🐛 Fix expressions
This commit is contained in:
167
lib/solver.dart
167
lib/solver.dart
@@ -401,25 +401,6 @@ class SolverService {
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final eqParts = input.split('=');
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if (eqParts.length != 2) throw Exception("方程格式错误，应包含一个 '='。");
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// Keep original equation for display
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final originalEquation = _formatOriginalEquation(input);
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// Parse coefficients symbolically (kept for potential future use)
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// final leftCoeffsSymbolic = _parsePolynomialSymbolic(eqParts[0]);
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// final rightCoeffsSymbolic = _parsePolynomialSymbolic(eqParts[1]);
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// final aSymbolic = _subtractCoefficients(
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// leftCoeffsSymbolic[2] ?? '0',
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// rightCoeffsSymbolic[2] ?? '0',
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// );
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// final bSymbolic = _subtractCoefficients(
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// leftCoeffsSymbolic[1] ?? '0',
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// rightCoeffsSymbolic[1] ?? '0',
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// );
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// final cSymbolic = _subtractCoefficients(
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// leftCoeffsSymbolic[0] ?? '0',
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// rightCoeffsSymbolic[0] ?? '0',
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// );
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// Also get numeric values for calculations
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final leftCoeffs = _parsePolynomial(eqParts[0], variable);
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final rightCoeffs = _parsePolynomial(eqParts[1], variable);
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@@ -431,12 +412,15 @@ class SolverService {
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return _solveLinearEquation('${b}x+$c=0');
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}
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// Create expanded equation display
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final expandedEquation = _formatExpandedEquation(input);
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steps.add(
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CalculationStep(
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stepNumber: 1,
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title: '整理方程',
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explanation: r'将方程整理成标准形式 $ax^2+bx+c=0$。',
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formula: originalEquation,
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formula: expandedEquation,
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),
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);
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@@ -1406,136 +1390,59 @@ ${b1}y &= ${c1 - a1 * x.toDouble()}
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int gcd(int a, int b) => b == 0 ? a : gcd(b, a % b);
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/// 格式化原始方程，保持符号形式
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String _formatOriginalEquation(String input) {
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// Parse the equation and convert to LaTeX
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/// 格式化展开后的方程
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String _formatExpandedEquation(String input) {
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// The input is already expanded, so we just need to format it for LaTeX display
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String result = input.replaceAll(' ', '');
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// 确保方程格式正确
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// Ensure equation format is correct
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if (!result.contains('=')) {
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result = '$result=0';
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}
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final parts = result.split('=');
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if (parts.length == 2) {
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// Check if the equation is already in standard polynomial form
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// If it doesn't contain parentheses and looks like a standard polynomial,
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// return it as-is to avoid unnecessary parsing
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final leftSide = parts[0];
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final rightSide = parts[1];
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// If left side is a standard polynomial (no parentheses, only x^2, x, and constants)
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// and right side is 0, return the original
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if (_isStandardPolynomial(leftSide) &&
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(rightSide == '0' || rightSide.isEmpty)) {
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result = '$leftSide=0';
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return '\$\$$result\$\$';
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}
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try {
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final leftParser = Parser(parts[0]);
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final leftExpr = leftParser.parse();
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final rightParser = Parser(parts[1]);
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final rightExpr = rightParser.parse();
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// Get the string representation and clean it up
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String leftStr = leftExpr.toString().replaceAll('*', '\\cdot');
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String rightStr = rightExpr.toString().replaceAll('*', '\\cdot');
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// Clean up unnecessary parentheses
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leftStr = _cleanParentheses(leftStr);
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rightStr = _cleanParentheses(rightStr);
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// Clean up the expanded expression directly without re-parsing
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// to avoid adding unnecessary parentheses
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String leftStr = _cleanExpandedExpressionForDisplay(parts[0]);
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String rightStr = _cleanExpandedExpressionForDisplay(parts[1]);
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result = '$leftStr=$rightStr';
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} catch (e) {
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// Fallback to original if parsing fails
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result = result.replaceAll('sqrt(', '\\sqrt{');
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result = result.replaceAll(')', '}');
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}
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} else {
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try {
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final parser = Parser(result.split('=')[0]);
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final expr = parser.parse();
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// Get the string representation and clean it up
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String exprStr = expr.toString().replaceAll('*', '\\cdot');
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exprStr = _cleanParentheses(exprStr);
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result = '$exprStr=0';
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} catch (e) {
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// Fallback
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result = result.replaceAll('sqrt(', '\\sqrt{');
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result = result.replaceAll(')', '}');
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}
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}
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return '\$\$$result\$\$';
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}
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/// 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）
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bool _isStandardPolynomial(String expr) {
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// Remove spaces
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final cleanExpr = expr.replaceAll(' ', '');
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/// 清理展开后的表达式用于显示，去除不必要的括号
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String _cleanExpandedExpressionForDisplay(String expr) {
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String result = expr;
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// If it contains parentheses, it's not standard
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if (cleanExpr.contains('(') || cleanExpr.contains(')')) {
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return false;
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// 移除最外层的括号，如果它们包围整个表达式
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if (result.startsWith('(') && result.endsWith(')')) {
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String inner = result.substring(1, result.length - 1);
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// 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
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if (!inner.contains('*') && !inner.contains('/')) {
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// 对于加减号，检查是否只有一个运算符
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final plusMinusCount =
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'+'.allMatches(inner).length + '-'.allMatches(inner).length;
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if (plusMinusCount <= 1) {
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result = inner;
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}
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// Check if it matches the pattern of a standard polynomial
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// Should only contain: digits, x, ^, +, -, and spaces (already removed)
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final validChars = RegExp(r'^[0-9x\^\+\-\.]*$');
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if (!validChars.hasMatch(cleanExpr)) {
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return false;
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}
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// Should not have complex expressions like x*x or 2x*3
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if (cleanExpr.contains('*') || cleanExpr.contains('/')) {
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return false;
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}
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// Should have proper x^2 format (not xx or x2)
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if (cleanExpr.contains('x^2') ||
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cleanExpr.contains('x^3') ||
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cleanExpr.contains('x^4')) {
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// This is likely a polynomial
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return true;
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}
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// Check for simple terms like x, 2x, x+1, etc.
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final termPattern = RegExp(
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r'^[+-]?(?:\d*\.?\d*)?x?(?:\^\d+)?(?:[+-][+-]?(?:\d*\.?\d*)?x?(?:\^\d+)?)*$',
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);
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return termPattern.hasMatch(cleanExpr);
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}
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/// 清理不必要的括号
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String _cleanParentheses(String expr) {
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// 移除最外层的括号，如果它们不影响运算顺序
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if (expr.startsWith('(') && expr.endsWith(')')) {
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String inner = expr.substring(1, expr.length - 1);
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// 检查移除括号是否会改变含义
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// 简单检查：如果内部没有运算符，或者只有加减号，可以移除
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if (!inner.contains('+') &&
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!inner.contains('-') &&
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!inner.contains('*') &&
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!inner.contains('/')) {
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return inner;
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}
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// 如果内部表达式是简单的，可以移除括号
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// 例如：(x+1) 可以变成 x+1, 但 (x+1)*(x-1) 不能移除
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final operators = RegExp(r'[+\-*/]');
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final matches = operators.allMatches(inner).toList();
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// 如果只有一个运算符且是加减号，可以移除
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if (matches.length == 1 && (inner.contains('+') || inner.contains('-'))) {
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return inner;
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}
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}
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return expr;
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// 移除内部不必要的括号
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result = result.replaceAll('(+', '(');
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result = result.replaceAll('(-', '(');
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// 格式化乘法符号
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result = result.replaceAll('*', '\\cdot');
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// 处理根号
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result = result.replaceAll('sqrt(', '\\sqrt{');
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result = result.replaceAll(')', '}');
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return result;
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}
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/// 清理展开后的表达式格式
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