mathhook-core 0.2.0

[
  {
    "id": "basic_add_latex",
    "input": "x + y",
    "language": "latex",
    "category": "basic_arithmetic",
    "description": "Simple addition",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "x + y",
    "formatted_wolfram": "Plus[x, y]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "basic_sub_latex",
    "input": "x - y",
    "language": "latex",
    "category": "basic_arithmetic",
    "description": "Subtraction",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "x - y",
    "formatted_wolfram": "Subtract[x, y]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "basic_mul_latex",
    "input": "x \\cdot y",
    "language": "latex",
    "category": "basic_arithmetic",
    "description": "Multiplication",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "x \\cdot y",
    "formatted_wolfram": "Times[x, y]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "basic_div_latex",
    "input": "\\frac{x}{y}",
    "language": "latex",
    "category": "basic_arithmetic",
    "description": "Division as fraction",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\frac{x}{y}",
    "formatted_wolfram": "Divide[x, y]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "basic_add_wolfram",
    "input": "x + y",
    "language": "wolfram",
    "category": "basic_arithmetic",
    "description": "Simple addition",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "x + y",
    "formatted_wolfram": "Plus[x, y]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "basic_mul_wolfram",
    "input": "Times[x, y]",
    "language": "wolfram",
    "category": "basic_arithmetic",
    "description": "Times function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "x \\cdot y",
    "formatted_wolfram": "Times[x, y]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "basic_div_wolfram",
    "input": "x / y",
    "language": "wolfram",
    "category": "basic_arithmetic",
    "description": "Division",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\frac{x}{y}",
    "formatted_wolfram": "Divide[x, y]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "simple_fraction_latex",
    "input": "\\frac{1}{2}",
    "language": "latex",
    "category": "fractions",
    "description": "Simple fraction",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\frac{1}{2}",
    "formatted_wolfram": "Times[1, Power[2, -1]]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "simple_power_latex",
    "input": "x^2",
    "language": "latex",
    "category": "powers_roots",
    "description": "Simple power",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "x^2",
    "formatted_wolfram": "Power[x, 2]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "sqrt_latex",
    "input": "\\sqrt{x}",
    "language": "latex",
    "category": "powers_roots",
    "description": "Square root",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sqrt{x}",
    "formatted_wolfram": "Sqrt[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "exponential_latex",
    "input": "e^x",
    "language": "latex",
    "category": "powers_roots",
    "description": "Exponential with e constant",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "e^x",
    "formatted_wolfram": "Power[E, x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "simple_power_wolfram",
    "input": "x^2",
    "language": "wolfram",
    "category": "powers_roots",
    "description": "Simple power",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "x^2",
    "formatted_wolfram": "Power[x, 2]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": false
  },
  {
    "id": "sqrt_wolfram",
    "input": "Sqrt[x]",
    "language": "wolfram",
    "category": "powers_roots",
    "description": "Square root",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sqrt{x}",
    "formatted_wolfram": "Sqrt[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "exponential_wolfram",
    "input": "Exp[x]",
    "language": "wolfram",
    "category": "powers_roots",
    "description": "Exponential function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\exp(x)",
    "formatted_wolfram": "Exp[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "sin_latex",
    "input": "\\sin(x)",
    "language": "latex",
    "category": "trigonometric",
    "description": "Sine function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sin(x)",
    "formatted_wolfram": "Sin[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "cos_latex",
    "input": "\\cos(x)",
    "language": "latex",
    "category": "trigonometric",
    "description": "Cosine function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\cos(x)",
    "formatted_wolfram": "Cos[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "sin_wolfram",
    "input": "Sin[x]",
    "language": "wolfram",
    "category": "trigonometric",
    "description": "Sine function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sin(x)",
    "formatted_wolfram": "Sin[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "cos_wolfram",
    "input": "Cos[x]",
    "language": "wolfram",
    "category": "trigonometric",
    "description": "Cosine function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\cos(x)",
    "formatted_wolfram": "Cos[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "ln_latex",
    "input": "\\ln(x)",
    "language": "latex",
    "category": "logarithmic",
    "description": "Natural logarithm",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\ln(x)",
    "formatted_wolfram": "Log[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "log_latex",
    "input": "\\log(x)",
    "language": "latex",
    "category": "logarithmic",
    "description": "Common logarithm",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\log(x)",
    "formatted_wolfram": "Log[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "ln_wolfram",
    "input": "Log[x]",
    "language": "wolfram",
    "category": "logarithmic",
    "description": "Natural logarithm",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\log(x)",
    "formatted_wolfram": "Log[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "pi_constant_latex",
    "input": "\\pi",
    "language": "latex",
    "category": "mathematical_constants",
    "description": "Pi constant",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\pi",
    "formatted_wolfram": "Pi",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "e_constant_latex",
    "input": "e",
    "language": "latex",
    "category": "mathematical_constants",
    "description": "Euler's number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "e",
    "formatted_wolfram": "E",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "i_constant_latex",
    "input": "i",
    "language": "latex",
    "category": "mathematical_constants",
    "description": "Imaginary unit",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "i",
    "formatted_wolfram": "I",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "infinity_latex",
    "input": "\\infty",
    "language": "latex",
    "category": "mathematical_constants",
    "description": "Infinity",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\infty",
    "formatted_wolfram": "Infinity",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "pi_constant_wolfram",
    "input": "Pi",
    "language": "wolfram",
    "category": "mathematical_constants",
    "description": "Pi constant",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\pi",
    "formatted_wolfram": "Pi",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "e_constant_wolfram",
    "input": "E",
    "language": "wolfram",
    "category": "mathematical_constants",
    "description": "Euler's number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "e",
    "formatted_wolfram": "E",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "i_constant_wolfram",
    "input": "I",
    "language": "wolfram",
    "category": "mathematical_constants",
    "description": "Imaginary unit",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "i",
    "formatted_wolfram": "I",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "complex_number_wolfram",
    "input": "3 + 4*I",
    "language": "wolfram",
    "category": "complex_numbers",
    "description": "Complex number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "3 + 4i",
    "formatted_wolfram": "Plus[3, Times[4, I]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "derivative_latex",
    "input": "\\frac{d}{dx} x^2",
    "language": "latex",
    "category": "calculus_first_class",
    "description": "First derivative - FIRST CLASS",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(259, \\\"d\\\"), 7), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "integral_latex",
    "input": "\\int x dx",
    "language": "latex",
    "category": "calculus_first_class",
    "description": "Indefinite integral - FIRST CLASS",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (7, Token(2, \\\"dx\\\"), 9), expected: [\\\"LPAREN\\\", \\\"DOT\\\", \\\"LBRACKET\\\", \\\"SUBSCRIPT\\\", \\\"DIFFERENTIAL\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "definite_integral_latex",
    "input": "\\int_0^1 x dx",
    "language": "latex",
    "category": "calculus_first_class",
    "description": "Definite integral - FIRST CLASS",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (5, Token(0, \\\"0\\\"), 6), expected: [\\\"LBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "sum_latex",
    "input": "\\sum_{i=1}^n i^2",
    "language": "latex",
    "category": "calculus_first_class",
    "description": "Summation - FIRST CLASS",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (11, Token(2, \\\"n\\\"), 12), expected: [\\\"LBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "derivative_wolfram",
    "input": "D[x^2, x]",
    "language": "wolfram",
    "category": "calculus_first_class",
    "description": "First derivative - FIRST CLASS",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\frac{d}{dx} x^2",
    "formatted_wolfram": "D[Power[x, 2], x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": false
  },
  {
    "id": "integral_wolfram",
    "input": "Integrate[x, x]",
    "language": "wolfram",
    "category": "calculus_first_class",
    "description": "Indefinite integral - FIRST CLASS",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\int x \\, dx",
    "formatted_wolfram": "Integrate[x, x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "definite_integral_wolfram",
    "input": "Integrate[x, {x, 0, 1}]",
    "language": "wolfram",
    "category": "calculus_first_class",
    "description": "Definite integral - FIRST CLASS",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\int x \\, d\\{x, 0, 1\\}",
    "formatted_wolfram": "Integrate[x, {x, 0, 1}]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "limit_wolfram",
    "input": "Limit[Sin[x], x -> 0]",
    "language": "wolfram",
    "category": "calculus_first_class",
    "description": "Limit - FIRST CLASS",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "limit(\\sin(x), approaches(x, 0))",
    "formatted_wolfram": "Limit[Sin[x], approaches[x, 0]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "sum_wolfram",
    "input": "Sum[i^2, {i, 1, n}]",
    "language": "wolfram",
    "category": "calculus_first_class",
    "description": "Summation - FIRST CLASS",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sum(i^2, \\{i, 1, n\\})",
    "formatted_wolfram": "Sum[Power[I, 2], {I, 1, n}]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": false
  },
  {
    "id": "matrix_latex",
    "input": "\\begin{pmatrix} 1 & 2 \\\\ 3 & 4 \\end{pmatrix}",
    "language": "latex",
    "category": "matrices_vectors",
    "description": "2x2 matrix",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (0, Token(130, \\\"\\\\\\\\begin\\\"), 6), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "matrix_wolfram",
    "input": "{{1, 2}, {3, 4}}",
    "language": "wolfram",
    "category": "matrices_vectors",
    "description": "2x2 matrix",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\{\\{1, 2\\}, \\{3, 4\\}\\}",
    "formatted_wolfram": "{{1, 2}, {3, 4}}",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "set_latex",
    "input": "\\{1, 2, 3\\}",
    "language": "latex",
    "category": "sets_intervals",
    "description": "Finite set",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\{1, 2, 3\\}",
    "formatted_wolfram": "{1, 2, 3}",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "interval_closed_latex",
    "input": "[0, 1]",
    "language": "latex",
    "category": "sets_intervals",
    "description": "Closed interval",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "[0, 1]",
    "formatted_wolfram": "interval",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "interval_open_latex",
    "input": "(0, 1)",
    "language": "latex",
    "category": "sets_intervals",
    "description": "Open interval",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "(0, 1)",
    "formatted_wolfram": "interval",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "set_wolfram",
    "input": "{1, 2, 3}",
    "language": "wolfram",
    "category": "sets_intervals",
    "description": "Finite set",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\{1, 2, 3\\}",
    "formatted_wolfram": "{1, 2, 3}",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "equation_latex",
    "input": "x = 5",
    "language": "latex",
    "category": "equations_relations",
    "description": "Simple equation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "x = 5",
    "formatted_wolfram": "Equal[x, 5]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "inequality_latex",
    "input": "x < y",
    "language": "latex",
    "category": "equations_relations",
    "description": "Less than inequality",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "x < y",
    "formatted_wolfram": "Less[x, y]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "equation_wolfram",
    "input": "x == 5",
    "language": "wolfram",
    "category": "equations_relations",
    "description": "Simple equation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "x = 5",
    "formatted_wolfram": "Equal[x, 5]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": false
  },
  {
    "id": "special_gamma_latex",
    "input": "\\Gamma(x)",
    "language": "latex",
    "category": "special_functions",
    "description": "Gamma function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\Gamma(x)",
    "formatted_wolfram": "Gamma[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "special_gamma_wolfram",
    "input": "Gamma[x]",
    "language": "wolfram",
    "category": "special_functions",
    "description": "Gamma function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\Gamma(x)",
    "formatted_wolfram": "Gamma[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "piecewise_latex",
    "input": "\\begin{cases} x & \\text{if } x > 0 \\\\ -x & \\text{if } x \\leq 0 \\end{cases}",
    "language": "latex",
    "category": "piecewise_functions",
    "description": "Absolute value as piecewise",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (0, Token(130, \\\"\\\\\\\\begin\\\"), 6), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "piecewise_wolfram",
    "input": "Piecewise[{{x, x > 0}, {-x, x <= 0}}]",
    "language": "wolfram",
    "category": "piecewise_functions",
    "description": "Absolute value as piecewise",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "piecewise(\\{\\{x, x > 0\\}, \\{-1 \\cdot x, x \\leq 0\\}\\})",
    "formatted_wolfram": "piecewise[{{x, Greater[x, 0]}, {Times[-1, x], LessEqual[x, 0]}}]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": false
  },
  {
    "id": "exponential_series_latex",
    "input": "\\sum_{n=0}^{\\infty} \\frac{x^n}{n!}",
    "language": "latex",
    "category": "complex_expressions",
    "description": "Exponential series - FIRST CLASS SUM",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sum(\\factorial^{-1}(n) \\cdot x^n, n = 0, \\infty)",
    "formatted_wolfram": "Sum[Times[Power[Factorial[n], -1], Power[x, n]], Equal[n, 0], Infinity]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": null
  },
  {
    "id": "limit_definition_e_latex",
    "input": "\\lim_{n \\to \\infty} \\left(1 + \\frac{1}{n}\\right)^n",
    "language": "latex",
    "category": "complex_expressions",
    "description": "Limit definition of e - FIRST CLASS",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (8, Token(240, \\\"\\\\\\\\to\\\"), 11), expected: [\\\"RBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "partial_derivative_latex",
    "input": "\\frac{\\partial f}{\\partial x}",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Partial derivative",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(208, \\\"\\\\\\\\partial\\\"), 14), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "mixed_partial_derivative_latex",
    "input": "\\frac{\\partial^2 f}{\\partial x \\partial y}",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Mixed partial derivative",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(208, \\\"\\\\\\\\partial\\\"), 14), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "gradient_latex",
    "input": "\\nabla f",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Gradient operator",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\nabla f",
    "formatted_wolfram": "gradient[f]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "divergence_latex",
    "input": "\\nabla \\cdot \\vec{F}",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Divergence operator",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\nabla \\cdot \\vec{F}",
    "formatted_wolfram": "divergence[vector[F]]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "curl_latex",
    "input": "\\nabla \\times \\vec{F}",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Curl operator",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\nabla \\times \\vec{F}",
    "formatted_wolfram": "curl[vector[F]]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "laplacian_latex",
    "input": "\\nabla^2 f",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Laplacian operator",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\nabla^2 f",
    "formatted_wolfram": "laplacian[f]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "double_integral_latex",
    "input": "\\iint_D f(x,y) \\, dx \\, dy",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Double integral over region",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (0, Token(169, \\\"\\\\\\\\iint\\\"), 5), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "triple_integral_latex",
    "input": "\\iiint_V f(x,y,z) \\, dx \\, dy \\, dz",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Triple integral over volume",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (0, Token(168, \\\"\\\\\\\\iiint\\\"), 6), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "line_integral_latex",
    "input": "\\int_C \\vec{F} \\cdot d\\vec{r}",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Line integral of vector field",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (5, Token(2, \\\"C\\\"), 6), expected: [\\\"LBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "surface_integral_latex",
    "input": "\\iint_S \\vec{F} \\cdot \\vec{n} \\, dS",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Surface integral of vector field",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (0, Token(169, \\\"\\\\\\\\iint\\\"), 5), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "directional_derivative_latex",
    "input": "D_{\\vec{u}} f",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Directional derivative",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(272, \\\"{\\\"), 3), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "jacobian_latex",
    "input": "J_f",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Jacobian matrix",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "J_f",
    "formatted_wolfram": "J_f",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "hessian_latex",
    "input": "H_f",
    "language": "latex",
    "category": "advanced_calculus",
    "description": "Hessian matrix",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "H_f",
    "formatted_wolfram": "H_f",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "partial_derivative_wolfram",
    "input": "D[f[x, y], x]",
    "language": "wolfram",
    "category": "advanced_calculus",
    "description": "Partial derivative",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\frac{d}{dx} f(x, y)",
    "formatted_wolfram": "D[f[x, y], x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "gradient_wolfram",
    "input": "Grad[f[x, y, z], {x, y, z}]",
    "language": "wolfram",
    "category": "advanced_calculus",
    "description": "Gradient operator",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "grad(f(x, y, z), \\{x, y, z\\})",
    "formatted_wolfram": "grad[f[x, y, z], {x, y, z}]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "divergence_wolfram",
    "input": "Div[{Fx, Fy, Fz}, {x, y, z}]",
    "language": "wolfram",
    "category": "advanced_calculus",
    "description": "Divergence operator",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "div(\\{Fx, Fy, Fz\\}, \\{x, y, z\\})",
    "formatted_wolfram": "div[{Fx, Fy, Fz}, {x, y, z}]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "curl_wolfram",
    "input": "Curl[{Fx, Fy, Fz}, {x, y, z}]",
    "language": "wolfram",
    "category": "advanced_calculus",
    "description": "Curl operator",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\nabla \\times \\{Fx, Fy, Fz\\}",
    "formatted_wolfram": "curl[{Fx, Fy, Fz}, {x, y, z}]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "taylor_series_latex",
    "input": "\\sum_{n=0}^{\\infty} \\frac{f^{(n)}(a)}{n!} (x-a)^n",
    "language": "latex",
    "category": "series_expansions",
    "description": "Taylor series expansion",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (33, Token(6, \\\"(\\\"), 34), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"RBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "maclaurin_series_latex",
    "input": "\\sum_{n=0}^{\\infty} \\frac{f^{(n)}(0)}{n!} x^n",
    "language": "latex",
    "category": "series_expansions",
    "description": "Maclaurin series expansion",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (33, Token(6, \\\"(\\\"), 34), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"RBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "fourier_series_latex",
    "input": "\\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\left( a_n \\cos\\left(\\frac{n\\pi x}{L}\\right) + b_n \\sin\\left(\\frac{n\\pi x}{L}\\right) \\right)",
    "language": "latex",
    "category": "series_expansions",
    "description": "Fourier series",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (47, Token(141, \\\"\\\\\\\\cos\\\"), 51), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHT\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "power_series_latex",
    "input": "\\sum_{n=0}^{\\infty} a_n (x-c)^n",
    "language": "latex",
    "category": "series_expansions",
    "description": "Power series",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sum^{n}(a_n(x - c))",
    "formatted_wolfram": "Power[Sum[a_n[Subtract[x, c]], Equal[n, 0], Infinity], n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": null
  },
  {
    "id": "laurent_series_latex",
    "input": "\\sum_{n=-\\infty}^{\\infty} a_n (z-c)^n",
    "language": "latex",
    "category": "series_expansions",
    "description": "Laurent series",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sum^{n}(a_n(z - c))",
    "formatted_wolfram": "Power[Sum[a_n[Subtract[z, c]], Equal[n, Times[-1, Infinity]], Infinity], n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": null
  },
  {
    "id": "geometric_series_latex",
    "input": "\\sum_{n=0}^{\\infty} ar^n",
    "language": "latex",
    "category": "series_expansions",
    "description": "Geometric series",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sum^{n}(ar)",
    "formatted_wolfram": "Power[Sum[ar, Equal[n, 0], Infinity], n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": null
  },
  {
    "id": "binomial_series_latex",
    "input": "\\sum_{k=0}^{\\infty} \\binom{\\alpha}{k} x^k",
    "language": "latex",
    "category": "series_expansions",
    "description": "Binomial series",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (38, Token(2, \\\"x\\\"), 39), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "first_order_ode_latex",
    "input": "\\frac{dy}{dx} = f(x, y)",
    "language": "latex",
    "category": "differential_equations",
    "description": "First-order ODE",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\frac{dy}{dx} = f(x, y)",
    "formatted_wolfram": "Equal[Divide[dy, dx], f[x, y]]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "wave_equation_latex",
    "input": "\\frac{\\partial^2 u}{\\partial t^2} = c^2 \\frac{\\partial^2 u}{\\partial x^2}",
    "language": "latex",
    "category": "differential_equations",
    "description": "Wave equation PDE",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(208, \\\"\\\\\\\\partial\\\"), 14), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "heat_equation_latex",
    "input": "\\frac{\\partial u}{\\partial t} = \\alpha \\frac{\\partial^2 u}{\\partial x^2}",
    "language": "latex",
    "category": "differential_equations",
    "description": "Heat equation PDE",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(208, \\\"\\\\\\\\partial\\\"), 14), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "laplace_equation_latex",
    "input": "\\nabla^2 u = 0",
    "language": "latex",
    "category": "differential_equations",
    "description": "Laplace equation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\nabla^2 u = 0",
    "formatted_wolfram": "Equal[laplacian[u], 0]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "poisson_equation_latex",
    "input": "\\nabla^2 u = f",
    "language": "latex",
    "category": "differential_equations",
    "description": "Poisson equation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\nabla^2 u = f",
    "formatted_wolfram": "Equal[laplacian[u], f]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "eigenvalue_problem_latex",
    "input": "A\\vec{v} = \\lambda \\vec{v}",
    "language": "latex",
    "category": "linear_algebra_advanced",
    "description": "Eigenvalue problem",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (1, Token(245, \\\"\\\\\\\\vec\\\"), 5), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "characteristic_polynomial_latex",
    "input": "\\det(A - \\lambda I)",
    "language": "latex",
    "category": "linear_algebra_advanced",
    "description": "Characteristic polynomial",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (0, Token(150, \\\"\\\\\\\\det\\\"), 4), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "matrix_exponential_latex",
    "input": "e^{At}",
    "language": "latex",
    "category": "linear_algebra_advanced",
    "description": "Matrix exponential",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "e^{At}",
    "formatted_wolfram": "Power[E, At]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "svd_latex",
    "input": "A = U\\Sigma V^T",
    "language": "latex",
    "category": "linear_algebra_advanced",
    "description": "Singular Value Decomposition",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 5 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "qr_decomposition_latex",
    "input": "A = QR",
    "language": "latex",
    "category": "linear_algebra_advanced",
    "description": "QR decomposition",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "A = QR",
    "formatted_wolfram": "Equal[A, QR]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "lu_decomposition_latex",
    "input": "A = LU",
    "language": "latex",
    "category": "linear_algebra_advanced",
    "description": "LU decomposition",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "A = LU",
    "formatted_wolfram": "Equal[A, LU]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "complex_conjugate_latex",
    "input": "\\overline{z}",
    "language": "latex",
    "category": "complex_analysis",
    "description": "Complex conjugate",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\overline{z}",
    "formatted_wolfram": "conjugate[z]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "complex_modulus_latex",
    "input": "|z|",
    "language": "latex",
    "category": "complex_analysis",
    "description": "Complex modulus",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "|z|",
    "formatted_wolfram": "abs[z]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "cauchy_riemann_latex",
    "input": "\\frac{\\partial u}{\\partial x} = \\frac{\\partial v}{\\partial y}",
    "language": "latex",
    "category": "complex_analysis",
    "description": "Cauchy-Riemann equation",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(208, \\\"\\\\\\\\partial\\\"), 14), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "contour_integral_latex",
    "input": "\\oint_C f(z) dz",
    "language": "latex",
    "category": "complex_analysis",
    "description": "Contour integral",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (5, Token(254, \\\"_\\\"), 6), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "residue_theorem_latex",
    "input": "\\oint_C f(z) dz = 2\\pi i \\sum \\text{Res}(f, z_k)",
    "language": "latex",
    "category": "complex_analysis",
    "description": "Residue theorem",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (5, Token(254, \\\"_\\\"), 6), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "bessel_function_latex",
    "input": "J_n(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Bessel function of first kind",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "J_n(x)",
    "formatted_wolfram": "bessel_j_indexed[n, x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "neumann_function_latex",
    "input": "Y_n(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Bessel function of second kind (Neumann)",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Y_n(x)",
    "formatted_wolfram": "bessel_y_indexed[n, x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "hankel_function_latex",
    "input": "H_n^{(1)}(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Hankel function of first kind",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (9, Token(6, \\\"(\\\"), 10), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "legendre_polynomial_latex",
    "input": "P_n(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Legendre polynomial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "P_n(x)",
    "formatted_wolfram": "legendre_p_indexed[n, x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "associated_legendre_latex",
    "input": "P_l^m(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Associated Legendre function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "P_l^{m(x)}",
    "formatted_wolfram": "Power[P_l, m[x]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "spherical_harmonic_latex",
    "input": "Y_l^m(\\theta, \\phi)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Spherical harmonic",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Y_l^{m(theta, \\phi)}",
    "formatted_wolfram": "Power[Y_l, m[theta, GoldenRatio]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "hermite_polynomial_latex",
    "input": "H_n(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Hermite polynomial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "H_n(x)",
    "formatted_wolfram": "hermite_indexed[n, x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "laguerre_polynomial_latex",
    "input": "L_n(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Laguerre polynomial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "L_n(x)",
    "formatted_wolfram": "laguerre_indexed[n, x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "chebyshev_polynomial_latex",
    "input": "T_n(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Chebyshev polynomial of first kind",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "T_n(x)",
    "formatted_wolfram": "chebyshev_first_indexed[n, x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "elliptic_integral_first_latex",
    "input": "F(\\phi, k)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Elliptic integral of first kind",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "F(\\phi, k)",
    "formatted_wolfram": "F[GoldenRatio, k]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "elliptic_integral_second_latex",
    "input": "E(\\phi, k)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Elliptic integral of second kind",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (1, Token(6, \\\"(\\\"), 2), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "beta_function_latex",
    "input": "B(x, y)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Beta function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "B(x, y)",
    "formatted_wolfram": "B[x, y]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "digamma_function_latex",
    "input": "\\psi(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Digamma function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\psi(x)",
    "formatted_wolfram": "digamma[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "polygamma_function_latex",
    "input": "\\psi^{(n)}(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Polygamma function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (10, Token(6, \\\"(\\\"), 11), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "riemann_zeta_latex",
    "input": "\\zeta(s)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Riemann zeta function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\zeta(s)",
    "formatted_wolfram": "riemann_zeta[s]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "dirichlet_eta_latex",
    "input": "\\eta(s)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Dirichlet eta function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\eta(s)",
    "formatted_wolfram": "eta[s]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "error_function_latex",
    "input": "\\text{erf}(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Error function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\erf(x)",
    "formatted_wolfram": "erf[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": null
  },
  {
    "id": "complementary_error_function_latex",
    "input": "\\text{erfc}(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Complementary error function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\erfc(x)",
    "formatted_wolfram": "erfc[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": null
  },
  {
    "id": "fresnel_integral_s_latex",
    "input": "S(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Fresnel integral S",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "S(x)",
    "formatted_wolfram": "S[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "fresnel_integral_c_latex",
    "input": "C(x)",
    "language": "latex",
    "category": "special_functions_advanced",
    "description": "Fresnel integral C",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "C(x)",
    "formatted_wolfram": "C[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "factorial_latex",
    "input": "n!",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Factorial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "n!",
    "formatted_wolfram": "Factorial[n]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "double_factorial_latex",
    "input": "n!!",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Double factorial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "n!!",
    "formatted_wolfram": "double_factorial[n]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "binomial_coefficient_latex",
    "input": "\\binom{n}{k}",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Binomial coefficient",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "binomial(n, k)",
    "formatted_wolfram": "binomial[n, k]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "multinomial_coefficient_latex",
    "input": "\\binom{n}{k_1, k_2, \\ldots, k_m}",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Multinomial coefficient",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (13, Token(10, \\\",\\\"), 14), expected: [\\\"RBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "stirling_first_latex",
    "input": "s(n, k)",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Stirling number of first kind",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "s(n, k)",
    "formatted_wolfram": "s[n, k]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "stirling_second_latex",
    "input": "S(n, k)",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Stirling number of second kind",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "S(n, k)",
    "formatted_wolfram": "S[n, k]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "bell_number_latex",
    "input": "B_n",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Bell number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "B_n",
    "formatted_wolfram": "B_n",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "catalan_number_latex",
    "input": "C_n",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Catalan number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "C_n",
    "formatted_wolfram": "C_n",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "fibonacci_number_latex",
    "input": "F_n",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Fibonacci number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "F_n",
    "formatted_wolfram": "F_n",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "lucas_number_latex",
    "input": "L_n",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Lucas number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "L_n",
    "formatted_wolfram": "L_n",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "euler_totient_latex",
    "input": "\\phi(n)",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Euler's totient function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "euler_phi(n)",
    "formatted_wolfram": "euler_phi[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "mobius_function_latex",
    "input": "\\mu(n)",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Möbius function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "mobius(n)",
    "formatted_wolfram": "mobius[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "divisor_function_latex",
    "input": "\\sigma_k(n)",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Divisor function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "prime_counting_latex",
    "input": "\\pi(x)",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Prime counting function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "prime_pi(x)",
    "formatted_wolfram": "prime_pi[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "legendre_symbol_latex",
    "input": "\\left(\\frac{a}{p}\\right)",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Legendre symbol",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\frac{a}{p}",
    "formatted_wolfram": "Divide[a, p]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "jacobi_symbol_latex",
    "input": "\\left(\\frac{a}{n}\\right)",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Jacobi symbol",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\frac{a}{n}",
    "formatted_wolfram": "Divide[a, n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "partition_function_latex",
    "input": "p(n)",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Partition function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "p(n)",
    "formatted_wolfram": "p[n]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "ramanujan_tau_latex",
    "input": "\\tau(n)",
    "language": "latex",
    "category": "combinatorics_number_theory",
    "description": "Ramanujan tau function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "ramanujan_tau(n)",
    "formatted_wolfram": "ramanujan_tau[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "hyperbolic_sin_latex",
    "input": "\\sinh(x)",
    "language": "latex",
    "category": "hyperbolic_functions",
    "description": "Hyperbolic sine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sinh(x)",
    "formatted_wolfram": "sinh[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "hyperbolic_cos_latex",
    "input": "\\cosh(x)",
    "language": "latex",
    "category": "hyperbolic_functions",
    "description": "Hyperbolic cosine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\cosh(x)",
    "formatted_wolfram": "cosh[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "hyperbolic_tan_latex",
    "input": "\\tanh(x)",
    "language": "latex",
    "category": "hyperbolic_functions",
    "description": "Hyperbolic tangent",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\tanh(x)",
    "formatted_wolfram": "tanh[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "inverse_hyperbolic_sin_latex",
    "input": "\\sinh^{-1}(x)",
    "language": "latex",
    "category": "hyperbolic_functions",
    "description": "Inverse hyperbolic sine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\arcsinh(x)",
    "formatted_wolfram": "arcsinh[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": null
  },
  {
    "id": "inverse_hyperbolic_cos_latex",
    "input": "\\cosh^{-1}(x)",
    "language": "latex",
    "category": "hyperbolic_functions",
    "description": "Inverse hyperbolic cosine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\arccosh(x)",
    "formatted_wolfram": "arccosh[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": null
  },
  {
    "id": "inverse_hyperbolic_tan_latex",
    "input": "\\tanh^{-1}(x)",
    "language": "latex",
    "category": "hyperbolic_functions",
    "description": "Inverse hyperbolic tangent",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\arctanh(x)",
    "formatted_wolfram": "arctanh[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": null
  },
  {
    "id": "inverse_trig_sin_latex",
    "input": "\\arcsin(x)",
    "language": "latex",
    "category": "inverse_trigonometric",
    "description": "Inverse sine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\arcsin(x)",
    "formatted_wolfram": "ArcSin[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "inverse_trig_cos_latex",
    "input": "\\arccos(x)",
    "language": "latex",
    "category": "inverse_trigonometric",
    "description": "Inverse cosine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\arccos(x)",
    "formatted_wolfram": "ArcCos[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "inverse_trig_tan_latex",
    "input": "\\arctan(x)",
    "language": "latex",
    "category": "inverse_trigonometric",
    "description": "Inverse tangent",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\arctan(x)",
    "formatted_wolfram": "ArcTan[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "atan2_latex",
    "input": "\\text{atan2}(y, x)",
    "language": "latex",
    "category": "inverse_trigonometric",
    "description": "Two-argument arctangent",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "atan2(y, x)",
    "formatted_wolfram": "atan2[y, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "secant_latex",
    "input": "\\sec(x)",
    "language": "latex",
    "category": "trigonometric_extended",
    "description": "Secant function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sec(x)",
    "formatted_wolfram": "Sec[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "cosecant_latex",
    "input": "\\csc(x)",
    "language": "latex",
    "category": "trigonometric_extended",
    "description": "Cosecant function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\csc(x)",
    "formatted_wolfram": "Csc[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "cotangent_latex",
    "input": "\\cot(x)",
    "language": "latex",
    "category": "trigonometric_extended",
    "description": "Cotangent function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\cot(x)",
    "formatted_wolfram": "Cot[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "probability_density_latex",
    "input": "f_X(x)",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Probability density function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "f_X(x)",
    "formatted_wolfram": "f_X[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "cumulative_distribution_latex",
    "input": "F_X(x)",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Cumulative distribution function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "F_X(x)",
    "formatted_wolfram": "F_X[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "expectation_latex",
    "input": "E[X]",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Expected value",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (1, Token(95, \\\"[\\\"), 2), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "variance_latex",
    "input": "\\text{Var}(X)",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Variance",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Var(X)",
    "formatted_wolfram": "Var[X]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "standard_deviation_latex",
    "input": "\\sigma_X",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Standard deviation",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "covariance_latex",
    "input": "\\text{Cov}(X, Y)",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Covariance",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Cov(X, Y)",
    "formatted_wolfram": "Cov[X, Y]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "correlation_latex",
    "input": "\\rho_{X,Y}",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Correlation coefficient",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (4, Token(254, \\\"_\\\"), 5), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "normal_distribution_latex",
    "input": "\\mathcal{N}(\\mu, \\sigma^2)",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Normal distribution",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "mathcal_n(mu, sigma^2)",
    "formatted_wolfram": "mathcal_n[mu, Power[sigma, 2]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "binomial_distribution_latex",
    "input": "\\text{Binomial}(n, p)",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Binomial distribution",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(24, \\\"Binomial\\\"), 14), expected: [\\\"IDENTIFIER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "poisson_distribution_latex",
    "input": "\\text{Poisson}(\\lambda)",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Poisson distribution",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Poisson(lambda)",
    "formatted_wolfram": "Poisson[lambda]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "t_distribution_latex",
    "input": "t(\\nu)",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Student's t-distribution",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "t(nu)",
    "formatted_wolfram": "t[nu]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "f_distribution_latex",
    "input": "F(d_1, d_2)",
    "language": "latex",
    "category": "probability_statistics",
    "description": "F-distribution",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "F(d_1, d_2)",
    "formatted_wolfram": "F[d_1, d_2]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "conditional_probability_latex",
    "input": "P(A|B)",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Conditional probability",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (3, Token(273, \\\"|\\\"), 4), expected: [\\\"RPAREN\\\", \\\"COMMA\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "bayes_theorem_latex",
    "input": "P(A|B) = \\frac{P(B|A)P(A)}{P(B)}",
    "language": "latex",
    "category": "probability_statistics",
    "description": "Bayes' theorem",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (3, Token(273, \\\"|\\\"), 4), expected: [\\\"RPAREN\\\", \\\"COMMA\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "metric_space_latex",
    "input": "d(x, y)",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Metric function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (0, Token(259, \\\"d\\\"), 1), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "norm_latex",
    "input": "\\|x\\|",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Norm",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "inner_product_latex",
    "input": "\\langle x, y \\rangle",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Inner product",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "cross_product_latex",
    "input": "\\vec{a} \\times \\vec{b}",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Cross product",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\vec{a} \\cdot \\vec{b}",
    "formatted_wolfram": "Times[vector[a], vector[b]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "dot_product_latex",
    "input": "\\vec{a} \\cdot \\vec{b}",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Dot product",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\vec{a} \\cdot \\vec{b}",
    "formatted_wolfram": "Times[vector[a], vector[b]]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "euclidean_distance_latex",
    "input": "\\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Euclidean distance formula",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sqrt{\\left(x_2 - x_1\\right)^2 + \\left(y_2 - y_1\\right)^2}",
    "formatted_wolfram": "Sqrt[Plus[Power[Subtract[x_2, x_1], 2], Power[Subtract[y_2, y_1], 2]]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "sphere_equation_latex",
    "input": "(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Sphere equation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\left(x - a\\right)^2 + \\left(y - b\\right)^2 + \\left(z - c\\right)^2 = r^2",
    "formatted_wolfram": "Equal[Plus[Power[Subtract[x, a], 2], Power[Subtract[y, b], 2], Power[Subtract[z, c], 2]], Power[r, 2]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "circle_equation_latex",
    "input": "(x-h)^2 + (y-k)^2 = r^2",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Circle equation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\left(x - h\\right)^2 + \\left(y - k\\right)^2 = r^2",
    "formatted_wolfram": "Equal[Plus[Power[Subtract[x, h], 2], Power[Subtract[y, k], 2]], Power[r, 2]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "ellipse_equation_latex",
    "input": "\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Ellipse equation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "a^{-2} \\cdot x^2 + b^{-2} \\cdot y^2 = 1",
    "formatted_wolfram": "Equal[Plus[Times[Power[a, -2], Power[x, 2]], Times[Power[b, -2], Power[y, 2]]], 1]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "hyperbola_equation_latex",
    "input": "\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Hyperbola equation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "-1 \\cdot b^{-2} \\cdot y^2 + a^{-2} \\cdot x^2 = 1",
    "formatted_wolfram": "Equal[Plus[Times[-1, Times[Power[b, -2], Power[y, 2]]], Times[Power[a, -2], Power[x, 2]]], 1]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "parabola_equation_latex",
    "input": "y = ax^2 + bx + c",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Parabola equation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "y = bx + c + ax^2",
    "formatted_wolfram": "Equal[y, Plus[bx, c, Power[ax, 2]]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "parametric_curve_latex",
    "input": "\\vec{r}(t) = \\langle x(t), y(t), z(t) \\rangle",
    "language": "latex",
    "category": "topology_geometry",
    "description": "Parametric curve",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (7, Token(6, \\\"(\\\"), 8), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "polar_coordinates_latex",
    "input": "x = r\\cos\\theta, y = r\\sin\\theta",
    "language": "latex",
    "category": "coordinate_systems",
    "description": "Polar to Cartesian conversion",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (5, Token(141, \\\"\\\\\\\\cos\\\"), 9), expected: [\\\"FACTORIAL\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LBRACKET\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_MP\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "cylindrical_coordinates_latex",
    "input": "x = r\\cos\\theta, y = r\\sin\\theta, z = z",
    "language": "latex",
    "category": "coordinate_systems",
    "description": "Cylindrical coordinates",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (5, Token(141, \\\"\\\\\\\\cos\\\"), 9), expected: [\\\"FACTORIAL\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LBRACKET\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_MP\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "spherical_coordinates_latex",
    "input": "x = \\rho\\sin\\phi\\cos\\theta",
    "language": "latex",
    "category": "coordinate_systems",
    "description": "Spherical coordinates",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (8, Token(223, \\\"\\\\\\\\sin\\\"), 12), expected: [\\\"FACTORIAL\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_MP\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "fourier_transform_latex",
    "input": "\\mathcal{F}[f(t)](\\omega) = \\int_{-\\infty}^{\\infty} f(t) e^{-i\\omega t} dt",
    "language": "latex",
    "category": "transforms",
    "description": "Fourier transform",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (11, Token(95, \\\"[\\\"), 12), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "laplace_transform_latex",
    "input": "\\mathcal{L}[f(t)](s) = \\int_0^{\\infty} f(t) e^{-st} dt",
    "language": "latex",
    "category": "transforms",
    "description": "Laplace transform",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (11, Token(95, \\\"[\\\"), 12), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "z_transform_latex",
    "input": "\\mathcal{Z}[x[n]](z) = \\sum_{n=-\\infty}^{\\infty} x[n] z^{-n}",
    "language": "latex",
    "category": "transforms",
    "description": "Z-transform",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (11, Token(95, \\\"[\\\"), 12), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "dirac_delta_latex",
    "input": "\\delta(x)",
    "language": "latex",
    "category": "generalized_functions",
    "description": "Dirac delta function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "dirac_delta(x)",
    "formatted_wolfram": "dirac_delta[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "heaviside_step_latex",
    "input": "H(x)",
    "language": "latex",
    "category": "generalized_functions",
    "description": "Heaviside step function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "hermite(x)",
    "formatted_wolfram": "hermite[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "sign_function_latex",
    "input": "\\text{sgn}(x)",
    "language": "latex",
    "category": "generalized_functions",
    "description": "Sign function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "sgn(x)",
    "formatted_wolfram": "sgn[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "floor_function_latex",
    "input": "\\lfloor x \\rfloor",
    "language": "latex",
    "category": "generalized_functions",
    "description": "Floor function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "ceiling_function_latex",
    "input": "\\lceil x \\rceil",
    "language": "latex",
    "category": "generalized_functions",
    "description": "Ceiling function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "fractional_part_latex",
    "input": "\\{x\\}",
    "language": "latex",
    "category": "generalized_functions",
    "description": "Fractional part",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\{x\\}",
    "formatted_wolfram": "{x}",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "min_function_latex",
    "input": "\\min(x, y)",
    "language": "latex",
    "category": "optimization",
    "description": "Minimum function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\min(x, y)",
    "formatted_wolfram": "min[x, y]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "max_function_latex",
    "input": "\\max(x, y)",
    "language": "latex",
    "category": "optimization",
    "description": "Maximum function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\max(x, y)",
    "formatted_wolfram": "max[x, y]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "argmin_latex",
    "input": "\\arg\\min_x f(x)",
    "language": "latex",
    "category": "optimization",
    "description": "Argument of minimum",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "argmax_latex",
    "input": "\\arg\\max_x f(x)",
    "language": "latex",
    "category": "optimization",
    "description": "Argument of maximum",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "lagrangian_latex",
    "input": "\\mathcal{L}(x, \\lambda) = f(x) + \\lambda g(x)",
    "language": "latex",
    "category": "optimization",
    "description": "Lagrangian function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (41, Token(2, \\\"g\\\"), 42), expected: [\\\"FACTORIAL\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_MP\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "hamiltonian_latex",
    "input": "H(q, p, t)",
    "language": "latex",
    "category": "physics_mathematics",
    "description": "Hamiltonian function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "hermite(q, p, t)",
    "formatted_wolfram": "hermite[q, p, t]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "schrodinger_equation_latex",
    "input": "i\\hbar \\frac{\\partial \\psi}{\\partial t} = \\hat{H} \\psi",
    "language": "latex",
    "category": "physics_mathematics",
    "description": "Schrödinger equation",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 1 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "maxwell_equation_latex",
    "input": "\\nabla \\times \\vec{E} = -\\frac{\\partial \\vec{B}}{\\partial t}",
    "language": "latex",
    "category": "physics_mathematics",
    "description": "Maxwell's equation (Faraday's law)",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (31, Token(208, \\\"\\\\\\\\partial\\\"), 39), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "einstein_field_equation_latex",
    "input": "G_{\\mu\\nu} = \\frac{8\\pi G}{c^4} T_{\\mu\\nu}",
    "language": "latex",
    "category": "physics_mathematics",
    "description": "Einstein field equation",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(272, \\\"{\\\"), 3), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "navier_stokes_latex",
    "input": "\\rho \\left(\\frac{\\partial \\vec{v}}{\\partial t} + \\vec{v} \\cdot \\nabla \\vec{v}\\right) = -\\nabla p + \\mu \\nabla^2 \\vec{v}",
    "language": "latex",
    "category": "physics_mathematics",
    "description": "Navier-Stokes equation",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (5, Token(181, \\\"\\\\\\\\left\\\"), 10), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "product_rule_latex",
    "input": "\\frac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)",
    "language": "latex",
    "category": "calculus_rules",
    "description": "Product rule for derivatives",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(259, \\\"d\\\"), 7), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "quotient_rule_latex",
    "input": "\\frac{d}{dx}\\left[\\frac{f(x)}{g(x)}\\right] = \\frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}",
    "language": "latex",
    "category": "calculus_rules",
    "description": "Quotient rule for derivatives",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(259, \\\"d\\\"), 7), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "chain_rule_latex",
    "input": "\\frac{d}{dx}[f(g(x))] = f'(g(x)) \\cdot g'(x)",
    "language": "latex",
    "category": "calculus_rules",
    "description": "Chain rule for derivatives",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(259, \\\"d\\\"), 7), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "integration_by_parts_latex",
    "input": "\\int u \\, dv = uv - \\int v \\, du",
    "language": "latex",
    "category": "calculus_rules",
    "description": "Integration by parts",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 7 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "fundamental_theorem_calculus_latex",
    "input": "\\frac{d}{dx} \\int_a^x f(t) \\, dt = f(x)",
    "language": "latex",
    "category": "calculus_rules",
    "description": "Fundamental theorem of calculus",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(259, \\\"d\\\"), 7), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "hyperbolic_sin_wolfram",
    "input": "Sinh[x]",
    "language": "wolfram",
    "category": "hyperbolic_functions",
    "description": "Hyperbolic sine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sinh(x)",
    "formatted_wolfram": "sinh[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "hyperbolic_cos_wolfram",
    "input": "Cosh[x]",
    "language": "wolfram",
    "category": "hyperbolic_functions",
    "description": "Hyperbolic cosine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\cosh(x)",
    "formatted_wolfram": "cosh[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "hyperbolic_tan_wolfram",
    "input": "Tanh[x]",
    "language": "wolfram",
    "category": "hyperbolic_functions",
    "description": "Hyperbolic tangent",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\tanh(x)",
    "formatted_wolfram": "tanh[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "inverse_hyperbolic_sin_wolfram",
    "input": "ArcSinh[x]",
    "language": "wolfram",
    "category": "hyperbolic_functions",
    "description": "Inverse hyperbolic sine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "arc_sinh(x)",
    "formatted_wolfram": "arc_sinh[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "inverse_hyperbolic_cos_wolfram",
    "input": "ArcCosh[x]",
    "language": "wolfram",
    "category": "hyperbolic_functions",
    "description": "Inverse hyperbolic cosine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "arc_cosh(x)",
    "formatted_wolfram": "arc_cosh[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "inverse_hyperbolic_tan_wolfram",
    "input": "ArcTanh[x]",
    "language": "wolfram",
    "category": "hyperbolic_functions",
    "description": "Inverse hyperbolic tangent",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "arc_tanh(x)",
    "formatted_wolfram": "arc_tanh[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "inverse_trig_sin_wolfram",
    "input": "ArcSin[x]",
    "language": "wolfram",
    "category": "inverse_trigonometric",
    "description": "Inverse sine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\arcsin(x)",
    "formatted_wolfram": "ArcSin[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "inverse_trig_cos_wolfram",
    "input": "ArcCos[x]",
    "language": "wolfram",
    "category": "inverse_trigonometric",
    "description": "Inverse cosine",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\arccos(x)",
    "formatted_wolfram": "ArcCos[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "inverse_trig_tan_wolfram",
    "input": "ArcTan[x]",
    "language": "wolfram",
    "category": "inverse_trigonometric",
    "description": "Inverse tangent",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\arctan(x)",
    "formatted_wolfram": "ArcTan[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "atan2_wolfram",
    "input": "ArcTan[x, y]",
    "language": "wolfram",
    "category": "inverse_trigonometric",
    "description": "Two-argument arctangent",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\arctan(x, y)",
    "formatted_wolfram": "ArcTan[x, y]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "secant_wolfram",
    "input": "Sec[x]",
    "language": "wolfram",
    "category": "trigonometric_extended",
    "description": "Secant function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sec(x)",
    "formatted_wolfram": "Sec[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "cosecant_wolfram",
    "input": "Csc[x]",
    "language": "wolfram",
    "category": "trigonometric_extended",
    "description": "Cosecant function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\csc(x)",
    "formatted_wolfram": "Csc[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "cotangent_wolfram",
    "input": "Cot[x]",
    "language": "wolfram",
    "category": "trigonometric_extended",
    "description": "Cotangent function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\cot(x)",
    "formatted_wolfram": "Cot[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "probability_density_wolfram",
    "input": "PDF[dist, x]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Probability density function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "p_d_f(dist, x)",
    "formatted_wolfram": "p_d_f[dist, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "cumulative_distribution_wolfram",
    "input": "CDF[dist, x]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Cumulative distribution function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "c_d_f(dist, x)",
    "formatted_wolfram": "c_d_f[dist, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "expectation_wolfram",
    "input": "Expectation[X, dist]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Expected value",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "expectation(X, dist)",
    "formatted_wolfram": "expectation[X, dist]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "variance_wolfram",
    "input": "Variance[X, dist]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Variance",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "variance(X, dist)",
    "formatted_wolfram": "variance[X, dist]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "standard_deviation_wolfram",
    "input": "StandardDeviation[X, dist]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Standard deviation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "std(X, dist)",
    "formatted_wolfram": "std[X, dist]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "covariance_wolfram",
    "input": "Covariance[X, Y]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Covariance",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "covariance(X, Y)",
    "formatted_wolfram": "covariance[X, Y]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "correlation_wolfram",
    "input": "Correlation[X, Y]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Correlation coefficient",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "correlation(X, Y)",
    "formatted_wolfram": "correlation[X, Y]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "normal_distribution_wolfram",
    "input": "NormalDistribution[μ, σ]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Normal distribution",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 19 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "binomial_distribution_wolfram",
    "input": "BinomialDistribution[n, p]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Binomial distribution",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "binomial_distribution(n, p)",
    "formatted_wolfram": "binomial_distribution[n, p]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "poisson_distribution_wolfram",
    "input": "PoissonDistribution[λ]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Poisson distribution",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 20 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "chi_squared_wolfram",
    "input": "ChiSquareDistribution[k]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Chi-squared distribution",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "chi_square_distribution(k)",
    "formatted_wolfram": "chi_square_distribution[k]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "t_distribution_wolfram",
    "input": "StudentTDistribution[ν]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Student's t-distribution",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 21 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "f_distribution_wolfram",
    "input": "FRatioDistribution[d1, d2]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "F-distribution",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "f_ratio_distribution(d1, d2)",
    "formatted_wolfram": "f_ratio_distribution[d1, d2]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "conditional_probability_wolfram",
    "input": "Probability[A, B]",
    "language": "wolfram",
    "category": "probability_statistics",
    "description": "Conditional probability",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "probability(A, B)",
    "formatted_wolfram": "probability[A, B]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "metric_space_wolfram",
    "input": "EuclideanDistance[x, y]",
    "language": "wolfram",
    "category": "topology_geometry",
    "description": "Metric function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "euclidean_distance(x, y)",
    "formatted_wolfram": "euclidean_distance[x, y]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "norm_wolfram",
    "input": "Norm[x]",
    "language": "wolfram",
    "category": "topology_geometry",
    "description": "Norm",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "norm(x)",
    "formatted_wolfram": "norm[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "inner_product_wolfram",
    "input": "Dot[x, y]",
    "language": "wolfram",
    "category": "topology_geometry",
    "description": "Inner product",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "dot(x, y)",
    "formatted_wolfram": "dot[x, y]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "cross_product_wolfram",
    "input": "Cross[a, b]",
    "language": "wolfram",
    "category": "topology_geometry",
    "description": "Cross product",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "cross(a, b)",
    "formatted_wolfram": "cross[a, b]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "dot_product_wolfram",
    "input": "Dot[a, b]",
    "language": "wolfram",
    "category": "topology_geometry",
    "description": "Dot product",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "dot(a, b)",
    "formatted_wolfram": "dot[a, b]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "fourier_transform_wolfram",
    "input": "FourierTransform[f[t], t, ω]",
    "language": "wolfram",
    "category": "transforms",
    "description": "Fourier transform",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 26 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "laplace_transform_wolfram",
    "input": "LaplaceTransform[f[t], t, s]",
    "language": "wolfram",
    "category": "transforms",
    "description": "Laplace transform",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "laplace_transform(f(t), t, s)",
    "formatted_wolfram": "laplace_transform[f[t], t, s]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "z_transform_wolfram",
    "input": "ZTransform[x[n], n, z]",
    "language": "wolfram",
    "category": "transforms",
    "description": "Z-transform",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "z_transform(x(n), n, z)",
    "formatted_wolfram": "z_transform[x[n], n, z]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "convolution_wolfram",
    "input": "Convolve[f, g, t, τ]",
    "language": "wolfram",
    "category": "transforms",
    "description": "Convolution",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 18 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "dirac_delta_wolfram",
    "input": "DiracDelta[x]",
    "language": "wolfram",
    "category": "generalized_functions",
    "description": "Dirac delta function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "dirac_delta(x)",
    "formatted_wolfram": "dirac_delta[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "heaviside_step_wolfram",
    "input": "HeavisideTheta[x]",
    "language": "wolfram",
    "category": "generalized_functions",
    "description": "Heaviside step function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "heaviside_theta(x)",
    "formatted_wolfram": "heaviside_theta[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "sign_function_wolfram",
    "input": "Sign[x]",
    "language": "wolfram",
    "category": "generalized_functions",
    "description": "Sign function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "sign(x)",
    "formatted_wolfram": "sign[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "floor_function_wolfram",
    "input": "Floor[x]",
    "language": "wolfram",
    "category": "generalized_functions",
    "description": "Floor function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "floor(x)",
    "formatted_wolfram": "floor[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "ceiling_function_wolfram",
    "input": "Ceiling[x]",
    "language": "wolfram",
    "category": "generalized_functions",
    "description": "Ceiling function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "ceiling(x)",
    "formatted_wolfram": "ceiling[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "fractional_part_wolfram",
    "input": "FractionalPart[x]",
    "language": "wolfram",
    "category": "generalized_functions",
    "description": "Fractional part",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "fractional_part(x)",
    "formatted_wolfram": "fractional_part[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "min_function_wolfram",
    "input": "Min[x, y]",
    "language": "wolfram",
    "category": "optimization",
    "description": "Minimum function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\min(x, y)",
    "formatted_wolfram": "min[x, y]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "max_function_wolfram",
    "input": "Max[x, y]",
    "language": "wolfram",
    "category": "optimization",
    "description": "Maximum function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\max(x, y)",
    "formatted_wolfram": "max[x, y]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "argmin_wolfram",
    "input": "ArgMin[f[x], x]",
    "language": "wolfram",
    "category": "optimization",
    "description": "Argument of minimum",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "arg_min(f(x), x)",
    "formatted_wolfram": "arg_min[f[x], x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "argmax_wolfram",
    "input": "ArgMax[f[x], x]",
    "language": "wolfram",
    "category": "optimization",
    "description": "Argument of maximum",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "arg_max(f(x), x)",
    "formatted_wolfram": "arg_max[f[x], x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "bessel_function_wolfram",
    "input": "BesselJ[n, x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Bessel function of first kind",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "bessel_j(n, x)",
    "formatted_wolfram": "bessel_j[n, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "neumann_function_wolfram",
    "input": "BesselY[n, x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Bessel function of second kind (Neumann)",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "bessel_y(n, x)",
    "formatted_wolfram": "bessel_y[n, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "hankel_function_wolfram",
    "input": "HankelH1[n, x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Hankel function of first kind",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "hankel_h1(n, x)",
    "formatted_wolfram": "hankel_h1[n, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "legendre_polynomial_wolfram",
    "input": "LegendreP[n, x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Legendre polynomial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "legendre_p(n, x)",
    "formatted_wolfram": "legendre_p[n, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "associated_legendre_wolfram",
    "input": "LegendreP[l, m, x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Associated Legendre function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "legendre_p(l, m, x)",
    "formatted_wolfram": "legendre_p[l, m, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "spherical_harmonic_wolfram",
    "input": "SphericalHarmonicY[l, m, θ, φ]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Spherical harmonic",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 25 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "hermite_polynomial_wolfram",
    "input": "HermiteH[n, x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Hermite polynomial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "hermite(n, x)",
    "formatted_wolfram": "hermite[n, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "laguerre_polynomial_wolfram",
    "input": "LaguerreL[n, x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Laguerre polynomial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "laguerre(n, x)",
    "formatted_wolfram": "laguerre[n, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "chebyshev_polynomial_wolfram",
    "input": "ChebyshevT[n, x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Chebyshev polynomial of first kind",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "chebyshev_first(n, x)",
    "formatted_wolfram": "chebyshev_first[n, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "elliptic_integral_first_wolfram",
    "input": "EllipticF[φ, k]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Elliptic integral of first kind",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 10 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "elliptic_integral_second_wolfram",
    "input": "EllipticE[φ, k]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Elliptic integral of second kind",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 10 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "beta_function_wolfram",
    "input": "Beta[x, y]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Beta function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "beta(x, y)",
    "formatted_wolfram": "Beta[x, y]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "digamma_function_wolfram",
    "input": "PolyGamma[x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Digamma function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "poly_gamma(x)",
    "formatted_wolfram": "poly_gamma[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "polygamma_function_wolfram",
    "input": "PolyGamma[n, x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Polygamma function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "poly_gamma(n, x)",
    "formatted_wolfram": "poly_gamma[n, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "riemann_zeta_wolfram",
    "input": "Zeta[s]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Riemann zeta function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "zeta(s)",
    "formatted_wolfram": "Zeta[s]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "dirichlet_eta_wolfram",
    "input": "DirichletEta[s]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Dirichlet eta function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "dirichlet_eta(s)",
    "formatted_wolfram": "dirichlet_eta[s]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "error_function_wolfram",
    "input": "Erf[x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Error function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\erf(x)",
    "formatted_wolfram": "erf[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "complementary_error_function_wolfram",
    "input": "Erfc[x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Complementary error function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\erfc(x)",
    "formatted_wolfram": "erfc[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "fresnel_integral_s_wolfram",
    "input": "FresnelS[x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Fresnel integral S",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "fresnel_s(x)",
    "formatted_wolfram": "fresnel_s[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "fresnel_integral_c_wolfram",
    "input": "FresnelC[x]",
    "language": "wolfram",
    "category": "special_functions_advanced",
    "description": "Fresnel integral C",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "fresnel_c(x)",
    "formatted_wolfram": "fresnel_c[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "factorial_wolfram",
    "input": "Factorial[n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Factorial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "n!",
    "formatted_wolfram": "Factorial[n]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "double_factorial_wolfram",
    "input": "Factorial2[n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Double factorial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "factorial2(n)",
    "formatted_wolfram": "factorial2[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "binomial_coefficient_wolfram",
    "input": "Binomial[n, k]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Binomial coefficient",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "binomial(n, k)",
    "formatted_wolfram": "binomial[n, k]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "multinomial_coefficient_wolfram",
    "input": "Multinomial[k1, k2, k3]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Multinomial coefficient",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "multinomial(k1, k2, k3)",
    "formatted_wolfram": "multinomial[k1, k2, k3]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "stirling_first_wolfram",
    "input": "StirlingS1[n, k]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Stirling number of first kind",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "stirling_s1(n, k)",
    "formatted_wolfram": "stirling_s1[n, k]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "stirling_second_wolfram",
    "input": "StirlingS2[n, k]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Stirling number of second kind",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "stirling_s2(n, k)",
    "formatted_wolfram": "stirling_s2[n, k]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "bell_number_wolfram",
    "input": "BellB[n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Bell number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "bell_b(n)",
    "formatted_wolfram": "bell_b[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "catalan_number_wolfram",
    "input": "CatalanNumber[n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Catalan number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "catalan_number(n)",
    "formatted_wolfram": "catalan_number[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "fibonacci_number_wolfram",
    "input": "Fibonacci[n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Fibonacci number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "fibonacci(n)",
    "formatted_wolfram": "fibonacci[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "lucas_number_wolfram",
    "input": "LucasL[n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Lucas number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "lucas_l(n)",
    "formatted_wolfram": "lucas_l[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "euler_totient_wolfram",
    "input": "EulerPhi[n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Euler's totient function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "euler_phi(n)",
    "formatted_wolfram": "euler_phi[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "mobius_function_wolfram",
    "input": "MoebiusMu[n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Möbius function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "mobius(n)",
    "formatted_wolfram": "mobius[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "divisor_function_wolfram",
    "input": "DivisorSigma[k, n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Divisor function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "divisor_sigma(k, n)",
    "formatted_wolfram": "divisor_sigma[k, n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "prime_counting_wolfram",
    "input": "PrimePi[x]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Prime counting function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "prime_pi(x)",
    "formatted_wolfram": "prime_pi[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "legendre_symbol_wolfram",
    "input": "JacobiSymbol[a, p]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Legendre symbol",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "jacobi_symbol(a, p)",
    "formatted_wolfram": "jacobi_symbol[a, p]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "jacobi_symbol_wolfram",
    "input": "JacobiSymbol[a, n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Jacobi symbol",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "jacobi_symbol(a, n)",
    "formatted_wolfram": "jacobi_symbol[a, n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "partition_function_wolfram",
    "input": "PartitionsP[n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Partition function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "partitions_p(n)",
    "formatted_wolfram": "partitions_p[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "ramanujan_tau_wolfram",
    "input": "RamanujanTau[n]",
    "language": "wolfram",
    "category": "combinatorics_number_theory",
    "description": "Ramanujan tau function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "ramanujan_tau(n)",
    "formatted_wolfram": "ramanujan_tau[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "double_integral_wolfram",
    "input": "Integrate[f[x, y], {x, a, b}, {y, c, d}]",
    "language": "wolfram",
    "category": "advanced_calculus",
    "description": "Double integral",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (37, Token(259, \\\"d\\\"), 38), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "triple_integral_wolfram",
    "input": "Integrate[f[x, y, z], {x, a, b}, {y, c, d}, {z, e, f}]",
    "language": "wolfram",
    "category": "advanced_calculus",
    "description": "Triple integral",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (40, Token(259, \\\"d\\\"), 41), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "line_integral_wolfram",
    "input": "Integrate[F · dr, {r, curve}]",
    "language": "wolfram",
    "category": "advanced_calculus",
    "description": "Line integral",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 12 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "surface_integral_wolfram",
    "input": "Integrate[F · n dS, {surface}]",
    "language": "wolfram",
    "category": "advanced_calculus",
    "description": "Surface integral",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 12 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "taylor_series_wolfram",
    "input": "Series[f[x], {x, a, n}]",
    "language": "wolfram",
    "category": "series_expansions",
    "description": "Taylor series",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "series(f(x), \\{x, a, n\\})",
    "formatted_wolfram": "series[f[x], {x, a, n}]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "fourier_series_wolfram",
    "input": "FourierSeries[f[x], x, n]",
    "language": "wolfram",
    "category": "series_expansions",
    "description": "Fourier series",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "fourier_series(f(x), x, n)",
    "formatted_wolfram": "fourier_series[f[x], x, n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "first_order_ode_wolfram",
    "input": "DSolve[y'[x] == f[x, y[x]], y[x], x]",
    "language": "wolfram",
    "category": "differential_equations",
    "description": "First-order ODE solver",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 8 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "second_order_ode_wolfram",
    "input": "DSolve[y''[x] + p[x]*y'[x] + q[x]*y[x] == g[x], y[x], x]",
    "language": "wolfram",
    "category": "differential_equations",
    "description": "Second-order ODE solver",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 8 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
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    "id": "eigenvalue_problem_wolfram",
    "input": "Eigenvalues[A]",
    "language": "wolfram",
    "category": "linear_algebra_advanced",
    "description": "Eigenvalues",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "eigenvalues(A)",
    "formatted_wolfram": "eigenvalues[A]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "eigenvectors_wolfram",
    "input": "Eigenvectors[A]",
    "language": "wolfram",
    "category": "linear_algebra_advanced",
    "description": "Eigenvectors",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "eigenvectors(A)",
    "formatted_wolfram": "eigenvectors[A]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "matrix_exponential_wolfram",
    "input": "MatrixExp[A*t]",
    "language": "wolfram",
    "category": "linear_algebra_advanced",
    "description": "Matrix exponential",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "matrix_exp(A \\cdot t)",
    "formatted_wolfram": "matrix_exp[Times[A, t]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "svd_wolfram",
    "input": "SingularValueDecomposition[A]",
    "language": "wolfram",
    "category": "linear_algebra_advanced",
    "description": "Singular Value Decomposition",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "svd(A)",
    "formatted_wolfram": "svd[A]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "qr_decomposition_wolfram",
    "input": "QRDecomposition[A]",
    "language": "wolfram",
    "category": "linear_algebra_advanced",
    "description": "QR decomposition",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "qr_decomposition(A)",
    "formatted_wolfram": "qr_decomposition[A]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "lu_decomposition_wolfram",
    "input": "LUDecomposition[A]",
    "language": "wolfram",
    "category": "linear_algebra_advanced",
    "description": "LU decomposition",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "lu_decomposition(A)",
    "formatted_wolfram": "lu_decomposition[A]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "complex_conjugate_wolfram",
    "input": "Conjugate[z]",
    "language": "wolfram",
    "category": "complex_analysis",
    "description": "Complex conjugate",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\overline{z}",
    "formatted_wolfram": "conjugate[z]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "complex_modulus_wolfram",
    "input": "Abs[z]",
    "language": "wolfram",
    "category": "complex_analysis",
    "description": "Complex modulus",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "|z|",
    "formatted_wolfram": "abs[z]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "contour_integral_wolfram",
    "input": "Integrate[f[z], {z, contour}]",
    "language": "wolfram",
    "category": "complex_analysis",
    "description": "Contour integral",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\int f(z) \\, d\\{z, contour\\}",
    "formatted_wolfram": "Integrate[f[z], {z, contour}]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "residue_wolfram",
    "input": "Residue[f[z], {z, z0}]",
    "language": "wolfram",
    "category": "complex_analysis",
    "description": "Residue calculation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "residue(f(z), \\{z, z0\\})",
    "formatted_wolfram": "residue[f[z], {z, z0}]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "gcd_latex",
    "input": "\\gcd(a, b)",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Greatest common divisor",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\gcd(a, b)",
    "formatted_wolfram": "gcd[a, b]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "lcm_latex",
    "input": "\\text{lcm}(a, b)",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Least common multiple",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\lcm(a, b)",
    "formatted_wolfram": "lcm[a, b]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "mod_latex",
    "input": "a \\bmod n",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Modular arithmetic",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "mod(a, n)",
    "formatted_wolfram": "mod[a, n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "tensor_product_latex",
    "input": "A \\otimes B",
    "language": "latex",
    "category": "tensor_operations",
    "description": "Tensor product",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "A \\cdot B",
    "formatted_wolfram": "Times[A, B]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "tensor_contraction_latex",
    "input": "T^{ij}_{ij}",
    "language": "latex",
    "category": "tensor_operations",
    "description": "Tensor contraction",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "commutator_latex",
    "input": "[A, B]",
    "language": "latex",
    "category": "quantum_mechanics",
    "description": "Commutator bracket",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "[A, B]",
    "formatted_wolfram": "interval",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "anticommutator_latex",
    "input": "\\{A, B\\}",
    "language": "latex",
    "category": "quantum_mechanics",
    "description": "Anticommutator",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\{A, B\\}",
    "formatted_wolfram": "{A, B}",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "bra_ket_latex",
    "input": "\\langle \\psi | \\phi \\rangle",
    "language": "latex",
    "category": "quantum_mechanics",
    "description": "Bra-ket notation",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "group_operation_latex",
    "input": "g \\circ h",
    "language": "latex",
    "category": "group_theory",
    "description": "Group operation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "compose(g, h)",
    "formatted_wolfram": "compose[g, h]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "group_inverse_latex",
    "input": "g^{-1}",
    "language": "latex",
    "category": "group_theory",
    "description": "Group inverse",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "g^{-1}",
    "formatted_wolfram": "Power[g, -1]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "covariant_derivative_latex",
    "input": "\\nabla_\\mu V^\\nu",
    "language": "latex",
    "category": "differential_geometry",
    "description": "Covariant derivative",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"POWER\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "lie_derivative_latex",
    "input": "\\mathcal{L}_X Y",
    "language": "latex",
    "category": "differential_geometry",
    "description": "Lie derivative",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (11, Token(254, \\\"_\\\"), 12), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "riemann_tensor_latex",
    "input": "R^\\rho_{\\sigma\\mu\\nu}",
    "language": "latex",
    "category": "differential_geometry",
    "description": "Riemann curvature tensor",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "ring_addition_latex",
    "input": "a +_R b",
    "language": "latex",
    "category": "algebraic_structures",
    "description": "Ring addition",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (3, Token(254, \\\"_\\\"), 4), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "field_multiplication_latex",
    "input": "a \\cdot_F b",
    "language": "latex",
    "category": "algebraic_structures",
    "description": "Field multiplication",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (7, Token(254, \\\"_\\\"), 8), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "homeomorphism_latex",
    "input": "X \\cong Y",
    "language": "latex",
    "category": "topology",
    "description": "Homeomorphism",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 2 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "measure_latex",
    "input": "\\mu(E)",
    "language": "latex",
    "category": "measure_theory",
    "description": "Measure of set E",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "mobius(e)",
    "formatted_wolfram": "mobius[E]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "lebesgue_integral_latex",
    "input": "\\int f \\, d\\mu",
    "language": "latex",
    "category": "measure_theory",
    "description": "Lebesgue integral",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 7 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "operator_norm_latex",
    "input": "\\|T\\|_{op}",
    "language": "latex",
    "category": "functional_analysis",
    "description": "Operator norm",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "dual_space_latex",
    "input": "X^*",
    "language": "latex",
    "category": "functional_analysis",
    "description": "Dual space",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(8, \\\"*\\\"), 3), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "morphism_latex",
    "input": "f: A \\to B",
    "language": "latex",
    "category": "category_theory",
    "description": "Morphism in category",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 1 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "functor_latex",
    "input": "F: \\mathcal{C} \\to \\mathcal{D}",
    "language": "latex",
    "category": "category_theory",
    "description": "Functor between categories",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 1 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "gcd_wolfram",
    "input": "GCD[a, b]",
    "language": "wolfram",
    "category": "number_theory_advanced",
    "description": "Greatest common divisor",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\gcd(a, b)",
    "formatted_wolfram": "gcd[a, b]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "lcm_wolfram",
    "input": "LCM[a, b]",
    "language": "wolfram",
    "category": "number_theory_advanced",
    "description": "Least common multiple",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\lcm(a, b)",
    "formatted_wolfram": "lcm[a, b]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "mod_wolfram",
    "input": "Mod[a, n]",
    "language": "wolfram",
    "category": "number_theory_advanced",
    "description": "Modular arithmetic",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "mod(a, n)",
    "formatted_wolfram": "mod[a, n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "airy_ai_latex",
    "input": "\\text{Ai}(x)",
    "language": "latex",
    "category": "special_functions_extended",
    "description": "Airy function Ai",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Ai(x)",
    "formatted_wolfram": "Ai[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "airy_bi_latex",
    "input": "\\text{Bi}(x)",
    "language": "latex",
    "category": "special_functions_extended",
    "description": "Airy function Bi",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Bi(x)",
    "formatted_wolfram": "Bi[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "mathieu_c_latex",
    "input": "C_n(a, q, z)",
    "language": "latex",
    "category": "special_functions_extended",
    "description": "Mathieu cosine function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "C_n(a, q, z)",
    "formatted_wolfram": "C_n[a, q, z]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "mathieu_s_latex",
    "input": "S_n(a, q, z)",
    "language": "latex",
    "category": "special_functions_extended",
    "description": "Mathieu sine function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "S_n(a, q, z)",
    "formatted_wolfram": "S_n[a, q, z]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "airy_ai_wolfram",
    "input": "AiryAi[x]",
    "language": "wolfram",
    "category": "special_functions_extended",
    "description": "Airy function Ai",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "airy_ai(x)",
    "formatted_wolfram": "airy_ai[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "airy_bi_wolfram",
    "input": "AiryBi[x]",
    "language": "wolfram",
    "category": "special_functions_extended",
    "description": "Airy function Bi",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "airy_bi(x)",
    "formatted_wolfram": "airy_bi[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "fractional_derivative_latex",
    "input": "D^\\alpha f(x)",
    "language": "latex",
    "category": "fractional_calculus",
    "description": "Fractional derivative",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (1, Token(253, \\\"^\\\"), 2), expected: [\\\"LBRACKET\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "riemann_liouville_latex",
    "input": "{}^{RL}D^\\alpha f(x)",
    "language": "latex",
    "category": "fractional_calculus",
    "description": "Riemann-Liouville derivative",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (1, Token(274, \\\"}\\\"), 2), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "ito_integral_latex",
    "input": "\\int_0^t X_s \\, dW_s",
    "language": "latex",
    "category": "stochastic_calculus",
    "description": "Itô integral",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (5, Token(0, \\\"0\\\"), 6), expected: [\\\"LBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "stratonovich_integral_latex",
    "input": "\\int_0^t X_s \\circ dW_s",
    "language": "latex",
    "category": "stochastic_calculus",
    "description": "Stratonovich integral",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (5, Token(0, \\\"0\\\"), 6), expected: [\\\"LBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "tribonacci_latex",
    "input": "T_n",
    "language": "latex",
    "category": "combinatorics_advanced",
    "description": "Tribonacci numbers",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "T_n",
    "formatted_wolfram": "T_n",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "motzkin_latex",
    "input": "M_n",
    "language": "latex",
    "category": "combinatorics_advanced",
    "description": "Motzkin numbers",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "M_n",
    "formatted_wolfram": "M_n",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "genocchi_latex",
    "input": "G_n",
    "language": "latex",
    "category": "combinatorics_advanced",
    "description": "Genocchi numbers",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "G_n",
    "formatted_wolfram": "G_n",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "andre_latex",
    "input": "A_n",
    "language": "latex",
    "category": "combinatorics_advanced",
    "description": "André numbers (Euler zigzag numbers)",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "A_n",
    "formatted_wolfram": "A_n",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "marcumq_latex",
    "input": "Q_M(a, b)",
    "language": "latex",
    "category": "special_functions_radio",
    "description": "Marcum Q-function (radio engineering)",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Q_M(a, b)",
    "formatted_wolfram": "legendre_q_indexed[M, a, b]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "meijerg_latex",
    "input": "G_{p,q}^{m,n}(z)",
    "language": "latex",
    "category": "hypergeometric_advanced",
    "description": "Meijer G-function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(272, \\\"{\\\"), 3), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "carmichael_latex",
    "input": "\\lambda(n)",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Carmichael function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "reduced_totient(n)",
    "formatted_wolfram": "reduced_totient[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "primenu_latex",
    "input": "\\nu(n)",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Number of distinct prime factors",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "primenu(n)",
    "formatted_wolfram": "primenu[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "primeomega_latex",
    "input": "\\Omega(n)",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Number of prime factors with multiplicity",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "reduced_totient_latex",
    "input": "\\lambda(n)",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Reduced totient function (Carmichael lambda)",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "reduced_totient(n)",
    "formatted_wolfram": "reduced_totient[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "kronecker_symbol_latex",
    "input": "\\left(\\frac{a}{n}\\right)",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Kronecker symbol",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\frac{a}{n}",
    "formatted_wolfram": "Divide[a, n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "lerchphi_latex",
    "input": "\\Phi(z, s, a)",
    "language": "latex",
    "category": "zeta_functions_advanced",
    "description": "Lerch transcendent function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "polylog_latex",
    "input": "\\text{Li}_s(z)",
    "language": "latex",
    "category": "zeta_functions_advanced",
    "description": "Polylogarithm function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (9, Token(254, \\\"_\\\"), 10), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "stieltjes_latex",
    "input": "\\gamma_n",
    "language": "latex",
    "category": "zeta_functions_advanced",
    "description": "Stieltjes constants",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "riemann_xi_latex",
    "input": "\\xi(s)",
    "language": "latex",
    "category": "zeta_functions_advanced",
    "description": "Riemann xi function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (3, Token(6, \\\"(\\\"), 4), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "levi_civita_latex",
    "input": "\\epsilon_{ijk}",
    "language": "latex",
    "category": "tensor_calculus",
    "description": "Levi-Civita symbol",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (8, Token(254, \\\"_\\\"), 9), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "kronecker_delta_latex",
    "input": "\\delta_{ij}",
    "language": "latex",
    "category": "tensor_calculus",
    "description": "Kronecker delta",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "eijk_latex",
    "input": "E_{ijk}",
    "language": "latex",
    "category": "tensor_calculus",
    "description": "Levi-Civita tensor (alternative notation)",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(272, \\\"{\\\"), 3), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "bspline_basis_latex",
    "input": "B_{i,p}(t)",
    "language": "latex",
    "category": "splines_interpolation",
    "description": "B-spline basis function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(272, \\\"{\\\"), 3), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "interpolating_spline_latex",
    "input": "S(x)",
    "language": "latex",
    "category": "splines_interpolation",
    "description": "Interpolating spline",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "S(x)",
    "formatted_wolfram": "S[x]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "polar_lift_latex",
    "input": "\\text{polar\\_lift}(z)",
    "language": "latex",
    "category": "complex_analysis_advanced",
    "description": "Polar lift function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 11 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "periodic_argument_latex",
    "input": "\\text{periodic\\_arg}(z)",
    "language": "latex",
    "category": "complex_analysis_advanced",
    "description": "Periodic argument function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 14 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "unbranched_argument_latex",
    "input": "\\text{unbranched\\_arg}(z)",
    "language": "latex",
    "category": "complex_analysis_advanced",
    "description": "Unbranched argument function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 16 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "principal_branch_latex",
    "input": "\\text{principal\\_branch}(z)",
    "language": "latex",
    "category": "complex_analysis_advanced",
    "description": "Principal branch function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 15 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "polarify_latex",
    "input": "\\text{polarify}(z)",
    "language": "latex",
    "category": "complex_analysis_advanced",
    "description": "Polarify function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "polarify(z)",
    "formatted_wolfram": "polarify[z]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "unpolarify_latex",
    "input": "\\text{unpolarify}(z)",
    "language": "latex",
    "category": "complex_analysis_advanced",
    "description": "Unpolarify function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "unpolarify(z)",
    "formatted_wolfram": "unpolarify[z]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "singularity_function_latex",
    "input": "\\langle x - a \\rangle^n",
    "language": "latex",
    "category": "singularity_functions",
    "description": "Singularity function (Macaulay brackets)",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "tribonacci_wolfram",
    "input": "Tribonacci[n]",
    "language": "wolfram",
    "category": "combinatorics_advanced",
    "description": "Tribonacci numbers",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "tribonacci(n)",
    "formatted_wolfram": "tribonacci[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "marcumq_wolfram",
    "input": "MarcumQ[M, a, b]",
    "language": "wolfram",
    "category": "special_functions_radio",
    "description": "Marcum Q-function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "marcum_q(M, a, b)",
    "formatted_wolfram": "marcum_q[M, a, b]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "appellf1_wolfram",
    "input": "AppellF1[a, b1, b2, c, x, y]",
    "language": "wolfram",
    "category": "hypergeometric_advanced",
    "description": "Appell hypergeometric function F1",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "appell_f1(a, b1, b2, c, x, y)",
    "formatted_wolfram": "appell_f1[a, b1, b2, c, x, y]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "meijerg_wolfram",
    "input": "MeijerG[{{a1, a2}, {a3}}, {{b1}, {b2, b3}}, z]",
    "language": "wolfram",
    "category": "hypergeometric_advanced",
    "description": "Meijer G-function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "meijer_g(\\{\\{a1, a2\\}, a3\\}, \\{b1, \\{b2, b3\\}\\}, z)",
    "formatted_wolfram": "meijer_g[{{a1, a2}, a3}, {b1, {b2, b3}}, z]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "lerchphi_wolfram",
    "input": "LerchPhi[z, s, a]",
    "language": "wolfram",
    "category": "zeta_functions_advanced",
    "description": "Lerch transcendent function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "lerch_phi(z, s, a)",
    "formatted_wolfram": "lerch_phi[z, s, a]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "polylog_wolfram",
    "input": "PolyLog[s, z]",
    "language": "wolfram",
    "category": "zeta_functions_advanced",
    "description": "Polylogarithm function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "poly_log(s, z)",
    "formatted_wolfram": "poly_log[s, z]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "stieltjes_wolfram",
    "input": "StieltjesGamma[n]",
    "language": "wolfram",
    "category": "zeta_functions_advanced",
    "description": "Stieltjes constants",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "stieltjes_gamma(n)",
    "formatted_wolfram": "stieltjes_gamma[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "tribonacci_constant_latex",
    "input": "\\alpha_3",
    "language": "latex",
    "category": "mathematical_constants_advanced",
    "description": "Tribonacci constant",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "plastic_number_latex",
    "input": "\\rho",
    "language": "latex",
    "category": "mathematical_constants_advanced",
    "description": "Plastic number (real root of x³ - x - 1 = 0)",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "rho",
    "formatted_wolfram": "rho",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "feigenbaum_delta_latex",
    "input": "\\delta",
    "language": "latex",
    "category": "mathematical_constants_advanced",
    "description": "Feigenbaum constant δ",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "delta",
    "formatted_wolfram": "delta",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "feigenbaum_alpha_latex",
    "input": "\\alpha",
    "language": "latex",
    "category": "mathematical_constants_advanced",
    "description": "Feigenbaum constant α",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "alpha",
    "formatted_wolfram": "alpha",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "matrix_exponential_latex",
    "input": "e^A",
    "language": "latex",
    "category": "matrix_functions_advanced",
    "description": "Matrix exponential",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "e^A",
    "formatted_wolfram": "Power[E, A]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "matrix_logarithm_latex",
    "input": "\\log(A)",
    "language": "latex",
    "category": "matrix_functions_advanced",
    "description": "Matrix logarithm",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\log(A)",
    "formatted_wolfram": "Log[A]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "matrix_power_latex",
    "input": "A^{1/2}",
    "language": "latex",
    "category": "matrix_functions_advanced",
    "description": "Matrix fractional power",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sqrt{A}",
    "formatted_wolfram": "Power[A, Times[1, Power[2, -1]]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": false
  },
  {
    "id": "matrix_exponential_wolfram",
    "input": "MatrixExp[A]",
    "language": "wolfram",
    "category": "matrix_functions_advanced",
    "description": "Matrix exponential",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "matrix_exp(A)",
    "formatted_wolfram": "matrix_exp[A]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "matrix_logarithm_wolfram",
    "input": "MatrixLog[A]",
    "language": "wolfram",
    "category": "matrix_functions_advanced",
    "description": "Matrix logarithm",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "matrix_log(A)",
    "formatted_wolfram": "matrix_log[A]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "matrix_power_wolfram",
    "input": "MatrixPower[A, 1/2]",
    "language": "wolfram",
    "category": "matrix_functions_advanced",
    "description": "Matrix fractional power",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "matrix_power(A, \\frac{1}{2})",
    "formatted_wolfram": "matrix_power[A, Times[1, Power[2, -1]]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": false
  },
  {
    "id": "hill_muscle_model_latex",
    "input": "F = F_0 \\cdot (a + b \\cdot v)/(b + v)",
    "language": "latex",
    "category": "biomechanics",
    "description": "Hill muscle model",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "F = F_0 \\cdot \\left(b + v\\right)^{-1} \\cdot \\left(a + b \\cdot v\\right)",
    "formatted_wolfram": "Equal[F, Times[F_0, Power[Plus[b, v], -1], Plus[a, Times[b, v]]]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "michaelis_menten_latex",
    "input": "v = \\frac{V_{max} [S]}{K_m + [S]}",
    "language": "latex",
    "category": "biomechanics",
    "description": "Michaelis-Menten kinetics",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (12, Token(272, \\\"{\\\"), 13), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\", \\\"RBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "stress_tensor_latex",
    "input": "\\sigma_{ij}",
    "language": "latex",
    "category": "continuum_mechanics",
    "description": "Stress tensor",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "strain_tensor_latex",
    "input": "\\epsilon_{ij}",
    "language": "latex",
    "category": "continuum_mechanics",
    "description": "Strain tensor",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (8, Token(254, \\\"_\\\"), 9), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "constitutive_relation_latex",
    "input": "\\sigma = C : \\epsilon",
    "language": "latex",
    "category": "continuum_mechanics",
    "description": "Constitutive relation",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 11 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "transfer_function_latex",
    "input": "G(s) = \\frac{N(s)}{D(s)}",
    "language": "latex",
    "category": "control_theory",
    "description": "Transfer function",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (20, Token(6, \\\"(\\\"), 21), expected: [\\\"LBRACKET\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "pid_controller_latex",
    "input": "u(t) = K_p e(t) + K_i \\int_0^t e(\\tau) d\\tau + K_d \\frac{de(t)}{dt}",
    "language": "latex",
    "category": "control_theory",
    "description": "PID controller",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (11, Token(260, \\\"e\\\"), 12), expected: [\\\"FACTORIAL\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LBRACKET\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_MP\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "routh_hurwitz_latex",
    "input": "\\text{RH}(s)",
    "language": "latex",
    "category": "control_theory",
    "description": "Routh-Hurwitz stability criterion",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "RH(s)",
    "formatted_wolfram": "RH[s]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "dirac_gamma_matrices_latex",
    "input": "\\gamma^\\mu",
    "language": "latex",
    "category": "high_energy_physics",
    "description": "Dirac gamma matrices",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\gamma^{mu}",
    "formatted_wolfram": "Power[EulerGamma, mu]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "pauli_matrices_latex",
    "input": "\\sigma_i",
    "language": "latex",
    "category": "high_energy_physics",
    "description": "Pauli matrices",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "feynman_slash_notation_latex",
    "input": "\\not{p}",
    "language": "latex",
    "category": "high_energy_physics",
    "description": "Feynman slash notation",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "yang_mills_latex",
    "input": "F_{\\mu\\nu}^a = \\partial_\\mu A_\\nu^a - \\partial_\\nu A_\\mu^a + g f^{abc} A_\\mu^b A_\\nu^c",
    "language": "latex",
    "category": "high_energy_physics",
    "description": "Yang-Mills field strength tensor",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(272, \\\"{\\\"), 3), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "creation_operator_latex",
    "input": "a^\\dagger",
    "language": "latex",
    "category": "quantum_optics",
    "description": "Creation operator",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 2 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "annihilation_operator_latex",
    "input": "a",
    "language": "latex",
    "category": "quantum_optics",
    "description": "Annihilation operator",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "a",
    "formatted_wolfram": "a",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "coherent_state_latex",
    "input": "|\\alpha\\rangle",
    "language": "latex",
    "category": "quantum_optics",
    "description": "Coherent state",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 7 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "squeezed_state_latex",
    "input": "S(\\xi) |0\\rangle",
    "language": "latex",
    "category": "quantum_optics",
    "description": "Squeezed state",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (7, Token(273, \\\"|\\\"), 8), expected: [] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "miller_indices_latex",
    "input": "(hkl)",
    "language": "latex",
    "category": "crystallography",
    "description": "Miller indices",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "hkl",
    "formatted_wolfram": "hkl",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "structure_factor_latex",
    "input": "F_{hkl}",
    "language": "latex",
    "category": "crystallography",
    "description": "Structure factor",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(272, \\\"{\\\"), 3), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "reynolds_number_latex",
    "input": "Re = \\frac{\\rho v L}{\\mu}",
    "language": "latex",
    "category": "fluid_dynamics",
    "description": "Reynolds number",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (3, Token(18, \\\"=\\\"), 4), expected: [\\\"LBRACKET\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "prandtl_number_latex",
    "input": "Pr = \\frac{\\nu}{\\alpha}",
    "language": "latex",
    "category": "fluid_dynamics",
    "description": "Prandtl number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Pr = \\frac{nu}{alpha}",
    "formatted_wolfram": "Equal[Pr, Divide[nu, alpha]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "mach_number_latex",
    "input": "Ma = \\frac{v}{c}",
    "language": "latex",
    "category": "fluid_dynamics",
    "description": "Mach number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Ma = \\frac{v}{c}",
    "formatted_wolfram": "Equal[Ma, Divide[v, c]]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "euler_equations_latex",
    "input": "\\frac{\\partial \\rho}{\\partial t} + \\nabla \\cdot (\\rho \\vec{v}) = 0",
    "language": "latex",
    "category": "fluid_dynamics",
    "description": "Euler equations for fluid flow",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(208, \\\"\\\\\\\\partial\\\"), 14), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "debye_length_latex",
    "input": "\\lambda_D = \\sqrt{\\frac{\\epsilon_0 k_B T_e}{n_e e^2}}",
    "language": "latex",
    "category": "plasma_physics",
    "description": "Debye length",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (7, Token(254, \\\"_\\\"), 8), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "plasma_frequency_latex",
    "input": "\\omega_p = \\sqrt{\\frac{n_e e^2}{\\epsilon_0 m_e}}",
    "language": "latex",
    "category": "plasma_physics",
    "description": "Plasma frequency",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "cyclotron_frequency_latex",
    "input": "\\omega_c = \\frac{eB}{m}",
    "language": "latex",
    "category": "plasma_physics",
    "description": "Cyclotron frequency",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(254, \\\"_\\\"), 7), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "lorentz_factor_latex",
    "input": "\\gamma = \\frac{1}{\\sqrt{1 - v^2/c^2}}",
    "language": "latex",
    "category": "relativity",
    "description": "Lorentz factor",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\gamma = \\sqrt^{-1}(1 + -1 \\cdot c^{-2} \\cdot v^2)",
    "formatted_wolfram": "Equal[EulerGamma, Power[Sqrt[Plus[1, Times[-1, Power[c, -2], Power[v, 2]]]], -1]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": null
  },
  {
    "id": "four_momentum_latex",
    "input": "p^\\mu",
    "language": "latex",
    "category": "relativity",
    "description": "Four-momentum",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "p^{mu}",
    "formatted_wolfram": "Power[p, mu]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "minkowski_metric_latex",
    "input": "\\eta_{\\mu\\nu}",
    "language": "latex",
    "category": "relativity",
    "description": "Minkowski metric tensor",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (4, Token(254, \\\"_\\\"), 5), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "hubble_parameter_latex",
    "input": "H(t) = \\frac{\\dot{a}(t)}{a(t)}",
    "language": "latex",
    "category": "cosmology",
    "description": "Hubble parameter",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (20, Token(6, \\\"(\\\"), 21), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"RBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "friedmann_equation_latex",
    "input": "H^2 = \\frac{8\\pi G}{3}\\rho - \\frac{kc^2}{a^2}",
    "language": "latex",
    "category": "cosmology",
    "description": "Friedmann equation",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (13, Token(210, \\\"\\\\\\\\pi\\\"), 16), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"RBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "scale_factor_latex",
    "input": "a(t)",
    "language": "latex",
    "category": "cosmology",
    "description": "Cosmological scale factor",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "a(t)",
    "formatted_wolfram": "a[t]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "chandrasekhar_limit_latex",
    "input": "M_{Ch} = 1.4 M_\\odot",
    "language": "latex",
    "category": "astrophysics",
    "description": "Chandrasekhar limit",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(272, \\\"{\\\"), 3), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "eddington_luminosity_latex",
    "input": "L_{Edd} = \\frac{4\\pi GMm_p c}{\\sigma_T}",
    "language": "latex",
    "category": "astrophysics",
    "description": "Eddington luminosity",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(272, \\\"{\\\"), 3), expected: [\\\"IDENTIFIER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "seismic_wave_velocity_latex",
    "input": "v_p = \\sqrt{\\frac{K + \\frac{4}{3}\\mu}{\\rho}}",
    "language": "latex",
    "category": "geophysics",
    "description": "P-wave velocity",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (33, Token(195, \\\"\\\\\\\\mu\\\"), 36), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"RBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "richter_magnitude_latex",
    "input": "M_L = \\log_{10} A - \\log_{10} A_0",
    "language": "latex",
    "category": "geophysics",
    "description": "Richter magnitude scale",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (10, Token(254, \\\"_\\\"), 11), expected: [\\\"LPAREN\\\", \\\"LBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "coriolis_parameter_latex",
    "input": "f = 2\\Omega \\sin\\phi",
    "language": "latex",
    "category": "geophysics",
    "description": "Coriolis parameter",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 5 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "transfer_function_wolfram",
    "input": "TransferFunctionModel[{{num}}, {{den}}, s]",
    "language": "wolfram",
    "category": "control_theory",
    "description": "Transfer function",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "transfer_function_model(num, den, s)",
    "formatted_wolfram": "transfer_function_model[num, den, s]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "gamma_matrix_wolfram",
    "input": "DiracGamma[mu]",
    "language": "wolfram",
    "category": "high_energy_physics",
    "description": "Dirac gamma matrices",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "dirac_gamma(mu)",
    "formatted_wolfram": "dirac_gamma[mu]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "pauli_matrix_wolfram",
    "input": "PauliMatrix[i]",
    "language": "wolfram",
    "category": "high_energy_physics",
    "description": "Pauli matrices",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "pauli_matrix(i)",
    "formatted_wolfram": "pauli_matrix[I]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "lorentz_factor_wolfram",
    "input": "1/Sqrt[1 - v^2/c^2]",
    "language": "wolfram",
    "category": "relativity",
    "description": "Lorentz factor",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\sqrt^{-1}(1 + -1 \\cdot c^{-2} \\cdot v^2)",
    "formatted_wolfram": "Power[Sqrt[Plus[1, Times[-1, Power[c, -2], Power[v, 2]]]], -1]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": false
  },
  {
    "id": "continued_fraction_latex",
    "input": "[a_0; a_1, a_2, a_3, \\ldots]",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Continued fraction representation",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (4, Token(15, \\\";\\\"), 5), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"COMMA\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "egyptian_fraction_latex",
    "input": "\\frac{1}{a_1} + \\frac{1}{a_2} + \\cdots + \\frac{1}{a_n}",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Egyptian fraction decomposition",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (32, Token(137, \\\"\\\\\\\\cdots\\\"), 38), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "quadratic_residue_latex",
    "input": "\\text{QR}(a, p)",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Quadratic residue",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "QR(a, p)",
    "formatted_wolfram": "QR[a, p]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "primitive_root_latex",
    "input": "\\text{PrimRoot}(n)",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Primitive root modulo n",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "PrimRoot(n)",
    "formatted_wolfram": "PrimRoot[n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "discrete_log_latex",
    "input": "\\log_g a \\pmod{p}",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Discrete logarithm",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (4, Token(254, \\\"_\\\"), 5), expected: [\\\"LPAREN\\\", \\\"LBRACE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "elliptic_curve_latex",
    "input": "y^2 = x^3 + ax + b",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Elliptic curve equation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "y^2 = ax + b + x^3",
    "formatted_wolfram": "Equal[Power[y, 2], Plus[ax, b, Power[x, 3]]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "class_number_latex",
    "input": "h(d)",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Class number of quadratic field",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(259, \\\"d\\\"), 3), expected: [\\\"INTEGER\\\", \\\"FLOAT\\\", \\\"IDENTIFIER\\\", \\\"LPAREN\\\", \\\"RPAREN\\\", \\\"MINUS\\\", \\\"WOLFRAM_ABS\\\", \\\"WOLFRAM_ARG\\\", \\\"WOLFRAM_BINOMIAL\\\", \\\"WOLFRAM_CEILING\\\", \\\"WOLFRAM_CHOLESKY\\\", \\\"WOLFRAM_CONJUGATE\\\", \\\"WOLFRAM_COS\\\", \\\"WOLFRAM_CROSS\\\", \\\"WOLFRAM_CYCLOTOMIC\\\", \\\"WOLFRAM_D\\\", \\\"WOLFRAM_DET\\\", \\\"WOLFRAM_DISCRIMINANT\\\", \\\"WOLFRAM_DIVIDE\\\", \\\"WOLFRAM_DOT\\\", \\\"WOLFRAM_E\\\", \\\"WOLFRAM_EIGENVALUES\\\", \\\"WOLFRAM_EIGENVECTORS\\\", \\\"WOLFRAM_EULER_PHI\\\", \\\"WOLFRAM_EXP\\\", \\\"WOLFRAM_FACTORIAL\\\", \\\"WOLFRAM_FLOOR\\\", \\\"WOLFRAM_GCD_CAPS\\\", \\\"WOLFRAM_GAMMA\\\", \\\"WOLFRAM_GROEBNER\\\", \\\"HERMITE_SUBSCRIPT\\\", \\\"WOLFRAM_I\\\", \\\"BESSEL_I_SUBSCRIPT\\\", \\\"WOLFRAM_IM\\\", \\\"WOLFRAM_INFINITY\\\", \\\"WOLFRAM_INNER\\\", \\\"WOLFRAM_INTEGRATE\\\", \\\"WOLFRAM_INVERSE\\\", \\\"BESSEL_J_SUBSCRIPT\\\", \\\"BESSEL_K_SUBSCRIPT\\\", \\\"WOLFRAM_KRONECKER\\\", \\\"WOLFRAM_LCM_CAPS\\\", \\\"WOLFRAM_LU\\\", \\\"LAGUERRE_SUBSCRIPT\\\", \\\"WOLFRAM_LEAST_SQUARES\\\", \\\"WOLFRAM_LIMIT\\\", \\\"WOLFRAM_LINEAR_SOLVE\\\", \\\"WOLFRAM_LOG\\\", \\\"WOLFRAM_MATRIX_EXP\\\", \\\"WOLFRAM_MATRIX_POWER\\\", \\\"WOLFRAM_MAX\\\", \\\"WOLFRAM_MIN\\\", \\\"WOLFRAM_MINIMAL\\\", \\\"WOLFRAM_MOD\\\", \\\"WOLFRAM_MOEBIUS\\\", \\\"WOLFRAM_NORM\\\", \\\"WOLFRAM_OUTER\\\", \\\"LEGENDRE_P_SUBSCRIPT\\\", \\\"WOLFRAM_PI\\\", \\\"WOLFRAM_PIECEWISE\\\", \\\"WOLFRAM_PLUS\\\", \\\"WOLFRAM_POLY_GCD\\\", \\\"WOLFRAM_PRIME_PI\\\", \\\"WOLFRAM_QR\\\", \\\"LEGENDRE_Q_SUBSCRIPT\\\", \\\"WOLFRAM_RE\\\", \\\"WOLFRAM_RESULTANT\\\", \\\"WOLFRAM_RIEMANN_SIEGEL\\\", \\\"WOLFRAM_ROUND\\\", \\\"WOLFRAM_SIGN\\\", \\\"WOLFRAM_SVD\\\", \\\"WOLFRAM_SQRT\\\", \\\"WOLFRAM_SUBTRACT\\\", \\\"WOLFRAM_SUM\\\", \\\"WOLFRAM_TIMES\\\", \\\"WOLFRAM_TR\\\", \\\"WOLFRAM_TRANSPOSE\\\", \\\"BESSEL_Y_SUBSCRIPT\\\", \\\"LBRACKET\\\", \\\"LATEX_GAMMA\\\", \\\"WOLFRAM_ALPHA\\\", \\\"WOLFRAM_BETA\\\", \\\"WOLFRAM_CHI\\\", \\\"WOLFRAM_DELTA\\\", \\\"WOLFRAM_EPSILON\\\", \\\"WOLFRAM_ETA\\\", \\\"WOLFRAM_IOTA\\\", \\\"WOLFRAM_KAPPA\\\", \\\"WOLFRAM_LAMBDA\\\", \\\"WOLFRAM_MU\\\", \\\"WOLFRAM_NU\\\", \\\"WOLFRAM_OMEGA\\\", \\\"WOLFRAM_OMICRON\\\", \\\"WOLFRAM_PSI\\\", \\\"WOLFRAM_RHO\\\", \\\"WOLFRAM_SIGMA\\\", \\\"WOLFRAM_TAU\\\", \\\"WOLFRAM_THETA\\\", \\\"WOLFRAM_UPSILON\\\", \\\"WOLFRAM_XI\\\", \\\"WOLFRAM_ZETA\\\", \\\"LATEX_ALPHA\\\", \\\"LATEX_ARCCOS\\\", \\\"LATEX_ARCSIN\\\", \\\"LATEX_ARCTAN\\\", \\\"LATEX_BAR\\\", \\\"LATEX_BETA\\\", \\\"LATEX_BINOM\\\", \\\"LATEX_CHI\\\", \\\"LATEX_CHOOSE\\\", \\\"LATEX_COS\\\", \\\"LATEX_COSH\\\", \\\"LATEX_COT\\\", \\\"LATEX_CSC\\\", \\\"LATEX_DDOT\\\", \\\"LATEX_DELTA\\\", \\\"LATEX_DOT\\\", \\\"LATEX_EPSILON\\\", \\\"LATEX_ETA\\\", \\\"LATEX_FRAC\\\", \\\"LATEX_EULER_GAMMA\\\", \\\"LATEX_GCD\\\", \\\"LATEX_HAT\\\", \\\"LATEX_INFTY\\\", \\\"LATEX_INT\\\", \\\"LATEX_IOTA\\\", \\\"LATEX_KAPPA\\\", \\\"LATEX_LAMBDA\\\", \\\"LATEX_LCM\\\", \\\"LATEX_LEFT\\\", \\\"LATEX_LIM\\\", \\\"LATEX_LN\\\", \\\"LATEX_LOG\\\", \\\"LATEX_MATHBB\\\", \\\"LATEX_MATHCAL\\\", \\\"LATEX_MAX\\\", \\\"LATEX_MIN\\\", \\\"LATEX_MU\\\", \\\"LATEX_NABLA\\\", \\\"LATEX_NU\\\", \\\"LATEX_OINT\\\", \\\"LATEX_OMEGA\\\", \\\"LATEX_OMICRON\\\", \\\"LATEX_OVERLINE\\\", \\\"LATEX_PHI\\\", \\\"LATEX_PI\\\", \\\"LATEX_PROD\\\", \\\"LATEX_PSI\\\", \\\"LATEX_RHO\\\", \\\"LATEX_SEC\\\", \\\"LATEX_SIGMA\\\", \\\"LATEX_SIN\\\", \\\"LATEX_SINH\\\", \\\"LATEX_SQRT\\\", \\\"LATEX_SUM\\\", \\\"LATEX_TAN\\\", \\\"LATEX_TANH\\\", \\\"LATEX_TAU\\\", \\\"LATEX_TEXT\\\", \\\"LATEX_THETA\\\", \\\"LATEX_TILDE\\\", \\\"LATEX_UNDERLINE\\\", \\\"LATEX_UPSILON\\\", \\\"LATEX_VARPHI\\\", \\\"LATEX_VEC\\\", \\\"LATEX_XI\\\", \\\"LATEX_ZETA\\\", \\\"LATEX_LBRACE\\\", \\\"E_CONST\\\", \\\"EULER_GAMMA\\\", \\\"GAMMA_CONST\\\", \\\"GOLDEN_RATIO\\\", \\\"I_CONST\\\", \\\"INFINITY\\\", \\\"PHI\\\", \\\"PI\\\", \\\"UNDEFINED\\\", \\\"LBRACE\\\", \\\"PIPE\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "quadratic_form_latex",
    "input": "ax^2 + bxy + cy^2",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Binary quadratic form",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "bxy + ax^2 + cy^2",
    "formatted_wolfram": "Plus[bxy, Power[ax, 2], Power[cy, 2]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "pell_equation_latex",
    "input": "x^2 - Dy^2 = 1",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Pell equation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "x^2 - Dy^2 = 1",
    "formatted_wolfram": "Equal[Subtract[Power[x, 2], Power[Dy, 2]], 1]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "sum_of_squares_latex",
    "input": "r_k(n)",
    "language": "latex",
    "category": "number_theory_advanced",
    "description": "Number of ways to write n as sum of k squares",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "r_k(n)",
    "formatted_wolfram": "r_k[n]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "cyclotomic_polynomial_latex",
    "input": "\\Phi_n(x)",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "n-th cyclotomic polynomial",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "minimal_polynomial_latex",
    "input": "\\text{MinPoly}(\\alpha, \\mathbb{Q})",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Minimal polynomial of algebraic number",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "MinPoly(alpha, mathbb_Q)",
    "formatted_wolfram": "MinPoly[alpha, mathbb_Q]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "irreducible_polynomial_latex",
    "input": "\\text{Irred}(f, \\mathbb{F}_p)",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Irreducible polynomial over finite field",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (26, Token(254, \\\"_\\\"), 27), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"RPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"COMMA\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "polynomial_gcd_latex",
    "input": "\\gcd(f(x), g(x))",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Polynomial greatest common divisor",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\gcd(f(x), g(x))",
    "formatted_wolfram": "gcd[f[x], g[x]]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "polynomial_lcm_latex",
    "input": "\\text{lcm}(f(x), g(x))",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Polynomial least common multiple",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "\\lcm(f(x), g(x))",
    "formatted_wolfram": "lcm[f[x], g[x]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "resultant_latex",
    "input": "\\text{Res}(f, g)",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Resultant of two polynomials",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Res(f, g)",
    "formatted_wolfram": "Res[f, g]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "discriminant_latex",
    "input": "\\Delta(f)",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Discriminant of polynomial",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 0 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "sylvester_matrix_latex",
    "input": "\\text{Syl}(f, g)",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Sylvester matrix",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Syl(f, g)",
    "formatted_wolfram": "Syl[f, g]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "polynomial_norm_latex",
    "input": "N_{L/K}(\\alpha)",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Norm of algebraic element",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (2, Token(272, \\\"{\\\"), 3), expected: [\\\"FACTORIAL\\\", \\\"NOT_EQUALS\\\", \\\"LPAREN\\\", \\\"MULTIPLY\\\", \\\"PLUS\\\", \\\"MINUS\\\", \\\"ARROW\\\", \\\"DOT\\\", \\\"DIVIDE\\\", \\\"LESS\\\", \\\"LESS_EQUAL\\\", \\\"EQUALS\\\", \\\"DOUBLE_EQUALS\\\", \\\"GREATER\\\", \\\"GREATER_EQUAL\\\", \\\"LBRACKET\\\", \\\"LATEX_APPROX\\\", \\\"LATEX_AST\\\", \\\"LATEX_BMOD\\\", \\\"LATEX_BULLET\\\", \\\"LATEX_CAP\\\", \\\"LATEX_CDOT\\\", \\\"LATEX_CIRC\\\", \\\"LATEX_CUP\\\", \\\"LATEX_DIV\\\", \\\"LATEX_EQUIV\\\", \\\"LATEX_GEQ\\\", \\\"LATEX_LEFTARROW\\\", \\\"LATEX_LEFTRIGHTARROW\\\", \\\"LATEX_LEQ\\\", \\\"LATEX_MP\\\", \\\"LATEX_NEQ\\\", \\\"LATEX_ODOT\\\", \\\"LATEX_OSLASH\\\", \\\"LATEX_OTIMES\\\", \\\"LATEX_PM\\\", \\\"LATEX_PROPTO\\\", \\\"LATEX_RIGHTARROW\\\", \\\"LATEX_SIM\\\", \\\"LATEX_STAR\\\", \\\"LATEX_TIMES\\\", \\\"LATEX_TO\\\", \\\"LATEX_VEE\\\", \\\"LATEX_WEDGE\\\", \\\"POWER\\\", \\\"SUBSCRIPT\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "polynomial_trace_latex",
    "input": "\\text{Tr}_{L/K}(\\alpha)",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Trace of algebraic element",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: UnrecognizedToken { token: (6, Token(91, \\\"Tr\\\"), 8), expected: [\\\"IDENTIFIER\\\"] }\")",
    "parse_error_category": "UnrecognizedToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "groebner_basis_latex",
    "input": "\\text{GB}(I)",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Gröbner basis of ideal",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "GB(i)",
    "formatted_wolfram": "GB[I]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "hilbert_polynomial_latex",
    "input": "H_I(t)",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Hilbert polynomial of ideal",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "H_I(t)",
    "formatted_wolfram": "hermite_indexed[I, t]",
    "exact_string_match": true,
    "normalized_match": true,
    "semantic_match": true
  },
  {
    "id": "polynomial_factorization_latex",
    "input": "\\text{Factor}(f, \\mathbb{Q})",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Polynomial factorization over field",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Factor(f, mathbb_Q)",
    "formatted_wolfram": "Factor[f, mathbb_Q]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "square_free_factorization_latex",
    "input": "\\text{SqFree}(f)",
    "language": "latex",
    "category": "polynomial_theory_advanced",
    "description": "Square-free factorization",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "SqFree(f)",
    "formatted_wolfram": "SqFree[f]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "galois_group_latex",
    "input": "\\text{Gal}(L/K)",
    "language": "latex",
    "category": "galois_theory",
    "description": "Galois group of field extension",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Gal(\\frac{L}{K})",
    "formatted_wolfram": "Gal[Divide[L, K]]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "splitting_field_latex",
    "input": "\\text{Split}(f, K)",
    "language": "latex",
    "category": "galois_theory",
    "description": "Splitting field of polynomial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "Split(f, K)",
    "formatted_wolfram": "Split[f, K]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "field_degree_latex",
    "input": "[L : K]",
    "language": "latex",
    "category": "galois_theory",
    "description": "Degree of field extension",
    "parse_success": false,
    "parse_error": "SyntaxError(\"LALRPOP parse error: InvalidToken { location: 3 }\")",
    "parse_error_category": "InvalidToken",
    "formatted_latex": null,
    "formatted_wolfram": null,
    "exact_string_match": null,
    "normalized_match": null,
    "semantic_match": null
  },
  {
    "id": "continued_fraction_wolfram",
    "input": "ContinuedFraction[x]",
    "language": "wolfram",
    "category": "number_theory_advanced",
    "description": "Continued fraction representation",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "continued_fraction(x)",
    "formatted_wolfram": "continued_fraction[x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "quadratic_residue_wolfram",
    "input": "JacobiSymbol[a, n]",
    "language": "wolfram",
    "category": "number_theory_advanced",
    "description": "Quadratic residue (Jacobi symbol)",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "jacobi_symbol(a, n)",
    "formatted_wolfram": "jacobi_symbol[a, n]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "elliptic_curve_wolfram",
    "input": "EllipticCurve[{a, b}]",
    "language": "wolfram",
    "category": "number_theory_advanced",
    "description": "Elliptic curve",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "elliptic_curve(\\{a, b\\})",
    "formatted_wolfram": "elliptic_curve[{a, b}]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "cyclotomic_polynomial_wolfram",
    "input": "CyclotomicPolynomial[n, x]",
    "language": "wolfram",
    "category": "polynomial_theory_advanced",
    "description": "Cyclotomic polynomial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "cyclotomic_polynomial(n, x)",
    "formatted_wolfram": "cyclotomic_polynomial[n, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "minimal_polynomial_wolfram",
    "input": "MinimalPolynomial[alpha, x]",
    "language": "wolfram",
    "category": "polynomial_theory_advanced",
    "description": "Minimal polynomial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "minimal_polynomial(alpha, x)",
    "formatted_wolfram": "minimal_polynomial[alpha, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "resultant_wolfram",
    "input": "Resultant[f, g, x]",
    "language": "wolfram",
    "category": "polynomial_theory_advanced",
    "description": "Resultant of polynomials",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "resultant(f, g, x)",
    "formatted_wolfram": "resultant[f, g, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "discriminant_wolfram",
    "input": "Discriminant[f, x]",
    "language": "wolfram",
    "category": "polynomial_theory_advanced",
    "description": "Discriminant of polynomial",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "discriminant(f, x)",
    "formatted_wolfram": "discriminant[f, x]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "groebner_basis_wolfram",
    "input": "GroebnerBasis[{f1, f2, f3}, {x, y, z}]",
    "language": "wolfram",
    "category": "polynomial_theory_advanced",
    "description": "Gröbner basis",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "groebner_basis(\\{f1, f2, f3\\}, \\{x, y, z\\})",
    "formatted_wolfram": "groebner_basis[{f1, f2, f3}, {x, y, z}]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  },
  {
    "id": "polynomial_gcd_wolfram",
    "input": "PolynomialGCD[f, g]",
    "language": "wolfram",
    "category": "polynomial_theory_advanced",
    "description": "Polynomial GCD",
    "parse_success": true,
    "parse_error": null,
    "parse_error_category": null,
    "formatted_latex": "polynomial_gcd(f, g)",
    "formatted_wolfram": "polynomial_gcd[f, g]",
    "exact_string_match": false,
    "normalized_match": false,
    "semantic_match": true
  }
]