newA}\$\$', + title: '求解 ${variable}', + explanation: '两边同时除以 ${variable} 的系数 ($newA)。', + formula: '\$\$${variable} = \\frac{$newD}{$newA}\$\$', ), ); - return CalculationResult(steps: steps, finalAnswer: '\$\$x = $x\$\$'); + return CalculationResult( + steps: steps, + finalAnswer: '\$\$${variable} = $x\$\$', + ); } /// 3. 求解一元二次方程 (升级版) - CalculationResult _solveQuadraticEquation(String input) { + CalculationResult _solveQuadraticEquation( + String input, [ + String variable = 'x', + ]) { final steps = []; final eqParts = input.split('='); @@ -376,8 +419,8 @@ class SolverService { // ); // Also get numeric values for calculations - final leftCoeffs = _parsePolynomial(eqParts[0]); - final rightCoeffs = _parsePolynomial(eqParts[1]); + final leftCoeffs = _parsePolynomial(eqParts[0], variable); + final rightCoeffs = _parsePolynomial(eqParts[1], variable); final a = (leftCoeffs[2] ?? 0) - (rightCoeffs[2] ?? 0); final b = (leftCoeffs[1] ?? 0) - (rightCoeffs[1] ?? 0); final c = (leftCoeffs[0] ?? 0) - (rightCoeffs[0] ?? 0); @@ -579,6 +622,7 @@ class SolverService { int n, double rightValue, String originalInput, + String variable, ) { final steps = []; @@ -666,8 +710,8 @@ class SolverService { } } - /// 3.6. 求解幂次方程 (x^n = a 的形式) - CalculationResult _solvePowerEquation(String input) { + /// 3.6. 求解幂次方程 (variable^n = a 的形式) + CalculationResult _solvePowerEquation(String input, [String variable = 'x']) { final steps = []; // 解析方程 @@ -677,10 +721,12 @@ class SolverService { final leftSide = parts[0].trim(); final rightSide = parts[1].trim(); - // 检查左边是否为 x^n 的形式 - final powerMatch = RegExp(r'^x\^(\d+)$').firstMatch(leftSide); + // 检查左边是否为 variable^n 的形式 + final powerMatch = RegExp( + r'^${RegExp.escape(variable)}\^(\d+)$', + ).firstMatch(leftSide); if (powerMatch == null) { - throw Exception("不支持的幂次方程格式。当前支持 x^n = a 的形式。"); + throw Exception("不支持的幂次方程格式。当前支持 ${variable}^n = a 的形式。"); } final n = int.parse(powerMatch.group(1)!); @@ -711,8 +757,8 @@ class SolverService { CalculationStep( stepNumber: 2, title: '对方程两边同时开 $n 次方', - explanation: '对方程两边同时开 $n 次方以解出 x。', - formula: '\$\$x = \\sqrt[$n]{$a}\$\$', + explanation: '对方程两边同时开 $n 次方以解出 ${variable}。', + formula: '\$\$${variable} = \\sqrt[$n]{$a}\$\$', ), ); @@ -740,18 +786,21 @@ class SolverService { stepNumber: 3, title: '计算结果', explanation: '计算开 $n 次方的结果。', - formula: '\$\$x = $resultStr\$\$', + formula: '\$\$${variable} = $resultStr\$\$', ), ); return CalculationResult( steps: steps, - finalAnswer: '\$\$x = $resultStr\$\$', + finalAnswer: '\$\$${variable} = $resultStr\$\$', ); } /// 4. 求解二元一次方程组 - CalculationResult _solveSystemOfLinearEquations(String input) { + CalculationResult _solveSystemOfLinearEquations( + String input, [ + Set variables = const {'x', 'y'}, + ]) { final steps = []; final equations = input.split(';'); if (equations.length != 2) throw Exception("格式错误, 请用 ';' 分隔两个方程。"); @@ -998,7 +1047,7 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} /// ---- 辅助函数 ---- - String _expandExpressions(String input) { + String _expandExpressions(String input, [String variable = 'x']) { String result = input; int maxIterations = 10; // Prevent infinite loops int iterationCount = 0; @@ -1017,7 +1066,7 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} } final factor = powerMatch.group(2)!; - final coeffs = _parsePolynomial(factor); + final coeffs = _parsePolynomial(factor, variable); final a = coeffs[1] ?? 0; final b = coeffs[0] ?? 0; @@ -1040,8 +1089,8 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} final factor2 = factorMulMatch.group(2)!; log('Expanding: ($factor1) * ($factor2)'); - final coeffs1 = _parsePolynomial(factor1); - final coeffs2 = _parsePolynomial(factor2); + final coeffs1 = _parsePolynomial(factor1, variable); + final coeffs2 = _parsePolynomial(factor2, variable); log('Coeffs1: $coeffs1, Coeffs2: $coeffs2'); final a = coeffs1[1] ?? 0; @@ -1078,8 +1127,8 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} } // Parse the term (coefficient and x power) - final termCoeffs = _parsePolynomial(termStr); - final factorCoeffs = _parsePolynomial(factorStr); + final termCoeffs = _parsePolynomial(termStr, variable); + final factorCoeffs = _parsePolynomial(factorStr, variable); final termA = termCoeffs[1] ?? 0; // x coefficient final termB = termCoeffs[0] ?? 0; // constant term @@ -1122,8 +1171,8 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} final rightSide = parts[1]; // 解析左边的多项式 - final leftCoeffs = _parsePolynomial(leftSide); - final rightCoeffs = _parsePolynomial(rightSide); + final leftCoeffs = _parsePolynomial(leftSide, variable); + final rightCoeffs = _parsePolynomial(rightSide, variable); // 计算标准形式 ax^2 + bx + c = 0 的系数 // A = B 转换为 A - B = 0，所以右边的系数要取相反数 @@ -1165,12 +1214,15 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} return result; } - LinearEquationParts _parseLinearEquation(String input) { + LinearEquationParts _parseLinearEquation( + String input, [ + String variable = 'x', + ]) { final parts = input.split('='); if (parts.length != 2) throw Exception("方程格式错误，应包含一个'='。"); - final leftCoeffs = _parsePolynomial(parts[0]); - final rightCoeffs = _parsePolynomial(parts[1]); + final leftCoeffs = _parsePolynomial(parts[0], variable); + final rightCoeffs = _parsePolynomial(parts[1], variable); return LinearEquationParts( (leftCoeffs[1] ?? 0.0), @@ -1180,7 +1232,7 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} ); } - Map _parsePolynomial(String side) { + Map _parsePolynomial(String side, [String variable = 'x']) { final coeffs = {}; // 如果输入包含括号，去掉括号 @@ -1189,9 +1241,12 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} cleanSide = cleanSide.substring(1, cleanSide.length - 1); } - // 扩展模式以支持 sqrt 函数 + // 扩展模式以支持 sqrt 函数，使用动态变量 + final escapedVar = RegExp.escape(variable); final pattern = RegExp( - r'([+-]?(?:\d*\.?\d*|sqrt\(\d+\)))x(?:\^(\d+))?|([+-]?(?:\d*\.?\d*|sqrt\(\d+\)))', + r'([+-]?(?:\d*\.?\d*|sqrt\(\d+\)))' + + escapedVar + + r'(?:\^(\d+))?|([+-]?(?:\d*\.?\d*|sqrt\(\d+\)))', ); var s = cleanSide.startsWith('+') || cleanSide.startsWith('-') ? cleanSide @@ -1206,7 +1261,7 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} final constValue = _parseCoefficientWithSqrt(constStr); coeffs[0] = (coeffs[0] ?? 0) + constValue; } else { - // x 的幂次项 + // 变量的幂次项 int power = match.group(2) != null ? int.parse(match.group(2)!) : 1; String coeffStr = match.group(1) ?? '+'; final coeff = _parseCoefficientWithSqrt(coeffStr);