[
{
"id": "basic_add_latex",
"language": "latex",
"category": "basic_arithmetic",
"input": "x + y",
"expected_expr": "x + y",
"description": "Simple addition"
},
{
"id": "basic_sub_latex",
"language": "latex",
"category": "basic_arithmetic",
"input": "x - y",
"expected_expr": "x + -1 * y",
"description": "Subtraction"
},
{
"id": "basic_mul_latex",
"language": "latex",
"category": "basic_arithmetic",
"input": "x \\cdot y",
"expected_expr": "x * y",
"description": "Multiplication"
},
{
"id": "basic_div_latex",
"language": "latex",
"category": "basic_arithmetic",
"input": "\\frac{x}{y}",
"expected_expr": "x * y^{-1}",
"description": "Division as fraction"
},
{
"id": "basic_add_wolfram",
"language": "wolfram",
"category": "basic_arithmetic",
"input": "x + y",
"expected_expr": "x + y",
"description": "Simple addition"
},
{
"id": "basic_mul_wolfram",
"language": "wolfram",
"category": "basic_arithmetic",
"input": "Times[x, y]",
"expected_expr": "x * y",
"description": "Times function"
},
{
"id": "basic_div_wolfram",
"language": "wolfram",
"category": "basic_arithmetic",
"input": "x / y",
"expected_expr": "Mul([Symbol(Symbol { name: \"x\" }), Pow(Box(Symbol(Symbol { name: \"y\" })), Number(Integer(-1)))])",
"description": "Division"
},
{
"id": "simple_fraction_latex",
"language": "latex",
"category": "fractions",
"input": "\\frac{1}{2}",
"expected_expr": "Number(Rational(1/2))",
"description": "Simple fraction"
},
{
"id": "simple_power_latex",
"language": "latex",
"category": "powers_roots",
"input": "x^2",
"expected_expr": "Pow(Box(Symbol(Symbol { name: \"x\" })), Number(Integer(2)))",
"description": "Simple power"
},
{
"id": "sqrt_latex",
"language": "latex",
"category": "powers_roots",
"input": "\\sqrt{x}",
"expected_expr": "Pow(Box(Symbol(Symbol { name: \"x\" })), Number(Rational(1/2)))",
"description": "Square root"
},
{
"id": "exponential_latex",
"language": "latex",
"category": "powers_roots",
"input": "e^x",
"expected_expr": "Pow(Box(Constant(E)), Symbol(Symbol { name: \"x\" }))",
"description": "Exponential with e constant"
},
{
"id": "simple_power_wolfram",
"language": "wolfram",
"category": "powers_roots",
"input": "x^2",
"expected_expr": "Pow(Box(Symbol(Symbol { name: \"x\" })), Number(Integer(2)))",
"description": "Simple power"
},
{
"id": "sqrt_wolfram",
"language": "wolfram",
"category": "powers_roots",
"input": "Sqrt[x]",
"expected_expr": "Pow(Box(Symbol(Symbol { name: \"x\" })), Number(Rational(1/2)))",
"description": "Square root"
},
{
"id": "exponential_wolfram",
"language": "wolfram",
"category": "powers_roots",
"input": "Exp[x]",
"expected_expr": "Pow(Box(Constant(E)), Symbol(Symbol { name: \"x\" }))",
"description": "Exponential function"
},
{
"id": "sin_latex",
"language": "latex",
"category": "trigonometric",
"input": "\\sin(x)",
"expected_expr": "Function{name:sin, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Sine function"
},
{
"id": "cos_latex",
"language": "latex",
"category": "trigonometric",
"input": "\\cos(x)",
"expected_expr": "Function{name:cos, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Cosine function"
},
{
"id": "sin_wolfram",
"language": "wolfram",
"category": "trigonometric",
"input": "Sin[x]",
"expected_expr": "Function{name:sin, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Sine function"
},
{
"id": "cos_wolfram",
"language": "wolfram",
"category": "trigonometric",
"input": "Cos[x]",
"expected_expr": "Function{name:cos, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Cosine function"
},
{
"id": "ln_latex",
"language": "latex",
"category": "logarithmic",
"input": "\\ln(x)",
"expected_expr": "Function{name:ln, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Natural logarithm"
},
{
"id": "log_latex",
"language": "latex",
"category": "logarithmic",
"input": "\\log(x)",
"expected_expr": "Function{name:log, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Common logarithm"
},
{
"id": "ln_wolfram",
"language": "wolfram",
"category": "logarithmic",
"input": "Log[x]",
"expected_expr": "Function{name:ln, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Natural logarithm"
},
{
"id": "pi_constant_latex",
"language": "latex",
"category": "mathematical_constants",
"input": "\\pi",
"expected_expr": "Constant(Pi)",
"description": "Pi constant"
},
{
"id": "e_constant_latex",
"language": "latex",
"category": "mathematical_constants",
"input": "e",
"expected_expr": "Constant(E)",
"description": "Euler's number"
},
{
"id": "i_constant_latex",
"language": "latex",
"category": "mathematical_constants",
"input": "i",
"expected_expr": "Constant(I)",
"description": "Imaginary unit"
},
{
"id": "infinity_latex",
"language": "latex",
"category": "mathematical_constants",
"input": "\\infty",
"expected_expr": "Constant(Infinity)",
"description": "Infinity"
},
{
"id": "pi_constant_wolfram",
"language": "wolfram",
"category": "mathematical_constants",
"input": "Pi",
"expected_expr": "Constant(Pi)",
"description": "Pi constant"
},
{
"id": "e_constant_wolfram",
"language": "wolfram",
"category": "mathematical_constants",
"input": "E",
"expected_expr": "Constant(E)",
"description": "Euler's number"
},
{
"id": "i_constant_wolfram",
"language": "wolfram",
"category": "mathematical_constants",
"input": "I",
"expected_expr": "Constant(I)",
"description": "Imaginary unit"
},
{
"id": "complex_number_wolfram",
"language": "wolfram",
"category": "complex_numbers",
"input": "3 + 4*I",
"expected_expr": "Complex(Box(ComplexData{real: Number(Integer(3)), imag: Number(Integer(4))}))",
"description": "Complex number"
},
{
"id": "derivative_latex",
"language": "latex",
"category": "calculus_first_class",
"input": "\\frac{d}{dx} x^2",
"expected_expr": "Calculus(Box(Calculus(Box(Derivative{expression: Pow(Box(Symbol(Symbol { name: \"x\" })))), Number(Integer(2))), variable: Symbol { name: \"x\" }, order: 1}))",
"description": "First derivative - FIRST CLASS"
},
{
"id": "integral_latex",
"language": "latex",
"category": "calculus_first_class",
"input": "\\int x dx",
"expected_expr": "Calculus(Box(Calculus(Box(Integral{integrand: Symbol(Symbol { name: \"x\" }))), variable: Symbol { name: \"x\" }, bounds: None}))",
"description": "Indefinite integral - FIRST CLASS"
},
{
"id": "definite_integral_latex",
"language": "latex",
"category": "calculus_first_class",
"input": "\\int_0^1 x dx",
"expected_expr": "Calculus(Box(Calculus(Box(Integral{integrand: Symbol(Symbol { name: \"x\" }))), variable: Symbol { name: \"x\" }, bounds: Some((Number(Integer(0)), Number(Integer(1))))}))",
"description": "Definite integral - FIRST CLASS"
},
{
"id": "sum_latex",
"language": "latex",
"category": "calculus_first_class",
"input": "\\sum_{i=1}^n i^2",
"expected_expr": "Calculus(Box(Calculus(Box(Sum{expression: Pow(Box(Symbol(Symbol { name: \"i\" })))), Number(Integer(2))), variable: Symbol { name: \"i\" }, start: Number(Integer(1)), end: Symbol(Symbol { name: \"n\" })}))",
"description": "Summation - FIRST CLASS"
},
{
"id": "derivative_wolfram",
"language": "wolfram",
"category": "calculus_first_class",
"input": "D[x^2, x]",
"expected_expr": "Calculus(Box(Derivative{expression: Box(Pow(Box(Symbol(Symbol { name: \"x\" })))), Number(Integer(2)))), variable: Symbol { name: \"x\" }, order: 1}",
"description": "First derivative - FIRST CLASS"
},
{
"id": "integral_wolfram",
"language": "wolfram",
"category": "calculus_first_class",
"input": "Integrate[x, x]",
"expected_expr": "Calculus(Box(Integral{integrand: Box(Symbol(Symbol { name: \"x\" })))), variable: Symbol { name: \"x\" }, bounds: None}",
"description": "Indefinite integral - FIRST CLASS"
},
{
"id": "definite_integral_wolfram",
"language": "wolfram",
"category": "calculus_first_class",
"input": "Integrate[x, {x, 0, 1}]",
"expected_expr": "Calculus(Box(Integral{integrand: Box(Symbol(Symbol { name: \"x\" })))), variable: Symbol { name: \"x\" }, bounds: Some((Box(Number(Integer(0))), Box(Number(Integer(1)))))}",
"description": "Definite integral - FIRST CLASS"
},
{
"id": "limit_wolfram",
"language": "wolfram",
"category": "calculus_first_class",
"input": "Limit[Sin[x], x -> 0]",
"expected_expr": "Calculus(Box(Limit{expression: Box(Function{name:sin, args:Box([Symbol(Symbol { name: \"x\" })))])}), variable: Symbol { name: \"x\" }, approach: Box(Number(Integer(0))), direction: Both}",
"description": "Limit - FIRST CLASS"
},
{
"id": "sum_wolfram",
"language": "wolfram",
"category": "calculus_first_class",
"input": "Sum[i^2, {i, 1, n}]",
"expected_expr": "Calculus(Box(Sum{expression: Box(Pow(Box(Symbol(Symbol { name: \"i\" })))), Number(Integer(2)))), variable: Symbol { name: \"i\" }, start: Box(Number(Integer(1))), end: Box(Symbol(Symbol { name: \"n\" }))}",
"description": "Summation - FIRST CLASS"
},
{
"id": "matrix_latex",
"language": "latex",
"category": "matrices_vectors",
"input": "\\begin{pmatrix} 1 & 2 \\\\ 3 & 4 \\end{pmatrix}",
"expected_expr": "Matrix(Box([[Number(Integer(1)), Number(Integer(2))], [Number(Integer(3)), Number(Integer(4))]]))",
"description": "2x2 matrix"
},
{
"id": "matrix_wolfram",
"language": "wolfram",
"category": "matrices_vectors",
"input": "{{1, 2}, {3, 4}}",
"expected_expr": "Matrix(Box([[Number(Integer(1)), Number(Integer(2))], [Number(Integer(3)), Number(Integer(4))]]))",
"description": "2x2 matrix"
},
{
"id": "set_latex",
"language": "latex",
"category": "sets_intervals",
"input": "\\{1, 2, 3\\}",
"expected_expr": "Set(Box([Number(Integer(1)), Number(Integer(2)), Number(Integer(3))]))",
"description": "Finite set"
},
{
"id": "interval_closed_latex",
"language": "latex",
"category": "sets_intervals",
"input": "[0, 1]",
"expected_expr": "Interval{start: Box(Number(Integer(0))), end: Box(Number(Integer(1))), start_inclusive: true, end_inclusive: true}",
"description": "Closed interval"
},
{
"id": "interval_open_latex",
"language": "latex",
"category": "sets_intervals",
"input": "(0, 1)",
"expected_expr": "Interval{start: Box(Number(Integer(0))), end: Box(Number(Integer(1))), start_inclusive: false, end_inclusive: false}",
"description": "Open interval"
},
{
"id": "set_wolfram",
"language": "wolfram",
"category": "sets_intervals",
"input": "{1, 2, 3}",
"expected_expr": "Set(Box([Number(Integer(1)), Number(Integer(2)), Number(Integer(3))]))",
"description": "Finite set"
},
{
"id": "equation_latex",
"language": "latex",
"category": "equations_relations",
"input": "x = 5",
"expected_expr": "Relation{left: Box(Symbol(Symbol { name: \"x\" })), right: Box(Number(Integer(5))), relation_type: Equal}",
"description": "Simple equation"
},
{
"id": "inequality_latex",
"language": "latex",
"category": "equations_relations",
"input": "x < y",
"expected_expr": "Relation{left: Box(Symbol(Symbol { name: \"x\" })), right: Box(Symbol(Symbol { name: \"y\" })), relation_type: Less}",
"description": "Less than inequality"
},
{
"id": "equation_wolfram",
"language": "wolfram",
"category": "equations_relations",
"input": "x == 5",
"expected_expr": "Relation{left: Box(Symbol(Symbol { name: \"x\" })), right: Box(Number(Integer(5))), relation_type: Equal}",
"description": "Simple equation"
},
{
"id": "special_gamma_latex",
"language": "latex",
"category": "special_functions",
"input": "\\Gamma(x)",
"expected_expr": "Function{name:gamma, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Gamma function"
},
{
"id": "special_gamma_wolfram",
"language": "wolfram",
"category": "special_functions",
"input": "Gamma[x]",
"expected_expr": "Function{name:gamma, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Gamma function"
},
{
"id": "piecewise_latex",
"language": "latex",
"category": "piecewise_functions",
"input": "\\begin{cases} x & \\text{if } x > 0 \\\\ -x & \\text{if } x \\leq 0 \\end{cases}",
"expected_expr": "Piecewise{cases: Box([(Relation{left: Box(Symbol(Symbol { name: \"x\" })), right: Box(Number(Integer(0))), relation_type: Greater}, Symbol(Symbol { name: \"x\" })), (Relation{left: Box(Symbol(Symbol { name: \"x\" })), right: Box(Number(Integer(0))), relation_type: LessEqual}, Mul([Number(Integer(-1)), Symbol(Symbol { name: \"x\" })]))])}",
"description": "Absolute value as piecewise"
},
{
"id": "piecewise_wolfram",
"language": "wolfram",
"category": "piecewise_functions",
"input": "Piecewise[{{x, x > 0}, {-x, x <= 0}}]",
"expected_expr": "Piecewise{cases: Box([(Relation{left: Box(Symbol(Symbol { name: \"x\" })), right: Box(Number(Integer(0))), relation_type: Greater}, Symbol(Symbol { name: \"x\" })), (Relation{left: Box(Symbol(Symbol { name: \"x\" })), right: Box(Number(Integer(0))), relation_type: LessEqual}, Mul([Number(Integer(-1)), Symbol(Symbol { name: \"x\" })]))])}",
"description": "Absolute value as piecewise"
},
{
"id": "exponential_series_latex",
"language": "latex",
"category": "complex_expressions",
"input": "\\sum_{n=0}^{\\infty} \\frac{x^n}{n!}",
"expected_expr": "Calculus(Box(Sum{expression: Box(Mul(Box([Pow(Box(Symbol(Symbol { name: \"x\" })))), Symbol(Symbol { name: \"n\" })), Pow(Box(Function{name:factorial, args:Box([Symbol(Symbol { name: \"n\" })])}), Box(Number(Integer(-1))))]))), variable: Symbol { name: \"n\" }, start: Box(Number(Integer(0))), end: Box(Constant(Infinity))}",
"description": "Exponential series - FIRST CLASS SUM"
},
{
"id": "limit_definition_e_latex",
"language": "latex",
"category": "complex_expressions",
"input": "\\lim_{n \\to \\infty} \\left(1 + \\frac{1}{n}\\right)^n",
"expected_expr": "Calculus(Box(Limit{expression: Box(Pow(Box(Add([Number(Integer(1)), Pow(Box(Symbol(Symbol { name: \"n\" })))), Number(Integer(-1)))])), Box(Symbol(Symbol { name: \"n\" })))), variable: Symbol { name: \"n\" }, approach: Box(Constant(Infinity)), direction: Both}",
"description": "Limit definition of e - FIRST CLASS"
},
{
"id": "partial_derivative_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "\\frac{\\partial f}{\\partial x}",
"expected_expr": "Function{name: \"partial_derivative\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"x\" }), Number(Integer(1))])}",
"description": "Partial derivative"
},
{
"id": "mixed_partial_derivative_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "\\frac{\\partial^2 f}{\\partial x \\partial y}",
"expected_expr": "Function{name: \"mixed_partial\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Mixed partial derivative"
},
{
"id": "gradient_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "\\nabla f",
"expected_expr": "Function{name: \"gradient\", args: Box([Symbol(Symbol { name: \"f\" })])}",
"description": "Gradient operator"
},
{
"id": "divergence_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "\\nabla \\cdot \\vec{F}",
"expected_expr": "Function{name: \"divergence\", args: Box([Function{name: \"vector\", args: Box([Symbol(Symbol { name: \"F\" })])}])}",
"description": "Divergence operator"
},
{
"id": "curl_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "\\nabla \\times \\vec{F}",
"expected_expr": "Function{name: \"curl\", args: Box([Function{name: \"vector\", args: Box([Symbol(Symbol { name: \"F\" })])}])}",
"description": "Curl operator"
},
{
"id": "laplacian_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "\\nabla^2 f",
"expected_expr": "Function{name: \"laplacian\", args: Box([Symbol(Symbol { name: \"f\" })])}",
"description": "Laplacian operator"
},
{
"id": "double_integral_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "\\iint_D f(x,y) \\, dx \\, dy",
"expected_expr": "Function{name: \"double_integral\", args: Box([Function{name: \"f\", args: Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}, Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" }), Symbol(Symbol { name: \"D\" })])}",
"description": "Double integral over region"
},
{
"id": "triple_integral_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "\\iiint_V f(x,y,z) \\, dx \\, dy \\, dz",
"expected_expr": "Function{name: \"triple_integral\", args: Box([Function{name: \"f\", args: Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" }), Symbol(Symbol { name: \"z\" })])}, Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" }), Symbol(Symbol { name: \"z\" }), Symbol(Symbol { name: \"V\" })])}",
"description": "Triple integral over volume"
},
{
"id": "line_integral_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "\\int_C \\vec{F} \\cdot d\\vec{r}",
"expected_expr": "Function{name: \"line_integral\", args: Box([Function{name: \"vector\", args: Box([Symbol(Symbol { name: \"F\" })])}, Symbol(Symbol { name: \"C\" })])}",
"description": "Line integral of vector field"
},
{
"id": "surface_integral_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "\\iint_S \\vec{F} \\cdot \\vec{n} \\, dS",
"expected_expr": "Function{name: \"surface_integral\", args: Box([Function{name: \"vector\", args: Box([Symbol(Symbol { name: \"F\" })])}, Symbol(Symbol { name: \"S\" })])}",
"description": "Surface integral of vector field"
},
{
"id": "directional_derivative_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "D_{\\vec{u}} f",
"expected_expr": "Function{name: \"directional_derivative\", args: Box([Symbol(Symbol { name: \"f\" }), Function{name: \"vector\", args: Box([Symbol(Symbol { name: \"u\" })])}])}",
"description": "Directional derivative"
},
{
"id": "jacobian_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "J_f",
"expected_expr": "Function{name: \"jacobian\", args: Box([Symbol(Symbol { name: \"f\" })])}",
"description": "Jacobian matrix"
},
{
"id": "hessian_latex",
"language": "latex",
"category": "advanced_calculus",
"input": "H_f",
"expected_expr": "Function{name: \"hessian\", args: Box([Symbol(Symbol { name: \"f\" })])}",
"description": "Hessian matrix"
},
{
"id": "partial_derivative_wolfram",
"language": "wolfram",
"category": "advanced_calculus",
"input": "D[f[x, y], x]",
"expected_expr": "PartialCalculus(Box(Derivative{expression: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"x\" }))), Symbol(Symbol { name: \"y\" })])}), variable: Symbol { name: \"x\" }, order: 1}",
"description": "Partial derivative"
},
{
"id": "gradient_wolfram",
"language": "wolfram",
"category": "advanced_calculus",
"input": "Grad[f[x, y, z], {x, y, z}]",
"expected_expr": "Function{name: \"gradient\", args: Box([Function{name: \"f\", args: Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" }), Symbol(Symbol { name: \"z\" })])}])}",
"description": "Gradient operator"
},
{
"id": "divergence_wolfram",
"language": "wolfram",
"category": "advanced_calculus",
"input": "Div[{Fx, Fy, Fz}, {x, y, z}]",
"expected_expr": "Function{name: \"divergence\", args: Box([Function{name: \"vector\", args: Box([Symbol(Symbol { name: \"Fx\" }), Symbol(Symbol { name: \"Fy\" }), Symbol(Symbol { name: \"Fz\" })])}])}",
"description": "Divergence operator"
},
{
"id": "curl_wolfram",
"language": "wolfram",
"category": "advanced_calculus",
"input": "Curl[{Fx, Fy, Fz}, {x, y, z}]",
"expected_expr": "Function{name: \"curl\", args: Box([Function{name: \"vector\", args: Box([Symbol(Symbol { name: \"Fx\" }), Symbol(Symbol { name: \"Fy\" }), Symbol(Symbol { name: \"Fz\" })])}])}",
"description": "Curl operator"
},
{
"id": "taylor_series_latex",
"language": "latex",
"category": "series_expansions",
"input": "\\sum_{n=0}^{\\infty} \\frac{f^{(n)}(a)}{n!} (x-a)^n",
"expected_expr": "Calculus(Box(Sum{expression: Box(Mul(Box([Mul(Box([Calculus(Box(Derivative{expression: Box(Symbol(Symbol { name: \"f\" })))))), variable: Symbol { name: \"x\" }, order: Symbol { name: \"n\" }}, Pow(Box(Function{name:factorial, args:Box([Symbol(Symbol { name: \"n\" })])}), Box(Number(Integer(-1))))])), Pow(Add([Symbol(Symbol { name: \"x\" }, Mul(Box([Number(Integer(-1)), Symbol(Symbol { name: \"a\" })])]))), Box(Symbol(Symbol { name: \"n\" })))]))), variable: Symbol { name: \"n\" }, start: Box(Number(Integer(0))), end: Box(Constant(Infinity))}",
"description": "Taylor series expansion"
},
{
"id": "maclaurin_series_latex",
"language": "latex",
"category": "series_expansions",
"input": "\\sum_{n=0}^{\\infty} \\frac{f^{(n)}(0)}{n!} x^n",
"expected_expr": "Calculus(Box(Sum{expression: Box(Mul(Box([Mul(Box([Calculus(Box(Derivative{expression: Box(Symbol(Symbol { name: \"f\" })))))), variable: Symbol { name: \"x\" }, order: Symbol { name: \"n\" }}, Pow(Box(Function{name:factorial, args:Box([Symbol(Symbol { name: \"n\" })])}), Box(Number(Integer(-1))))])), Pow(Box(Symbol(Symbol { name: \"x\" })), Symbol(Symbol { name: \"n\" }))]))), variable: Symbol { name: \"n\" }, start: Box(Number(Integer(0))), end: Box(Constant(Infinity))}",
"description": "Maclaurin series expansion"
},
{
"id": "fourier_series_latex",
"language": "latex",
"category": "series_expansions",
"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)",
"expected_expr": "Add([Mul(Box([Symbol(Symbol { name: \"a_0\" }), Number(Rational(1/2))]), Calculus(Box(Sum{expression: Box(Add([Mul(Box([Symbol(Symbol { name: \"a_n\" }))), Function{name:cos, args:Box([Mul(Box([Symbol(Symbol { name: \"n\" }), Constant(Pi), Symbol(Symbol { name: \"x\" }), Pow(Box(Symbol(Symbol { name: \"L\" })), Number(Integer(-1)))])])}])), Mul([Symbol(Symbol { name: \"b_n\" }), Function{name:sin, args:Box([Mul(Box([Symbol(Symbol { name: \"n\" }), Constant(Pi), Symbol(Symbol { name: \"x\" }), Pow(Box(Symbol(Symbol { name: \"L\" })), Number(Integer(-1)))])])}]))]))), variable: Symbol { name: \"n\" }, start: Box(Number(Integer(1))), end: Box(Constant(Infinity))}]))",
"description": "Fourier series"
},
{
"id": "power_series_latex",
"language": "latex",
"category": "series_expansions",
"input": "\\sum_{n=0}^{\\infty} a_n (x-c)^n",
"expected_expr": "Calculus(Box(Sum{expression: Box(Mul(Box([Symbol(Symbol { name: \"a_n\" }))), Pow(Add([Symbol(Symbol { name: \"x\" }, Mul(Box([Number(Integer(-1)), Symbol(Symbol { name: \"c\" })])]))), Box(Symbol(Symbol { name: \"n\" })))]))), variable: Symbol { name: \"n\" }, start: Box(Number(Integer(0))), end: Box(Constant(Infinity))}",
"description": "Power series"
},
{
"id": "laurent_series_latex",
"language": "latex",
"category": "series_expansions",
"input": "\\sum_{n=-\\infty}^{\\infty} a_n (z-c)^n",
"expected_expr": "Calculus(Box(Sum{expression: Box(Mul(Box([Symbol(Symbol { name: \"a_n\" }))), Pow(Add([Symbol(Symbol { name: \"z\" }, Mul(Box([Number(Integer(-1)), Symbol(Symbol { name: \"c\" })])]))), Box(Symbol(Symbol { name: \"n\" })))]))), variable: Symbol { name: \"n\" }, start: Box(Mul([Number(Integer(-1)), Constant(Infinity)])), end: Box(Constant(Infinity))}",
"description": "Laurent series"
},
{
"id": "geometric_series_latex",
"language": "latex",
"category": "series_expansions",
"input": "\\sum_{n=0}^{\\infty} ar^n",
"expected_expr": "Calculus(Box(Sum{expression: Box(Mul([Symbol(Symbol { name: \"a\" }))), Pow(Box(Symbol(Symbol { name: \"r\" })), Symbol(Symbol { name: \"n\" }))])), variable: Symbol { name: \"n\" }, start: Box(Number(Integer(0))), end: Box(Constant(Infinity))}",
"description": "Geometric series"
},
{
"id": "binomial_series_latex",
"language": "latex",
"category": "series_expansions",
"input": "\\sum_{k=0}^{\\infty} \\binom{\\alpha}{k} x^k",
"expected_expr": "Calculus(Box(Sum{expression: Box(Mul(Box([Function{name:binomial, args:Box([Symbol(Symbol { name: \"alpha\" }))), Symbol(Symbol { name: \"k\" })])}, Pow(Box(Symbol(Symbol { name: \"x\" })), Symbol(Symbol { name: \"k\" }))]))), variable: Symbol { name: \"k\" }, start: Box(Number(Integer(0))), end: Box(Constant(Infinity))}",
"description": "Binomial series"
},
{
"id": "first_order_ode_latex",
"language": "latex",
"category": "differential_equations",
"input": "\\frac{dy}{dx} = f(x, y)",
"expected_expr": "Relation{left: Box(Calculus(Box(Derivative{expression: Box(Symbol(Symbol { name: \"y\" })))), variable: Symbol { name: \"x\" }, order: 1}), right: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}), relation_type: Equal}",
"description": "First-order ODE"
},
{
"id": "wave_equation_latex",
"language": "latex",
"category": "differential_equations",
"input": "\\frac{\\partial^2 u}{\\partial t^2} = c^2 \\frac{\\partial^2 u}{\\partial x^2}",
"expected_expr": "Relation{left: Box(PartialCalculus(Box(Derivative{expression: Box(Symbol(Symbol { name: \"u\" })))), variable: Symbol { name: \"t\" }, order: 2}), right: Box(Mul([Pow(Box(Symbol(Symbol { name: \"c\" })), Number(Integer(2))), PartialCalculus(Box(Derivative{expression: Box(Symbol(Symbol { name: \"u\" })))), variable: Symbol { name: \"x\" }, order: 2}])), relation_type: Equal}",
"description": "Wave equation PDE"
},
{
"id": "heat_equation_latex",
"language": "latex",
"category": "differential_equations",
"input": "\\frac{\\partial u}{\\partial t} = \\alpha \\frac{\\partial^2 u}{\\partial x^2}",
"expected_expr": "Relation{left: Box(PartialCalculus(Box(Derivative{expression: Box(Symbol(Symbol { name: \"u\" })))), variable: Symbol { name: \"t\" }, order: 1}), right: Box(Mul([Symbol(Symbol { name: \"alpha\" }), PartialCalculus(Box(Derivative{expression: Box(Symbol(Symbol { name: \"u\" })))), variable: Symbol { name: \"x\" }, order: 2}])), relation_type: Equal}",
"description": "Heat equation PDE"
},
{
"id": "laplace_equation_latex",
"language": "latex",
"category": "differential_equations",
"input": "\\nabla^2 u = 0",
"expected_expr": "Relation{left: Box(Laplacian{expression: Box(Symbol(Symbol { name: \"u\" }))}), right: Box(Number(Integer(0))), relation_type: Equal}",
"description": "Laplace equation"
},
{
"id": "poisson_equation_latex",
"language": "latex",
"category": "differential_equations",
"input": "\\nabla^2 u = f",
"expected_expr": "Relation{left: Box(Laplacian{expression: Box(Symbol(Symbol { name: \"u\" }))}), right: Box(Symbol(Symbol { name: \"f\" })), relation_type: Equal}",
"description": "Poisson equation"
},
{
"id": "eigenvalue_problem_latex",
"language": "latex",
"category": "linear_algebra_advanced",
"input": "A\\vec{v} = \\lambda \\vec{v}",
"expected_expr": "Relation{left: Box(Mul(Box([Matrix(Box([[Symbol(Symbol { name: \"A\" })]])), Vector{components: Box([Symbol(Symbol { name: \"v\" })])}]))), right: Box(Mul(Box([Symbol(Symbol { name: \"lambda\" }), Vector{components: Box([Symbol(Symbol { name: \"v\" })])}]))), relation_type: Equal}",
"description": "Eigenvalue problem"
},
{
"id": "characteristic_polynomial_latex",
"language": "latex",
"category": "linear_algebra_advanced",
"input": "\\det(A - \\lambda I)",
"expected_expr": "Function{name:det, args:Box([Add(Box([Matrix(Box([[Symbol(Symbol { name: \"A\" })]])), Mul(Box([Number(Integer(-1)), Symbol(Symbol { name: \"lambda\" }), Matrix(Box([[Symbol(Symbol { name: \"I\" })]]))]))]))])}",
"description": "Characteristic polynomial"
},
{
"id": "matrix_exponential_latex",
"language": "latex",
"category": "linear_algebra_advanced",
"input": "e^{At}",
"expected_expr": "Pow(Box(Constant(E)), Box(Mul(Box([Matrix(Box([[Symbol(Symbol { name: \"A\" })]])), Symbol(Symbol { name: \"t\" })]))))",
"description": "Matrix exponential"
},
{
"id": "svd_latex",
"language": "latex",
"category": "linear_algebra_advanced",
"input": "A = U\\Sigma V^T",
"expected_expr": "Relation{left: Box(Matrix(Box([[Symbol(Symbol { name: \"A\" })]]))), right: Box(Mul(Box([Matrix(Box([[Symbol(Symbol { name: \"U\" })]])), Matrix(Box([[Symbol(Symbol { name: \"Sigma\" })]])), Pow(Box(Matrix(Box([[Symbol(Symbol { name: \"V\" })]]))), Symbol(Symbol { name: \"T\" }))]))), relation_type: Equal}",
"description": "Singular Value Decomposition"
},
{
"id": "qr_decomposition_latex",
"language": "latex",
"category": "linear_algebra_advanced",
"input": "A = QR",
"expected_expr": "Relation{left: Box(Matrix(Box([[Symbol(Symbol { name: \"A\" })]]))), right: Box(Mul(Box([Matrix(Box([[Symbol(Symbol { name: \"Q\" })]])), Matrix(Box([[Symbol(Symbol { name: \"R\" })]]))]))), relation_type: Equal}",
"description": "QR decomposition"
},
{
"id": "lu_decomposition_latex",
"language": "latex",
"category": "linear_algebra_advanced",
"input": "A = LU",
"expected_expr": "Relation{left: Box(Matrix(Box([[Symbol(Symbol { name: \"A\" })]]))), right: Box(Mul(Box([Matrix(Box([[Symbol(Symbol { name: \"L\" })]])), Matrix(Box([[Symbol(Symbol { name: \"U\" })]]))]))), relation_type: Equal}",
"description": "LU decomposition"
},
{
"id": "complex_conjugate_latex",
"language": "latex",
"category": "complex_analysis",
"input": "\\overline{z}",
"expected_expr": "Function{name:conjugate, args:Box([Symbol(Symbol { name: \"z\" })])}",
"description": "Complex conjugate"
},
{
"id": "complex_modulus_latex",
"language": "latex",
"category": "complex_analysis",
"input": "|z|",
"expected_expr": "Function{name:abs, args:Box([Symbol(Symbol { name: \"z\" })])}",
"description": "Complex modulus"
},
{
"id": "cauchy_riemann_latex",
"language": "latex",
"category": "complex_analysis",
"input": "\\frac{\\partial u}{\\partial x} = \\frac{\\partial v}{\\partial y}",
"expected_expr": "Relation{left: Box(PartialCalculus(Box(Derivative{expression: Box(Symbol(Symbol { name: \"u\" })))), variable: Symbol { name: \"x\" }, order: 1}), right: Box(PartialCalculus(Box(Derivative{expression: Box(Symbol(Symbol { name: \"v\" })))), variable: Symbol { name: \"y\" }, order: 1}), relation_type: Equal}",
"description": "Cauchy-Riemann equation"
},
{
"id": "contour_integral_latex",
"language": "latex",
"category": "complex_analysis",
"input": "\\oint_C f(z) dz",
"expected_expr": "ContourCalculus(Box(Integral{integrand: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"z\" })))])}), contour: Symbol { name: \"C\" }}",
"description": "Contour integral"
},
{
"id": "residue_theorem_latex",
"language": "latex",
"category": "complex_analysis",
"input": "\\oint_C f(z) dz = 2\\pi i \\sum \\text{Res}(f, z_k)",
"expected_expr": "Relation{left: Box(ContourCalculus(Box(Integral{integrand: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"z\" })))])}), contour: Symbol { name: \"C\" }}), right: Box(Mul(Box([Number(Integer(2)), Constant(Pi), Constant(I), Calculus(Box(Sum{expression: Box(Function{name:residue, args:Box([Symbol(Symbol { name: \"f\" }))), Symbol(Symbol { name: \"z_k\" })])}), variable: Symbol { name: \"k\" }, start: Box(Number(Integer(1))), end: Box(Symbol(Symbol { name: \"n\" }))}]))), relation_type: Equal}",
"description": "Residue theorem"
},
{
"id": "bessel_function_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "J_n(x)",
"expected_expr": "Function{name:bessel_j, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Bessel function of first kind"
},
{
"id": "neumann_function_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "Y_n(x)",
"expected_expr": "Function{name:bessel_y, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Bessel function of second kind (Neumann)"
},
{
"id": "hankel_function_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "H_n^{(1)}(x)",
"expected_expr": "Function{name:hankel_h1, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Hankel function of first kind"
},
{
"id": "legendre_polynomial_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "P_n(x)",
"expected_expr": "Function{name:legendre_p, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Legendre polynomial"
},
{
"id": "associated_legendre_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "P_l^m(x)",
"expected_expr": "Function{name:assoc_legendre, args:Box([Symbol(Symbol { name: \"l\" }), Symbol(Symbol { name: \"m\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Associated Legendre function"
},
{
"id": "spherical_harmonic_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "Y_l^m(\\theta, \\phi)",
"expected_expr": "Function{name:spherical_harmonic, args:Box([Symbol(Symbol { name: \"l\" }), Symbol(Symbol { name: \"m\" }), Symbol(Symbol { name: \"theta\" }), Symbol(Symbol { name: \"phi\" })])}",
"description": "Spherical harmonic"
},
{
"id": "hermite_polynomial_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "H_n(x)",
"expected_expr": "Function{name:hermite, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Hermite polynomial"
},
{
"id": "laguerre_polynomial_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "L_n(x)",
"expected_expr": "Function{name:laguerre, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Laguerre polynomial"
},
{
"id": "chebyshev_polynomial_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "T_n(x)",
"expected_expr": "Function{name:chebyshev_t, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Chebyshev polynomial of first kind"
},
{
"id": "elliptic_integral_first_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "F(\\phi, k)",
"expected_expr": "Function{name:elliptic_f, args:Box([Symbol(Symbol { name: \"phi\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Elliptic integral of first kind"
},
{
"id": "elliptic_integral_second_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "E(\\phi, k)",
"expected_expr": "Function{name:elliptic_e, args:Box([Symbol(Symbol { name: \"phi\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Elliptic integral of second kind"
},
{
"id": "beta_function_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "B(x, y)",
"expected_expr": "Function{name:beta, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Beta function"
},
{
"id": "digamma_function_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "\\psi(x)",
"expected_expr": "Function{name:digamma, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Digamma function"
},
{
"id": "polygamma_function_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "\\psi^{(n)}(x)",
"expected_expr": "Function{name:polygamma, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Polygamma function"
},
{
"id": "riemann_zeta_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "\\zeta(s)",
"expected_expr": "Function{name:zeta, args:Box([Symbol(Symbol { name: \"s\" })])}",
"description": "Riemann zeta function"
},
{
"id": "dirichlet_eta_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "\\eta(s)",
"expected_expr": "Function{name:dirichlet_eta, args:Box([Symbol(Symbol { name: \"s\" })])}",
"description": "Dirichlet eta function"
},
{
"id": "error_function_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "\\text{erf}(x)",
"expected_expr": "Function{name:erf, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Error function"
},
{
"id": "complementary_error_function_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "\\text{erfc}(x)",
"expected_expr": "Function{name:erfc, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Complementary error function"
},
{
"id": "fresnel_integral_s_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "S(x)",
"expected_expr": "Function{name:fresnel_s, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Fresnel integral S"
},
{
"id": "fresnel_integral_c_latex",
"language": "latex",
"category": "special_functions_advanced",
"input": "C(x)",
"expected_expr": "Function{name:fresnel_c, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Fresnel integral C"
},
{
"id": "factorial_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "n!",
"expected_expr": "Function{name:factorial, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Factorial"
},
{
"id": "double_factorial_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "n!!",
"expected_expr": "Function{name:double_factorial, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Double factorial"
},
{
"id": "binomial_coefficient_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "\\binom{n}{k}",
"expected_expr": "Function{name:binomial, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Binomial coefficient"
},
{
"id": "multinomial_coefficient_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "\\binom{n}{k_1, k_2, \\ldots, k_m}",
"expected_expr": "Function{name:multinomial, args:Box([Symbol(Symbol { name: \"n\" }), Vector{components: Box([Symbol(Symbol { name: \"k_1\" }), Symbol(Symbol { name: \"k_2\" }), Symbol(Symbol { name: \"k_m\" })])}])}",
"description": "Multinomial coefficient"
},
{
"id": "stirling_first_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "s(n, k)",
"expected_expr": "Function{name:stirling_first, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Stirling number of first kind"
},
{
"id": "stirling_second_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "S(n, k)",
"expected_expr": "Function{name:stirling_second, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Stirling number of second kind"
},
{
"id": "bell_number_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "B_n",
"expected_expr": "Function{name:bell, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Bell number"
},
{
"id": "catalan_number_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "C_n",
"expected_expr": "Function{name:catalan, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Catalan number"
},
{
"id": "fibonacci_number_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "F_n",
"expected_expr": "Function{name:fibonacci, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Fibonacci number"
},
{
"id": "lucas_number_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "L_n",
"expected_expr": "Function{name:lucas, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Lucas number"
},
{
"id": "euler_totient_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "\\phi(n)",
"expected_expr": "Function{name:euler_phi, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Euler's totient function"
},
{
"id": "mobius_function_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "\\mu(n)",
"expected_expr": "Function{name:mobius, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "M\u00f6bius function"
},
{
"id": "divisor_function_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "\\sigma_k(n)",
"expected_expr": "Function{name:divisor_sigma, args:Box([Symbol(Symbol { name: \"k\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Divisor function"
},
{
"id": "prime_counting_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "\\pi(x)",
"expected_expr": "Function{name:prime_pi, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Prime counting function"
},
{
"id": "legendre_symbol_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "\\left(\\frac{a}{p}\\right)",
"expected_expr": "Function{name:legendre_symbol, args:Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"p\" })])}",
"description": "Legendre symbol"
},
{
"id": "jacobi_symbol_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "\\left(\\frac{a}{n}\\right)",
"expected_expr": "Function{name:jacobi_symbol, args:Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Jacobi symbol"
},
{
"id": "partition_function_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "p(n)",
"expected_expr": "Function{name:partition, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Partition function"
},
{
"id": "ramanujan_tau_latex",
"language": "latex",
"category": "combinatorics_number_theory",
"input": "\\tau(n)",
"expected_expr": "Function{name:ramanujan_tau, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Ramanujan tau function"
},
{
"id": "hyperbolic_sin_latex",
"language": "latex",
"category": "hyperbolic_functions",
"input": "\\sinh(x)",
"expected_expr": "Function{name:sinh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Hyperbolic sine"
},
{
"id": "hyperbolic_cos_latex",
"language": "latex",
"category": "hyperbolic_functions",
"input": "\\cosh(x)",
"expected_expr": "Function{name:cosh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Hyperbolic cosine"
},
{
"id": "hyperbolic_tan_latex",
"language": "latex",
"category": "hyperbolic_functions",
"input": "\\tanh(x)",
"expected_expr": "Function{name:tanh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Hyperbolic tangent"
},
{
"id": "inverse_hyperbolic_sin_latex",
"language": "latex",
"category": "hyperbolic_functions",
"input": "\\sinh^{-1}(x)",
"expected_expr": "Function{name:asinh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse hyperbolic sine"
},
{
"id": "inverse_hyperbolic_cos_latex",
"language": "latex",
"category": "hyperbolic_functions",
"input": "\\cosh^{-1}(x)",
"expected_expr": "Function{name:acosh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse hyperbolic cosine"
},
{
"id": "inverse_hyperbolic_tan_latex",
"language": "latex",
"category": "hyperbolic_functions",
"input": "\\tanh^{-1}(x)",
"expected_expr": "Function{name:atanh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse hyperbolic tangent"
},
{
"id": "inverse_trig_sin_latex",
"language": "latex",
"category": "inverse_trigonometric",
"input": "\\arcsin(x)",
"expected_expr": "Function{name:asin, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse sine"
},
{
"id": "inverse_trig_cos_latex",
"language": "latex",
"category": "inverse_trigonometric",
"input": "\\arccos(x)",
"expected_expr": "Function{name:acos, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse cosine"
},
{
"id": "inverse_trig_tan_latex",
"language": "latex",
"category": "inverse_trigonometric",
"input": "\\arctan(x)",
"expected_expr": "Function{name:atan, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse tangent"
},
{
"id": "atan2_latex",
"language": "latex",
"category": "inverse_trigonometric",
"input": "\\text{atan2}(y, x)",
"expected_expr": "Function{name:atan2, args:Box([Symbol(Symbol { name: \"y\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Two-argument arctangent"
},
{
"id": "secant_latex",
"language": "latex",
"category": "trigonometric_extended",
"input": "\\sec(x)",
"expected_expr": "Function{name:sec, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Secant function"
},
{
"id": "cosecant_latex",
"language": "latex",
"category": "trigonometric_extended",
"input": "\\csc(x)",
"expected_expr": "Function{name:csc, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Cosecant function"
},
{
"id": "cotangent_latex",
"language": "latex",
"category": "trigonometric_extended",
"input": "\\cot(x)",
"expected_expr": "Function{name:cot, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Cotangent function"
},
{
"id": "probability_density_latex",
"language": "latex",
"category": "probability_statistics",
"input": "f_X(x)",
"expected_expr": "Function{name:pdf, args:Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Probability density function"
},
{
"id": "cumulative_distribution_latex",
"language": "latex",
"category": "probability_statistics",
"input": "F_X(x)",
"expected_expr": "Function{name:cdf, args:Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Cumulative distribution function"
},
{
"id": "expectation_latex",
"language": "latex",
"category": "probability_statistics",
"input": "E[X]",
"expected_expr": "Function{name:expectation, args:Box([Symbol(Symbol { name: \"X\" })])}",
"description": "Expected value"
},
{
"id": "variance_latex",
"language": "latex",
"category": "probability_statistics",
"input": "\\text{Var}(X)",
"expected_expr": "Function{name:variance, args:Box([Symbol(Symbol { name: \"X\" })])}",
"description": "Variance"
},
{
"id": "standard_deviation_latex",
"language": "latex",
"category": "probability_statistics",
"input": "\\sigma_X",
"expected_expr": "Function{name:std_dev, args:Box([Symbol(Symbol { name: \"X\" })])}",
"description": "Standard deviation"
},
{
"id": "covariance_latex",
"language": "latex",
"category": "probability_statistics",
"input": "\\text{Cov}(X, Y)",
"expected_expr": "Function{name:covariance, args:Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"Y\" })])}",
"description": "Covariance"
},
{
"id": "correlation_latex",
"language": "latex",
"category": "probability_statistics",
"input": "\\rho_{X,Y}",
"expected_expr": "Function{name:correlation, args:Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"Y\" })])}",
"description": "Correlation coefficient"
},
{
"id": "normal_distribution_latex",
"language": "latex",
"category": "probability_statistics",
"input": "\\mathcal{N}(\\mu, \\sigma^2)",
"expected_expr": "Function{name:normal_dist, args:Box([Symbol(Symbol { name: \"mu\" }), Pow(Box(Symbol(Symbol { name: \"sigma\" })), Number(Integer(2)))])}",
"description": "Normal distribution"
},
{
"id": "binomial_distribution_latex",
"language": "latex",
"category": "probability_statistics",
"input": "\\text{Binomial}(n, p)",
"expected_expr": "Function{name:binomial_dist, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"p\" })])}",
"description": "Binomial distribution"
},
{
"id": "poisson_distribution_latex",
"language": "latex",
"category": "probability_statistics",
"input": "\\text{Poisson}(\\lambda)",
"expected_expr": "Function{name:poisson_dist, args:Box([Symbol(Symbol { name: \"lambda\" })])}",
"description": "Poisson distribution"
},
{
"id": "t_distribution_latex",
"language": "latex",
"category": "probability_statistics",
"input": "t(\\nu)",
"expected_expr": "Function{name:t_dist, args:Box([Symbol(Symbol { name: \"nu\" })])}",
"description": "Student's t-distribution"
},
{
"id": "f_distribution_latex",
"language": "latex",
"category": "probability_statistics",
"input": "F(d_1, d_2)",
"expected_expr": "Function{name:f_dist, args:Box([Symbol(Symbol { name: \"d_1\" }), Symbol(Symbol { name: \"d_2\" })])}",
"description": "F-distribution"
},
{
"id": "conditional_probability_latex",
"language": "latex",
"category": "probability_statistics",
"input": "P(A|B)",
"expected_expr": "Function{name:conditional_prob, args:Box([Symbol(Symbol { name: \"A\" }), Symbol(Symbol { name: \"B\" })])}",
"description": "Conditional probability"
},
{
"id": "bayes_theorem_latex",
"language": "latex",
"category": "probability_statistics",
"input": "P(A|B) = \\frac{P(B|A)P(A)}{P(B)}",
"expected_expr": "Relation{left: Box(Function{name:conditional_prob, args:Box([Symbol(Symbol { name: \"A\" }), Symbol(Symbol { name: \"B\" })])}), right: Box(Mul(Box([Mul(Box([Function{name:conditional_prob, args:Box([Symbol(Symbol { name: \"B\" }), Symbol(Symbol { name: \"A\" })])}, Function{name:prob, args:Box([Symbol(Symbol { name: \"A\" })])}])), Pow(Box(Function{name:prob, args:Box([Symbol(Symbol { name: \"B\" })])}), Box(Number(Integer(-1))))]))), relation_type: Equal}",
"description": "Bayes' theorem"
},
{
"id": "metric_space_latex",
"language": "latex",
"category": "topology_geometry",
"input": "d(x, y)",
"expected_expr": "Function{name:metric, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Metric function"
},
{
"id": "norm_latex",
"language": "latex",
"category": "topology_geometry",
"input": "\\|x\\|",
"expected_expr": "Function{name:norm, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Norm"
},
{
"id": "inner_product_latex",
"language": "latex",
"category": "topology_geometry",
"input": "\\langle x, y \\rangle",
"expected_expr": "Function{name:inner_product, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Inner product"
},
{
"id": "cross_product_latex",
"language": "latex",
"category": "topology_geometry",
"input": "\\vec{a} \\times \\vec{b}",
"expected_expr": "Function{name:cross_product, args:Box([Vector{components: Box([Symbol(Symbol { name: \"a\" })])}, Vector{components: Box([Symbol(Symbol { name: \"b\" })])}])}",
"description": "Cross product"
},
{
"id": "dot_product_latex",
"language": "latex",
"category": "topology_geometry",
"input": "\\vec{a} \\cdot \\vec{b}",
"expected_expr": "Function{name:dot_product, args:Box([Vector{components: Box([Symbol(Symbol { name: \"a\" })])}, Vector{components: Box([Symbol(Symbol { name: \"b\" })])}])}",
"description": "Dot product"
},
{
"id": "euclidean_distance_latex",
"language": "latex",
"category": "topology_geometry",
"input": "\\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}",
"expected_expr": "Pow(Add([Pow(Box(Add(Box([Symbol(Symbol { name: \"x_2\" }, Mul(Box([Number(Integer(-1)), Symbol(Symbol { name: \"x_1\" })])]))), Box(Number(Integer(2)))), Pow(Add([Symbol(Symbol { name: \"y_2\" }, Mul(Box([Number(Integer(-1)), Symbol(Symbol { name: \"y_1\" })])]))), Box(Number(Integer(2))))]))), Box(Number(Rational(1/2))))",
"description": "Euclidean distance formula"
},
{
"id": "sphere_equation_latex",
"language": "latex",
"category": "topology_geometry",
"input": "(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2",
"expected_expr": "Relation{left: Box(Add([Pow(Add(Box([Symbol(Symbol { name: \"x\" }, Mul(Box([Number(Integer(-1)), Symbol(Symbol { name: \"a\" })])]))), Box(Number(Integer(2)))), Pow(Add([Symbol(Symbol { name: \"y\" }, Mul(Box([Number(Integer(-1)), Symbol(Symbol { name: \"b\" })])]))), Box(Number(Integer(2)))), Pow(Add([Symbol(Symbol { name: \"z\" }, Mul(Box([Number(Integer(-1)), Symbol(Symbol { name: \"c\" })])]))), Box(Number(Integer(2))))]))), right: Box(Pow(Box(Symbol(Symbol { name: \"r\" })), Number(Integer(2)))), relation_type: Equal}",
"description": "Sphere equation"
},
{
"id": "circle_equation_latex",
"language": "latex",
"category": "topology_geometry",
"input": "(x-h)^2 + (y-k)^2 = r^2",
"expected_expr": "Relation{left: Box(Add([Pow(Add(Box([Symbol(Symbol { name: \"x\" }, Mul(Box([Number(Integer(-1)), Symbol(Symbol { name: \"h\" })])]))), Box(Number(Integer(2)))), Pow(Add([Symbol(Symbol { name: \"y\" }, Mul(Box([Number(Integer(-1)), Symbol(Symbol { name: \"k\" })])]))), Box(Number(Integer(2))))]))), right: Box(Pow(Box(Symbol(Symbol { name: \"r\" })), Number(Integer(2)))), relation_type: Equal}",
"description": "Circle equation"
},
{
"id": "ellipse_equation_latex",
"language": "latex",
"category": "topology_geometry",
"input": "\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1",
"expected_expr": "Relation{left: Box(Add([Mul(Box([Pow(Box(Symbol(Symbol { name: \"x\" })), Number(Integer(2))), Pow(Box(Pow(Box(Symbol(Symbol { name: \"a\" })), Number(Integer(2)))), Box(Number(Integer(-1))))]), Mul([Pow(Box(Symbol(Symbol { name: \"y\" })), Number(Integer(2))), Pow(Box(Pow(Box(Symbol(Symbol { name: \"b\" })), Number(Integer(2)))), Box(Number(Integer(-1))))])]))), right: Box(Number(Integer(1))), relation_type: Equal}",
"description": "Ellipse equation"
},
{
"id": "hyperbola_equation_latex",
"language": "latex",
"category": "topology_geometry",
"input": "\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1",
"expected_expr": "Relation{left: Box(Add([Mul(Box([Pow(Box(Symbol(Symbol { name: \"x\" })), Number(Integer(2))), Pow(Box(Pow(Box(Symbol(Symbol { name: \"a\" })), Number(Integer(2)))), Box(Number(Integer(-1))))]), Mul([Number(Integer(-1)), Pow(Box(Symbol(Symbol { name: \"y\" })), Number(Integer(2))), Pow(Box(Pow(Box(Symbol(Symbol { name: \"b\" })), Number(Integer(2)))), Box(Number(Integer(-1))))])]))), right: Box(Number(Integer(1))), relation_type: Equal}",
"description": "Hyperbola equation"
},
{
"id": "parabola_equation_latex",
"language": "latex",
"category": "topology_geometry",
"input": "y = ax^2 + bx + c",
"expected_expr": "Relation{left: Box(Symbol(Symbol { name: \"y\" })), right: Box(Add([Mul(Box([Symbol(Symbol { name: \"a\" }), Pow(Box(Symbol(Symbol { name: \"x\" })), Number(Integer(2)))]), Mul([Symbol(Symbol { name: \"b\" }), Symbol(Symbol { name: \"x\" })]), Symbol(Symbol { name: \"c\" })]))), relation_type: Equal}",
"description": "Parabola equation"
},
{
"id": "parametric_curve_latex",
"language": "latex",
"category": "topology_geometry",
"input": "\\vec{r}(t) = \\langle x(t), y(t), z(t) \\rangle",
"expected_expr": "Relation{left: Box(Function{name:r, args:Box([Symbol(Symbol { name: \"t\" })])}), right: Box(Vector{components: Box([Function{name:x, args:Box([Symbol(Symbol { name: \"t\" })])}, Function{name:y, args:Box([Symbol(Symbol { name: \"t\" })])}, Function{name:z, args:Box([Symbol(Symbol { name: \"t\" })])}])}), relation_type: Equal}",
"description": "Parametric curve"
},
{
"id": "polar_coordinates_latex",
"language": "latex",
"category": "coordinate_systems",
"input": "x = r\\cos\\theta, y = r\\sin\\theta",
"expected_expr": "Relation{left: Box(Symbol(Symbol { name: \"x\" })), right: Box(Mul(Box([Symbol(Symbol { name: \"r\" }), Function{name:cos, args:Box([Symbol(Symbol { name: \"theta\" })])}]))), relation_type: Equal}",
"description": "Polar to Cartesian conversion"
},
{
"id": "cylindrical_coordinates_latex",
"language": "latex",
"category": "coordinate_systems",
"input": "x = r\\cos\\theta, y = r\\sin\\theta, z = z",
"expected_expr": "Relation{left: Box(Symbol(Symbol { name: \"x\" })), right: Box(Mul(Box([Symbol(Symbol { name: \"r\" }), Function{name:cos, args:Box([Symbol(Symbol { name: \"theta\" })])}]))), relation_type: Equal}",
"description": "Cylindrical coordinates"
},
{
"id": "spherical_coordinates_latex",
"language": "latex",
"category": "coordinate_systems",
"input": "x = \\rho\\sin\\phi\\cos\\theta",
"expected_expr": "Relation{left: Box(Symbol(Symbol { name: \"x\" })), right: Box(Mul(Box([Symbol(Symbol { name: \"rho\" }), Function{name:sin, args:Box([Symbol(Symbol { name: \"phi\" })])}, Function{name:cos, args:Box([Symbol(Symbol { name: \"theta\" })])}]))), relation_type: Equal}",
"description": "Spherical coordinates"
},
{
"id": "fourier_transform_latex",
"language": "latex",
"category": "transforms",
"input": "\\mathcal{F}[f(t)](\\omega) = \\int_{-\\infty}^{\\infty} f(t) e^{-i\\omega t} dt",
"expected_expr": "Relation{left: Box(Function{name:fourier_transform, args:Box([Function{name:f, args:Box([Symbol(Symbol { name: \"t\" })])}, Symbol(Symbol { name: \"omega\" })])}), right: Box(Calculus(Box(Integral{integrand: Box(Mul(Box([Function{name:f, args:Box([Symbol(Symbol { name: \"t\" })))])}, Pow(Box(Constant(E)), Mul([Number(Integer(-1), Constant(I), Symbol(Symbol { name: \"omega\" }), Symbol(Symbol { name: \"t\" })])))]))), variable: Symbol { name: \"t\" }, bounds: Some((Box(Mul([Number(Integer(-1)), Constant(Infinity)])), Box(Constant(Infinity))))}), relation_type: Equal}",
"description": "Fourier transform"
},
{
"id": "laplace_transform_latex",
"language": "latex",
"category": "transforms",
"input": "\\mathcal{L}[f(t)](s) = \\int_0^{\\infty} f(t) e^{-st} dt",
"expected_expr": "Relation{left: Box(Function{name:laplace_transform, args:Box([Function{name:f, args:Box([Symbol(Symbol { name: \"t\" })])}, Symbol(Symbol { name: \"s\" })])}), right: Box(Calculus(Box(Integral{integrand: Box(Mul(Box([Function{name:f, args:Box([Symbol(Symbol { name: \"t\" })))])}, Pow(Box(Constant(E)), Mul([Number(Integer(-1), Symbol(Symbol { name: \"s\" }), Symbol(Symbol { name: \"t\" })])))]))), variable: Symbol { name: \"t\" }, bounds: Some((Box(Number(Integer(0))), Box(Constant(Infinity))))}), relation_type: Equal}",
"description": "Laplace transform"
},
{
"id": "z_transform_latex",
"language": "latex",
"category": "transforms",
"input": "\\mathcal{Z}[x[n]](z) = \\sum_{n=-\\infty}^{\\infty} x[n] z^{-n}",
"expected_expr": "Relation{left: Box(Function{name:z_transform, args:Box([Function{name:x, args:Box([Symbol(Symbol { name: \"n\" })])}, Symbol(Symbol { name: \"z\" })])}), right: Box(Calculus(Box(Sum{expression: Box(Mul(Box([Function{name:x, args:Box([Symbol(Symbol { name: \"n\" })))])}, Pow(Box(Symbol(Symbol { name: \"z\" })), Mul([Number(Integer(-1), Symbol(Symbol { name: \"n\" })])))]))), variable: Symbol { name: \"n\" }, start: Box(Mul([Number(Integer(-1)), Constant(Infinity)])), end: Box(Constant(Infinity))}), relation_type: Equal}",
"description": "Z-transform"
},
{
"id": "dirac_delta_latex",
"language": "latex",
"category": "generalized_functions",
"input": "\\delta(x)",
"expected_expr": "Function{name:dirac_delta, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Dirac delta function"
},
{
"id": "heaviside_step_latex",
"language": "latex",
"category": "generalized_functions",
"input": "H(x)",
"expected_expr": "Function{name:heaviside, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Heaviside step function"
},
{
"id": "sign_function_latex",
"language": "latex",
"category": "generalized_functions",
"input": "\\text{sgn}(x)",
"expected_expr": "Function{name:sign, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Sign function"
},
{
"id": "floor_function_latex",
"language": "latex",
"category": "generalized_functions",
"input": "\\lfloor x \\rfloor",
"expected_expr": "Function{name:floor, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Floor function"
},
{
"id": "ceiling_function_latex",
"language": "latex",
"category": "generalized_functions",
"input": "\\lceil x \\rceil",
"expected_expr": "Function{name:ceil, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Ceiling function"
},
{
"id": "fractional_part_latex",
"language": "latex",
"category": "generalized_functions",
"input": "\\{x\\}",
"expected_expr": "Function{name:frac, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Fractional part"
},
{
"id": "min_function_latex",
"language": "latex",
"category": "optimization",
"input": "\\min(x, y)",
"expected_expr": "Function{name:min, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Minimum function"
},
{
"id": "max_function_latex",
"language": "latex",
"category": "optimization",
"input": "\\max(x, y)",
"expected_expr": "Function{name:max, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Maximum function"
},
{
"id": "argmin_latex",
"language": "latex",
"category": "optimization",
"input": "\\arg\\min_x f(x)",
"expected_expr": "Function{name:argmin, args:Box([Symbol(Symbol { name: \"x\" }), Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })])}])}",
"description": "Argument of minimum"
},
{
"id": "argmax_latex",
"language": "latex",
"category": "optimization",
"input": "\\arg\\max_x f(x)",
"expected_expr": "Function{name:argmax, args:Box([Symbol(Symbol { name: \"x\" }), Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })])}])}",
"description": "Argument of maximum"
},
{
"id": "lagrangian_latex",
"language": "latex",
"category": "optimization",
"input": "\\mathcal{L}(x, \\lambda) = f(x) + \\lambda g(x)",
"expected_expr": "Relation{left: Box(Function{name:lagrangian, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"lambda\" })])}), right: Box(Add(Box([Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })])}, Mul(Box([Symbol(Symbol { name: \"lambda\" }), Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })])}]))]))), relation_type: Equal}",
"description": "Lagrangian function"
},
{
"id": "hamiltonian_latex",
"language": "latex",
"category": "physics_mathematics",
"input": "H(q, p, t)",
"expected_expr": "Function{name:hamiltonian, args:Box([Symbol(Symbol { name: \"q\" }), Symbol(Symbol { name: \"p\" }), Symbol(Symbol { name: \"t\" })])}",
"description": "Hamiltonian function"
},
{
"id": "schrodinger_equation_latex",
"language": "latex",
"category": "physics_mathematics",
"input": "i\\hbar \\frac{\\partial \\psi}{\\partial t} = \\hat{H} \\psi",
"expected_expr": "Relation{left: Box(Mul([Constant(I), Symbol(Symbol { name: \"hbar\" }), PartialCalculus(Box(Derivative{expression: Box(Symbol(Symbol { name: \"psi\" })))), variable: Symbol { name: \"t\" }, order: 1}])), right: Box(Mul(Box([Function{name:operator, args:Box([Symbol(Symbol { name: \"H\" })])}, Symbol(Symbol { name: \"psi\" })]))), relation_type: Equal}",
"description": "Schr\u00f6dinger equation"
},
{
"id": "maxwell_equation_latex",
"language": "latex",
"category": "physics_mathematics",
"input": "\\nabla \\times \\vec{E} = -\\frac{\\partial \\vec{B}}{\\partial t}",
"expected_expr": "Relation{left: Box(Function{name: \"curl\", args: Box([Function{name: \"vector\", args: Box([Symbol(Symbol { name: \"E\" })])}])}), right: Box(Mul(Box([Number(Integer(-1)), PartialCalculus(Box(Derivative{expression: Box(Vector{components: Box([Symbol(Symbol { name: \"B\" })))])}), variable: Symbol { name: \"t\" }, order: 1}]))), relation_type: Equal}",
"description": "Maxwell's equation (Faraday's law)"
},
{
"id": "einstein_field_equation_latex",
"language": "latex",
"category": "physics_mathematics",
"input": "G_{\\mu\\nu} = \\frac{8\\pi G}{c^4} T_{\\mu\\nu}",
"expected_expr": "Relation{left: Box(Tensor{indices: Box([Symbol(Symbol { name: \"mu\" }), Symbol(Symbol { name: \"nu\" })]), name: Symbol { name: \"G\" }}), right: Box(Mul([Mul(Box([Number(Integer(8)), Constant(Pi), Symbol(Symbol { name: \"G\" })]), Pow(Box(Pow(Box(Symbol(Symbol { name: \"c\" })), Number(Integer(4)))), Box(Number(Integer(-1)))), Tensor{indices: Box([Symbol(Symbol { name: \"mu\" }), Symbol(Symbol { name: \"nu\" })]), name: Symbol { name: \"T\" }}]))), relation_type: Equal}",
"description": "Einstein field equation"
},
{
"id": "navier_stokes_latex",
"language": "latex",
"category": "physics_mathematics",
"input": "\\rho \\left(\\frac{\\partial \\vec{v}}{\\partial t} + \\vec{v} \\cdot \\nabla \\vec{v}\\right) = -\\nabla p + \\mu \\nabla^2 \\vec{v}",
"expected_expr": "Function{name: \"navier_stokes\", args: Box([Symbol(Symbol { name: \"rho\" }), Function{name: \"vector\", args: Box([Symbol(Symbol { name: \"v\" })])}, Symbol(Symbol { name: \"p\" }), Symbol(Symbol { name: \"mu\" })])}",
"description": "Navier-Stokes equation"
},
{
"id": "product_rule_latex",
"language": "latex",
"category": "calculus_rules",
"input": "\\frac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)",
"expected_expr": "Relation{left: Box(Calculus(Box(Derivative{expression: Box(Mul(Box([Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })))])}, Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })])}]))), variable: Symbol { name: \"x\" }, order: 1}), right: Box(Add(Box([Mul(Box([Calculus(Box(Derivative{expression: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })))])}), variable: Symbol { name: \"x\" }, order: 1}, Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })])}])), Mul(Box([Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })])}, Calculus(Box(Derivative{expression: Box(Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })))])}), variable: Symbol { name: \"x\" }, order: 1}]))]))), relation_type: Equal}",
"description": "Product rule for derivatives"
},
{
"id": "quotient_rule_latex",
"language": "latex",
"category": "calculus_rules",
"input": "\\frac{d}{dx}\\left[\\frac{f(x)}{g(x)}\\right] = \\frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}",
"expected_expr": "Relation{left: Box(Calculus(Box(Derivative{expression: Box(Mul(Box([Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })))])}, Pow(Box(Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })])}), Box(Number(Integer(-1))))]))), variable: Symbol { name: \"x\" }, order: 1}), right: Box(Mul(Box([Add(Box([Mul(Box([Calculus(Box(Derivative{expression: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })))])}), variable: Symbol { name: \"x\" }, order: 1}, Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })])}])), Mul(Box([Number(Integer(-1)), Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })])}, Calculus(Box(Derivative{expression: Box(Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })))])}), variable: Symbol { name: \"x\" }, order: 1}]))])), Pow(Box(Pow(Box(Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })])}), Box(Number(Integer(2))))), Box(Number(Integer(-1))))]))), relation_type: Equal}",
"description": "Quotient rule for derivatives"
},
{
"id": "chain_rule_latex",
"language": "latex",
"category": "calculus_rules",
"input": "\\frac{d}{dx}[f(g(x))] = f'(g(x)) \\cdot g'(x)",
"expected_expr": "Relation{left: Box(Calculus(Box(Derivative{expression: Box(Function{name:f, args:Box([Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })))])}])}), variable: Symbol { name: \"x\" }, order: 1}), right: Box(Mul(Box([Calculus(Box(Derivative{expression: Box(Function{name:f, args:Box([Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })))])}])}), variable: Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })])}, order: 1}, Calculus(Box(Derivative{expression: Box(Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })))])}), variable: Symbol { name: \"x\" }, order: 1}]))), relation_type: Equal}",
"description": "Chain rule for derivatives"
},
{
"id": "integration_by_parts_latex",
"language": "latex",
"category": "calculus_rules",
"input": "\\int u \\, dv = uv - \\int v \\, du",
"expected_expr": "Relation{left: Box(Calculus(Box(Integral{integrand: Box(Mul([Symbol(Symbol { name: \"u\" }))), Symbol(Symbol { name: \"dv\" })])), variable: Symbol { name: \"x\" }, bounds: None}), right: Box(Add([Mul(Box([Symbol(Symbol { name: \"u\" }), Symbol(Symbol { name: \"v\" })]), Mul([Number(Integer(-1)), Calculus(Box(Integral{integrand: Box(Mul(Box([Symbol(Symbol { name: \"v\" }))), Symbol(Symbol { name: \"du\" })])), variable: Symbol { name: \"x\" }, bounds: None}]))]))), relation_type: Equal}",
"description": "Integration by parts"
},
{
"id": "fundamental_theorem_calculus_latex",
"language": "latex",
"category": "calculus_rules",
"input": "\\frac{d}{dx} \\int_a^x f(t) \\, dt = f(x)",
"expected_expr": "Relation{left: Box(Calculus(Box(Derivative{expression: Box(Calculus(Box(Integral{integrand: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"t\" })))))])}), variable: Symbol { name: \"t\" }, bounds: Some((Box(Symbol(Symbol { name: \"a\" })), Box(Symbol(Symbol { name: \"x\" }))))}), variable: Symbol { name: \"x\" }, order: 1}), right: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })])}), relation_type: Equal}",
"description": "Fundamental theorem of calculus"
},
{
"id": "hyperbolic_sin_wolfram",
"language": "wolfram",
"category": "hyperbolic_functions",
"input": "Sinh[x]",
"expected_expr": "Function{name:sinh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Hyperbolic sine"
},
{
"id": "hyperbolic_cos_wolfram",
"language": "wolfram",
"category": "hyperbolic_functions",
"input": "Cosh[x]",
"expected_expr": "Function{name:cosh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Hyperbolic cosine"
},
{
"id": "hyperbolic_tan_wolfram",
"language": "wolfram",
"category": "hyperbolic_functions",
"input": "Tanh[x]",
"expected_expr": "Function{name:tanh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Hyperbolic tangent"
},
{
"id": "inverse_hyperbolic_sin_wolfram",
"language": "wolfram",
"category": "hyperbolic_functions",
"input": "ArcSinh[x]",
"expected_expr": "Function{name:asinh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse hyperbolic sine"
},
{
"id": "inverse_hyperbolic_cos_wolfram",
"language": "wolfram",
"category": "hyperbolic_functions",
"input": "ArcCosh[x]",
"expected_expr": "Function{name:acosh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse hyperbolic cosine"
},
{
"id": "inverse_hyperbolic_tan_wolfram",
"language": "wolfram",
"category": "hyperbolic_functions",
"input": "ArcTanh[x]",
"expected_expr": "Function{name:atanh, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse hyperbolic tangent"
},
{
"id": "inverse_trig_sin_wolfram",
"language": "wolfram",
"category": "inverse_trigonometric",
"input": "ArcSin[x]",
"expected_expr": "Function{name:asin, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse sine"
},
{
"id": "inverse_trig_cos_wolfram",
"language": "wolfram",
"category": "inverse_trigonometric",
"input": "ArcCos[x]",
"expected_expr": "Function{name:acos, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse cosine"
},
{
"id": "inverse_trig_tan_wolfram",
"language": "wolfram",
"category": "inverse_trigonometric",
"input": "ArcTan[x]",
"expected_expr": "Function{name:atan, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Inverse tangent"
},
{
"id": "atan2_wolfram",
"language": "wolfram",
"category": "inverse_trigonometric",
"input": "ArcTan[x, y]",
"expected_expr": "Function{name:atan2, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Two-argument arctangent"
},
{
"id": "secant_wolfram",
"language": "wolfram",
"category": "trigonometric_extended",
"input": "Sec[x]",
"expected_expr": "Function{name:sec, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Secant function"
},
{
"id": "cosecant_wolfram",
"language": "wolfram",
"category": "trigonometric_extended",
"input": "Csc[x]",
"expected_expr": "Function{name:csc, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Cosecant function"
},
{
"id": "cotangent_wolfram",
"language": "wolfram",
"category": "trigonometric_extended",
"input": "Cot[x]",
"expected_expr": "Function{name:cot, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Cotangent function"
},
{
"id": "probability_density_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "PDF[dist, x]",
"expected_expr": "Function{name:pdf, args:Box([Symbol(Symbol { name: \"dist\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Probability density function"
},
{
"id": "cumulative_distribution_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "CDF[dist, x]",
"expected_expr": "Function{name:cdf, args:Box([Symbol(Symbol { name: \"dist\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Cumulative distribution function"
},
{
"id": "expectation_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "Expectation[X, dist]",
"expected_expr": "Function{name:expectation, args:Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"dist\" })])}",
"description": "Expected value"
},
{
"id": "variance_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "Variance[X, dist]",
"expected_expr": "Function{name:variance, args:Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"dist\" })])}",
"description": "Variance"
},
{
"id": "standard_deviation_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "StandardDeviation[X, dist]",
"expected_expr": "Function{name:std_dev, args:Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"dist\" })])}",
"description": "Standard deviation"
},
{
"id": "covariance_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "Covariance[X, Y]",
"expected_expr": "Function{name:covariance, args:Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"Y\" })])}",
"description": "Covariance"
},
{
"id": "correlation_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "Correlation[X, Y]",
"expected_expr": "Function{name:correlation, args:Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"Y\" })])}",
"description": "Correlation coefficient"
},
{
"id": "normal_distribution_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "NormalDistribution[\u03bc, \u03c3]",
"expected_expr": "Function{name:normal_dist, args:Box([Symbol(Symbol { name: \"\u03bc\" }), Symbol(Symbol { name: \"\u03c3\" })])}",
"description": "Normal distribution"
},
{
"id": "binomial_distribution_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "BinomialDistribution[n, p]",
"expected_expr": "Function{name:binomial_dist, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"p\" })])}",
"description": "Binomial distribution"
},
{
"id": "poisson_distribution_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "PoissonDistribution[\u03bb]",
"expected_expr": "Function{name:poisson_dist, args:Box([Symbol(Symbol { name: \"\u03bb\" })])}",
"description": "Poisson distribution"
},
{
"id": "chi_squared_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "ChiSquareDistribution[k]",
"expected_expr": "Function{name:chi_squared, args:Box([Symbol(Symbol { name: \"k\" })])}",
"description": "Chi-squared distribution"
},
{
"id": "t_distribution_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "StudentTDistribution[\u03bd]",
"expected_expr": "Function{name:t_dist, args:Box([Symbol(Symbol { name: \"\u03bd\" })])}",
"description": "Student's t-distribution"
},
{
"id": "f_distribution_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "FRatioDistribution[d1, d2]",
"expected_expr": "Function{name:f_dist, args:Box([Symbol(Symbol { name: \"d1\" }), Symbol(Symbol { name: \"d2\" })])}",
"description": "F-distribution"
},
{
"id": "conditional_probability_wolfram",
"language": "wolfram",
"category": "probability_statistics",
"input": "Probability[A, B]",
"expected_expr": "Function{name:conditional_prob, args:Box([Symbol(Symbol { name: \"A\" }), Symbol(Symbol { name: \"B\" })])}",
"description": "Conditional probability"
},
{
"id": "metric_space_wolfram",
"language": "wolfram",
"category": "topology_geometry",
"input": "EuclideanDistance[x, y]",
"expected_expr": "Function{name:metric, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Metric function"
},
{
"id": "norm_wolfram",
"language": "wolfram",
"category": "topology_geometry",
"input": "Norm[x]",
"expected_expr": "Function{name:norm, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Norm"
},
{
"id": "inner_product_wolfram",
"language": "wolfram",
"category": "topology_geometry",
"input": "Dot[x, y]",
"expected_expr": "Function{name:inner_product, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Inner product"
},
{
"id": "cross_product_wolfram",
"language": "wolfram",
"category": "topology_geometry",
"input": "Cross[a, b]",
"expected_expr": "Function{name:cross_product, args:Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" })])}",
"description": "Cross product"
},
{
"id": "dot_product_wolfram",
"language": "wolfram",
"category": "topology_geometry",
"input": "Dot[a, b]",
"expected_expr": "Function{name:dot_product, args:Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" })])}",
"description": "Dot product"
},
{
"id": "fourier_transform_wolfram",
"language": "wolfram",
"category": "transforms",
"input": "FourierTransform[f[t], t, \u03c9]",
"expected_expr": "Function{name:fourier_transform, args:Box([Function{name:f, args:Box([Symbol(Symbol { name: \"t\" })])}, Symbol(Symbol { name: \"t\" }), Symbol(Symbol { name: \"\u03c9\" })])}",
"description": "Fourier transform"
},
{
"id": "laplace_transform_wolfram",
"language": "wolfram",
"category": "transforms",
"input": "LaplaceTransform[f[t], t, s]",
"expected_expr": "Function{name:laplace_transform, args:Box([Function{name:f, args:Box([Symbol(Symbol { name: \"t\" })])}, Symbol(Symbol { name: \"t\" }), Symbol(Symbol { name: \"s\" })])}",
"description": "Laplace transform"
},
{
"id": "z_transform_wolfram",
"language": "wolfram",
"category": "transforms",
"input": "ZTransform[x[n], n, z]",
"expected_expr": "Function{name:z_transform, args:Box([Function{name:x, args:Box([Symbol(Symbol { name: \"n\" })])}, Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"z\" })])}",
"description": "Z-transform"
},
{
"id": "convolution_wolfram",
"language": "wolfram",
"category": "transforms",
"input": "Convolve[f, g, t, \u03c4]",
"expected_expr": "Function{name:convolution, args:Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"g\" }), Symbol(Symbol { name: \"t\" }), Symbol(Symbol { name: \"\u03c4\" })])}",
"description": "Convolution"
},
{
"id": "dirac_delta_wolfram",
"language": "wolfram",
"category": "generalized_functions",
"input": "DiracDelta[x]",
"expected_expr": "Function{name:dirac_delta, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Dirac delta function"
},
{
"id": "heaviside_step_wolfram",
"language": "wolfram",
"category": "generalized_functions",
"input": "HeavisideTheta[x]",
"expected_expr": "Function{name:heaviside, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Heaviside step function"
},
{
"id": "sign_function_wolfram",
"language": "wolfram",
"category": "generalized_functions",
"input": "Sign[x]",
"expected_expr": "Function{name:sign, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Sign function"
},
{
"id": "floor_function_wolfram",
"language": "wolfram",
"category": "generalized_functions",
"input": "Floor[x]",
"expected_expr": "Function{name:floor, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Floor function"
},
{
"id": "ceiling_function_wolfram",
"language": "wolfram",
"category": "generalized_functions",
"input": "Ceiling[x]",
"expected_expr": "Function{name:ceil, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Ceiling function"
},
{
"id": "fractional_part_wolfram",
"language": "wolfram",
"category": "generalized_functions",
"input": "FractionalPart[x]",
"expected_expr": "Function{name:frac, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Fractional part"
},
{
"id": "min_function_wolfram",
"language": "wolfram",
"category": "optimization",
"input": "Min[x, y]",
"expected_expr": "Function{name:min, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Minimum function"
},
{
"id": "max_function_wolfram",
"language": "wolfram",
"category": "optimization",
"input": "Max[x, y]",
"expected_expr": "Function{name:max, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Maximum function"
},
{
"id": "argmin_wolfram",
"language": "wolfram",
"category": "optimization",
"input": "ArgMin[f[x], x]",
"expected_expr": "Function{name:argmin, args:Box([Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })])}, Symbol(Symbol { name: \"x\" })])}",
"description": "Argument of minimum"
},
{
"id": "argmax_wolfram",
"language": "wolfram",
"category": "optimization",
"input": "ArgMax[f[x], x]",
"expected_expr": "Function{name:argmax, args:Box([Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })])}, Symbol(Symbol { name: \"x\" })])}",
"description": "Argument of maximum"
},
{
"id": "bessel_function_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "BesselJ[n, x]",
"expected_expr": "Function{name:bessel_j, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Bessel function of first kind"
},
{
"id": "neumann_function_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "BesselY[n, x]",
"expected_expr": "Function{name:bessel_y, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Bessel function of second kind (Neumann)"
},
{
"id": "hankel_function_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "HankelH1[n, x]",
"expected_expr": "Function{name:hankel_h1, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Hankel function of first kind"
},
{
"id": "legendre_polynomial_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "LegendreP[n, x]",
"expected_expr": "Function{name:legendre_p, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Legendre polynomial"
},
{
"id": "associated_legendre_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "LegendreP[l, m, x]",
"expected_expr": "Function{name:assoc_legendre, args:Box([Symbol(Symbol { name: \"l\" }), Symbol(Symbol { name: \"m\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Associated Legendre function"
},
{
"id": "spherical_harmonic_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "SphericalHarmonicY[l, m, \u03b8, \u03c6]",
"expected_expr": "Function{name:spherical_harmonic, args:Box([Symbol(Symbol { name: \"l\" }), Symbol(Symbol { name: \"m\" }), Symbol(Symbol { name: \"\u03b8\" }), Symbol(Symbol { name: \"\u03c6\" })])}",
"description": "Spherical harmonic"
},
{
"id": "hermite_polynomial_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "HermiteH[n, x]",
"expected_expr": "Function{name:hermite, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Hermite polynomial"
},
{
"id": "laguerre_polynomial_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "LaguerreL[n, x]",
"expected_expr": "Function{name:laguerre, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Laguerre polynomial"
},
{
"id": "chebyshev_polynomial_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "ChebyshevT[n, x]",
"expected_expr": "Function{name:chebyshev_t, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Chebyshev polynomial of first kind"
},
{
"id": "elliptic_integral_first_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "EllipticF[\u03c6, k]",
"expected_expr": "Function{name:elliptic_f, args:Box([Symbol(Symbol { name: \"\u03c6\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Elliptic integral of first kind"
},
{
"id": "elliptic_integral_second_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "EllipticE[\u03c6, k]",
"expected_expr": "Function{name:elliptic_e, args:Box([Symbol(Symbol { name: \"\u03c6\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Elliptic integral of second kind"
},
{
"id": "beta_function_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "Beta[x, y]",
"expected_expr": "Function{name:beta, args:Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Beta function"
},
{
"id": "digamma_function_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "PolyGamma[x]",
"expected_expr": "Function{name:digamma, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Digamma function"
},
{
"id": "polygamma_function_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "PolyGamma[n, x]",
"expected_expr": "Function{name:polygamma, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Polygamma function"
},
{
"id": "riemann_zeta_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "Zeta[s]",
"expected_expr": "Function{name:zeta, args:Box([Symbol(Symbol { name: \"s\" })])}",
"description": "Riemann zeta function"
},
{
"id": "dirichlet_eta_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "DirichletEta[s]",
"expected_expr": "Function{name:dirichlet_eta, args:Box([Symbol(Symbol { name: \"s\" })])}",
"description": "Dirichlet eta function"
},
{
"id": "error_function_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "Erf[x]",
"expected_expr": "Function{name:erf, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Error function"
},
{
"id": "complementary_error_function_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "Erfc[x]",
"expected_expr": "Function{name:erfc, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Complementary error function"
},
{
"id": "fresnel_integral_s_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "FresnelS[x]",
"expected_expr": "Function{name:fresnel_s, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Fresnel integral S"
},
{
"id": "fresnel_integral_c_wolfram",
"language": "wolfram",
"category": "special_functions_advanced",
"input": "FresnelC[x]",
"expected_expr": "Function{name:fresnel_c, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Fresnel integral C"
},
{
"id": "factorial_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "Factorial[n]",
"expected_expr": "Function{name:factorial, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Factorial"
},
{
"id": "double_factorial_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "Factorial2[n]",
"expected_expr": "Function{name:double_factorial, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Double factorial"
},
{
"id": "binomial_coefficient_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "Binomial[n, k]",
"expected_expr": "Function{name:binomial, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Binomial coefficient"
},
{
"id": "multinomial_coefficient_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "Multinomial[k1, k2, k3]",
"expected_expr": "Function{name:multinomial, args:Box([Symbol(Symbol { name: \"k1\" }), Symbol(Symbol { name: \"k2\" }), Symbol(Symbol { name: \"k3\" })])}",
"description": "Multinomial coefficient"
},
{
"id": "stirling_first_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "StirlingS1[n, k]",
"expected_expr": "Function{name:stirling_first, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Stirling number of first kind"
},
{
"id": "stirling_second_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "StirlingS2[n, k]",
"expected_expr": "Function{name:stirling_second, args:Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Stirling number of second kind"
},
{
"id": "bell_number_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "BellB[n]",
"expected_expr": "Function{name:bell, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Bell number"
},
{
"id": "catalan_number_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "CatalanNumber[n]",
"expected_expr": "Function{name:catalan, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Catalan number"
},
{
"id": "fibonacci_number_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "Fibonacci[n]",
"expected_expr": "Function{name:fibonacci, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Fibonacci number"
},
{
"id": "lucas_number_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "LucasL[n]",
"expected_expr": "Function{name:lucas, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Lucas number"
},
{
"id": "euler_totient_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "EulerPhi[n]",
"expected_expr": "Function{name:euler_phi, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Euler's totient function"
},
{
"id": "mobius_function_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "MoebiusMu[n]",
"expected_expr": "Function{name:mobius, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "M\u00f6bius function"
},
{
"id": "divisor_function_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "DivisorSigma[k, n]",
"expected_expr": "Function{name:divisor_sigma, args:Box([Symbol(Symbol { name: \"k\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Divisor function"
},
{
"id": "prime_counting_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "PrimePi[x]",
"expected_expr": "Function{name:prime_pi, args:Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Prime counting function"
},
{
"id": "legendre_symbol_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "JacobiSymbol[a, p]",
"expected_expr": "Function{name:legendre_symbol, args:Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"p\" })])}",
"description": "Legendre symbol"
},
{
"id": "jacobi_symbol_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "JacobiSymbol[a, n]",
"expected_expr": "Function{name:jacobi_symbol, args:Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Jacobi symbol"
},
{
"id": "partition_function_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "PartitionsP[n]",
"expected_expr": "Function{name:partition, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Partition function"
},
{
"id": "ramanujan_tau_wolfram",
"language": "wolfram",
"category": "combinatorics_number_theory",
"input": "RamanujanTau[n]",
"expected_expr": "Function{name:ramanujan_tau, args:Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Ramanujan tau function"
},
{
"id": "double_integral_wolfram",
"language": "wolfram",
"category": "advanced_calculus",
"input": "Integrate[f[x, y], {x, a, b}, {y, c, d}]",
"expected_expr": "MultipleCalculus(Box(Integral{integrand: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"x\" }))), Symbol(Symbol { name: \"y\" })])}), variables: Box([Symbol { name: \"x\" }, Symbol { name: \"y\" }]), bounds: Some(Box([(Box(Symbol(Symbol { name: \"a\" })), Box(Symbol(Symbol { name: \"b\" }))), (Box(Symbol(Symbol { name: \"c\" })), Box(Symbol(Symbol { name: \"d\" })))]))}",
"description": "Double integral"
},
{
"id": "triple_integral_wolfram",
"language": "wolfram",
"category": "advanced_calculus",
"input": "Integrate[f[x, y, z], {x, a, b}, {y, c, d}, {z, e, f}]",
"expected_expr": "MultipleCalculus(Box(Integral{integrand: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"x\" }))), Symbol(Symbol { name: \"y\" }), Symbol(Symbol { name: \"z\" })])}), variables: Box([Symbol { name: \"x\" }, Symbol { name: \"y\" }, Symbol { name: \"z\" }]), bounds: Some(Box([(Box(Symbol(Symbol { name: \"a\" })), Box(Symbol(Symbol { name: \"b\" }))), (Box(Symbol(Symbol { name: \"c\" })), Box(Symbol(Symbol { name: \"d\" }))), (Box(Symbol(Symbol { name: \"e\" })), Box(Symbol(Symbol { name: \"f\" })))]))}",
"description": "Triple integral"
},
{
"id": "line_integral_wolfram",
"language": "wolfram",
"category": "advanced_calculus",
"input": "Integrate[F \u00b7 dr, {r, curve}]",
"expected_expr": "LineCalculus(Box(Integral{vector_field: Box(Symbol(Symbol { name: \"F\" })))), curve: Symbol { name: \"curve\" }}",
"description": "Line integral"
},
{
"id": "surface_integral_wolfram",
"language": "wolfram",
"category": "advanced_calculus",
"input": "Integrate[F \u00b7 n dS, {surface}]",
"expected_expr": "SurfaceCalculus(Box(Integral{vector_field: Box(Symbol(Symbol { name: \"F\" })))), surface: Symbol { name: \"surface\" }}",
"description": "Surface integral"
},
{
"id": "taylor_series_wolfram",
"language": "wolfram",
"category": "series_expansions",
"input": "Series[f[x], {x, a, n}]",
"expected_expr": "Function{name:taylor_series, args:Box([Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })])}, Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Taylor series"
},
{
"id": "fourier_series_wolfram",
"language": "wolfram",
"category": "series_expansions",
"input": "FourierSeries[f[x], x, n]",
"expected_expr": "Function{name:fourier_series, args:Box([Function{name:f, args:Box([Symbol(Symbol { name: \"x\" })])}, Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Fourier series"
},
{
"id": "first_order_ode_wolfram",
"language": "wolfram",
"category": "differential_equations",
"input": "DSolve[y'[x] == f[x, y[x]], y[x], x]",
"expected_expr": "Function{name:dsolve, args:Box([Relation{left: Box(Calculus(Box(Derivative{expression: Box(Function{name:y, args:Box([Symbol(Symbol { name: \"x\" })))])}), variable: Symbol { name: \"x\" }, order: 1}), right: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"x\" }), Function{name:y, args:Box([Symbol(Symbol { name: \"x\" })])}])}), relation_type: Equal}, Function{name:y, args:Box([Symbol(Symbol { name: \"x\" })])}, Symbol(Symbol { name: \"x\" })])}",
"description": "First-order ODE solver"
},
{
"id": "second_order_ode_wolfram",
"language": "wolfram",
"category": "differential_equations",
"input": "DSolve[y''[x] + p[x]*y'[x] + q[x]*y[x] == g[x], y[x], x]",
"expected_expr": "Function{name:dsolve, args:Box([Relation{left: Box(Add(Box([Calculus(Box(Derivative{expression: Box(Function{name:y, args:Box([Symbol(Symbol { name: \"x\" })))])}), variable: Symbol { name: \"x\" }, order: 2}, Mul(Box([Function{name:p, args:Box([Symbol(Symbol { name: \"x\" })])}, Calculus(Box(Derivative{expression: Box(Function{name:y, args:Box([Symbol(Symbol { name: \"x\" })))])}), variable: Symbol { name: \"x\" }, order: 1}])), Mul(Box([Function{name:q, args:Box([Symbol(Symbol { name: \"x\" })])}, Function{name:y, args:Box([Symbol(Symbol { name: \"x\" })])}]))]))), right: Box(Function{name:g, args:Box([Symbol(Symbol { name: \"x\" })])}), relation_type: Equal}, Function{name:y, args:Box([Symbol(Symbol { name: \"x\" })])}, Symbol(Symbol { name: \"x\" })])}",
"description": "Second-order ODE solver"
},
{
"id": "eigenvalue_problem_wolfram",
"language": "wolfram",
"category": "linear_algebra_advanced",
"input": "Eigenvalues[A]",
"expected_expr": "Function{name:eigenvalues, args:Box([Matrix(Box([[Symbol(Symbol { name: \"A\" })]]))])}",
"description": "Eigenvalues"
},
{
"id": "eigenvectors_wolfram",
"language": "wolfram",
"category": "linear_algebra_advanced",
"input": "Eigenvectors[A]",
"expected_expr": "Function{name:eigenvectors, args:Box([Matrix(Box([[Symbol(Symbol { name: \"A\" })]]))])}",
"description": "Eigenvectors"
},
{
"id": "matrix_exponential_wolfram",
"language": "wolfram",
"category": "linear_algebra_advanced",
"input": "MatrixExp[A*t]",
"expected_expr": "Function{name:matrix_exp, args:Box([Mul(Box([Matrix(Box([[Symbol(Symbol { name: \"A\" })]])), Symbol(Symbol { name: \"t\" })]))])}",
"description": "Matrix exponential"
},
{
"id": "svd_wolfram",
"language": "wolfram",
"category": "linear_algebra_advanced",
"input": "SingularValueDecomposition[A]",
"expected_expr": "Function{name:svd, args:Box([Matrix(Box([[Symbol(Symbol { name: \"A\" })]]))])}",
"description": "Singular Value Decomposition"
},
{
"id": "qr_decomposition_wolfram",
"language": "wolfram",
"category": "linear_algebra_advanced",
"input": "QRDecomposition[A]",
"expected_expr": "Function{name:qr_decomposition, args:Box([Matrix(Box([[Symbol(Symbol { name: \"A\" })]]))])}",
"description": "QR decomposition"
},
{
"id": "lu_decomposition_wolfram",
"language": "wolfram",
"category": "linear_algebra_advanced",
"input": "LUDecomposition[A]",
"expected_expr": "Function{name:lu_decomposition, args:Box([Matrix(Box([[Symbol(Symbol { name: \"A\" })]]))])}",
"description": "LU decomposition"
},
{
"id": "complex_conjugate_wolfram",
"language": "wolfram",
"category": "complex_analysis",
"input": "Conjugate[z]",
"expected_expr": "Function{name:conjugate, args:Box([Symbol(Symbol { name: \"z\" })])}",
"description": "Complex conjugate"
},
{
"id": "complex_modulus_wolfram",
"language": "wolfram",
"category": "complex_analysis",
"input": "Abs[z]",
"expected_expr": "Function{name:abs, args:Box([Symbol(Symbol { name: \"z\" })])}",
"description": "Complex modulus"
},
{
"id": "contour_integral_wolfram",
"language": "wolfram",
"category": "complex_analysis",
"input": "Integrate[f[z], {z, contour}]",
"expected_expr": "ContourCalculus(Box(Integral{integrand: Box(Function{name:f, args:Box([Symbol(Symbol { name: \"z\" })))])}), contour: Symbol { name: \"contour\" }}",
"description": "Contour integral"
},
{
"id": "residue_wolfram",
"language": "wolfram",
"category": "complex_analysis",
"input": "Residue[f[z], {z, z0}]",
"expected_expr": "Function{name:residue, args:Box([Function{name:f, args:Box([Symbol(Symbol { name: \"z\" })])}, Symbol(Symbol { name: \"z\" }), Symbol(Symbol { name: \"z0\" })])}",
"description": "Residue calculation"
},
{
"id": "gcd_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "\\gcd(a, b)",
"expected_expr": "Function{name: \"gcd\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" })])}",
"description": "Greatest common divisor"
},
{
"id": "lcm_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "\\text{lcm}(a, b)",
"expected_expr": "Function{name: \"lcm\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" })])}",
"description": "Least common multiple"
},
{
"id": "mod_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "a \\bmod n",
"expected_expr": "Function{name: \"mod\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Modular arithmetic"
},
{
"id": "tensor_product_latex",
"language": "latex",
"category": "tensor_operations",
"input": "A \\otimes B",
"expected_expr": "Function{name: \"tensor_product\", args: Box([Symbol(Symbol { name: \"A\" }), Symbol(Symbol { name: \"B\" })])}",
"description": "Tensor product"
},
{
"id": "tensor_contraction_latex",
"language": "latex",
"category": "tensor_operations",
"input": "T^{ij}_{ij}",
"expected_expr": "Function{name: \"tensor_contraction\", args: Box([Symbol(Symbol { name: \"T\" })])}",
"description": "Tensor contraction"
},
{
"id": "commutator_latex",
"language": "latex",
"category": "quantum_mechanics",
"input": "[A, B]",
"expected_expr": "Function{name: \"commutator\", args: Box([Symbol(Symbol { name: \"A\" }), Symbol(Symbol { name: \"B\" })])}",
"description": "Commutator bracket"
},
{
"id": "anticommutator_latex",
"language": "latex",
"category": "quantum_mechanics",
"input": "\\{A, B\\}",
"expected_expr": "Function{name: \"anticommutator\", args: Box([Symbol(Symbol { name: \"A\" }), Symbol(Symbol { name: \"B\" })])}",
"description": "Anticommutator"
},
{
"id": "bra_ket_latex",
"language": "latex",
"category": "quantum_mechanics",
"input": "\\langle \\psi | \\phi \\rangle",
"expected_expr": "Function{name: \"inner_product\", args: Box([Symbol(Symbol { name: \"psi\" }), Symbol(Symbol { name: \"phi\" })])}",
"description": "Bra-ket notation"
},
{
"id": "group_operation_latex",
"language": "latex",
"category": "group_theory",
"input": "g \\circ h",
"expected_expr": "Function{name: \"group_op\", args: Box([Symbol(Symbol { name: \"g\" }), Symbol(Symbol { name: \"h\" })])}",
"description": "Group operation"
},
{
"id": "group_inverse_latex",
"language": "latex",
"category": "group_theory",
"input": "g^{-1}",
"expected_expr": "Function{name: \"group_inverse\", args: Box([Symbol(Symbol { name: \"g\" })])}",
"description": "Group inverse"
},
{
"id": "covariant_derivative_latex",
"language": "latex",
"category": "differential_geometry",
"input": "\\nabla_\\mu V^\\nu",
"expected_expr": "Function{name: \"covariant_derivative\", args: Box([Symbol(Symbol { name: \"mu\" }), Symbol(Symbol { name: \"V\" }), Symbol(Symbol { name: \"nu\" })])}",
"description": "Covariant derivative"
},
{
"id": "lie_derivative_latex",
"language": "latex",
"category": "differential_geometry",
"input": "\\mathcal{L}_X Y",
"expected_expr": "Function{name: \"lie_derivative\", args: Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"Y\" })])}",
"description": "Lie derivative"
},
{
"id": "riemann_tensor_latex",
"language": "latex",
"category": "differential_geometry",
"input": "R^\\rho_{\\sigma\\mu\\nu}",
"expected_expr": "Function{name: \"riemann_tensor\", args: Box([Symbol(Symbol { name: \"rho\" }), Symbol(Symbol { name: \"sigma\" }), Symbol(Symbol { name: \"mu\" }), Symbol(Symbol { name: \"nu\" })])}",
"description": "Riemann curvature tensor"
},
{
"id": "ring_addition_latex",
"language": "latex",
"category": "algebraic_structures",
"input": "a +_R b",
"expected_expr": "Function{name: \"ring_add\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" }), Symbol(Symbol { name: \"R\" })])}",
"description": "Ring addition"
},
{
"id": "field_multiplication_latex",
"language": "latex",
"category": "algebraic_structures",
"input": "a \\cdot_F b",
"expected_expr": "Function{name: \"field_mul\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" }), Symbol(Symbol { name: \"F\" })])}",
"description": "Field multiplication"
},
{
"id": "homeomorphism_latex",
"language": "latex",
"category": "topology",
"input": "X \\cong Y",
"expected_expr": "Function{name: \"homeomorphic\", args: Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"Y\" })])}",
"description": "Homeomorphism"
},
{
"id": "measure_latex",
"language": "latex",
"category": "measure_theory",
"input": "\\mu(E)",
"expected_expr": "Function{name: \"measure\", args: Box([Symbol(Symbol { name: \"mu\" }), Symbol(Symbol { name: \"E\" })])}",
"description": "Measure of set E"
},
{
"id": "lebesgue_integral_latex",
"language": "latex",
"category": "measure_theory",
"input": "\\int f \\, d\\mu",
"expected_expr": "Function{name: \"lebesgue_integral\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"mu\" })])}",
"description": "Lebesgue integral"
},
{
"id": "operator_norm_latex",
"language": "latex",
"category": "functional_analysis",
"input": "\\|T\\|_{op}",
"expected_expr": "Function{name: \"operator_norm\", args: Box([Symbol(Symbol { name: \"T\" })])}",
"description": "Operator norm"
},
{
"id": "dual_space_latex",
"language": "latex",
"category": "functional_analysis",
"input": "X^*",
"expected_expr": "Function{name: \"dual_space\", args: Box([Symbol(Symbol { name: \"X\" })])}",
"description": "Dual space"
},
{
"id": "morphism_latex",
"language": "latex",
"category": "category_theory",
"input": "f: A \\to B",
"expected_expr": "Function{name: \"morphism\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"A\" }), Symbol(Symbol { name: \"B\" })])}",
"description": "Morphism in category"
},
{
"id": "functor_latex",
"language": "latex",
"category": "category_theory",
"input": "F: \\mathcal{C} \\to \\mathcal{D}",
"expected_expr": "Function{name: \"functor\", args: Box([Symbol(Symbol { name: \"F\" }), Symbol(Symbol { name: \"C\" }), Symbol(Symbol { name: \"D\" })])}",
"description": "Functor between categories"
},
{
"id": "gcd_wolfram",
"language": "wolfram",
"category": "number_theory_advanced",
"input": "GCD[a, b]",
"expected_expr": "Function{name: \"gcd\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" })])}",
"description": "Greatest common divisor"
},
{
"id": "lcm_wolfram",
"language": "wolfram",
"category": "number_theory_advanced",
"input": "LCM[a, b]",
"expected_expr": "Function{name: \"lcm\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" })])}",
"description": "Least common multiple"
},
{
"id": "mod_wolfram",
"language": "wolfram",
"category": "number_theory_advanced",
"input": "Mod[a, n]",
"expected_expr": "Function{name: \"mod\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Modular arithmetic"
},
{
"id": "airy_ai_latex",
"language": "latex",
"category": "special_functions_extended",
"input": "\\text{Ai}(x)",
"expected_expr": "Function{name: \"airy_ai\", args: Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Airy function Ai"
},
{
"id": "airy_bi_latex",
"language": "latex",
"category": "special_functions_extended",
"input": "\\text{Bi}(x)",
"expected_expr": "Function{name: \"airy_bi\", args: Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Airy function Bi"
},
{
"id": "mathieu_c_latex",
"language": "latex",
"category": "special_functions_extended",
"input": "C_n(a, q, z)",
"expected_expr": "Function{name: \"mathieu_c\", args: Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"q\" }), Symbol(Symbol { name: \"z\" })])}",
"description": "Mathieu cosine function"
},
{
"id": "mathieu_s_latex",
"language": "latex",
"category": "special_functions_extended",
"input": "S_n(a, q, z)",
"expected_expr": "Function{name: \"mathieu_s\", args: Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"q\" }), Symbol(Symbol { name: \"z\" })])}",
"description": "Mathieu sine function"
},
{
"id": "airy_ai_wolfram",
"language": "wolfram",
"category": "special_functions_extended",
"input": "AiryAi[x]",
"expected_expr": "Function{name: \"airy_ai\", args: Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Airy function Ai"
},
{
"id": "airy_bi_wolfram",
"language": "wolfram",
"category": "special_functions_extended",
"input": "AiryBi[x]",
"expected_expr": "Function{name: \"airy_bi\", args: Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Airy function Bi"
},
{
"id": "fractional_derivative_latex",
"language": "latex",
"category": "fractional_calculus",
"input": "D^\\alpha f(x)",
"expected_expr": "Function{name: \"fractional_derivative\", args: Box([Symbol(Symbol { name: \"alpha\" }), Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Fractional derivative"
},
{
"id": "riemann_liouville_latex",
"language": "latex",
"category": "fractional_calculus",
"input": "{}^{RL}D^\\alpha f(x)",
"expected_expr": "Function{name: \"riemann_liouville\", args: Box([Symbol(Symbol { name: \"alpha\" }), Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Riemann-Liouville derivative"
},
{
"id": "ito_integral_latex",
"language": "latex",
"category": "stochastic_calculus",
"input": "\\int_0^t X_s \\, dW_s",
"expected_expr": "Function{name: \"ito_integral\", args: Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"W\" }), Number(Integer(0)), Symbol(Symbol { name: \"t\" })])}",
"description": "It\u00f4 integral"
},
{
"id": "stratonovich_integral_latex",
"language": "latex",
"category": "stochastic_calculus",
"input": "\\int_0^t X_s \\circ dW_s",
"expected_expr": "Function{name: \"stratonovich_integral\", args: Box([Symbol(Symbol { name: \"X\" }), Symbol(Symbol { name: \"W\" }), Number(Integer(0)), Symbol(Symbol { name: \"t\" })])}",
"description": "Stratonovich integral"
},
{
"id": "tribonacci_latex",
"language": "latex",
"category": "combinatorics_advanced",
"input": "T_n",
"expected_expr": "Function{name: \"tribonacci\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Tribonacci numbers"
},
{
"id": "motzkin_latex",
"language": "latex",
"category": "combinatorics_advanced",
"input": "M_n",
"expected_expr": "Function{name: \"motzkin\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Motzkin numbers"
},
{
"id": "genocchi_latex",
"language": "latex",
"category": "combinatorics_advanced",
"input": "G_n",
"expected_expr": "Function{name: \"genocchi\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Genocchi numbers"
},
{
"id": "andre_latex",
"language": "latex",
"category": "combinatorics_advanced",
"input": "A_n",
"expected_expr": "Function{name: \"andre\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Andr\u00e9 numbers (Euler zigzag numbers)"
},
{
"id": "marcumq_latex",
"language": "latex",
"category": "special_functions_radio",
"input": "Q_M(a, b)",
"expected_expr": "Function{name: \"marcumq\", args: Box([Symbol(Symbol { name: \"M\" }), Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" })])}",
"description": "Marcum Q-function (radio engineering)"
},
{
"id": "meijerg_latex",
"language": "latex",
"category": "hypergeometric_advanced",
"input": "G_{p,q}^{m,n}(z)",
"expected_expr": "Function{name: \"meijer_g\", args: Box([Symbol(Symbol { name: \"p\" }), Symbol(Symbol { name: \"q\" }), Symbol(Symbol { name: \"m\" }), Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"z\" })])}",
"description": "Meijer G-function"
},
{
"id": "carmichael_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "\\lambda(n)",
"expected_expr": "Function{name: \"carmichael\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Carmichael function"
},
{
"id": "primenu_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "\\nu(n)",
"expected_expr": "Function{name: \"primenu\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Number of distinct prime factors"
},
{
"id": "primeomega_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "\\Omega(n)",
"expected_expr": "Function{name: \"primeomega\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Number of prime factors with multiplicity"
},
{
"id": "reduced_totient_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "\\lambda(n)",
"expected_expr": "Function{name: \"reduced_totient\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Reduced totient function (Carmichael lambda)"
},
{
"id": "kronecker_symbol_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "\\left(\\frac{a}{n}\\right)",
"expected_expr": "Function{name: \"kronecker_symbol\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Kronecker symbol"
},
{
"id": "lerchphi_latex",
"language": "latex",
"category": "zeta_functions_advanced",
"input": "\\Phi(z, s, a)",
"expected_expr": "Function{name: \"lerch_phi\", args: Box([Symbol(Symbol { name: \"z\" }), Symbol(Symbol { name: \"s\" }), Symbol(Symbol { name: \"a\" })])}",
"description": "Lerch transcendent function"
},
{
"id": "polylog_latex",
"language": "latex",
"category": "zeta_functions_advanced",
"input": "\\text{Li}_s(z)",
"expected_expr": "Function{name: \"polylog\", args: Box([Symbol(Symbol { name: \"s\" }), Symbol(Symbol { name: \"z\" })])}",
"description": "Polylogarithm function"
},
{
"id": "stieltjes_latex",
"language": "latex",
"category": "zeta_functions_advanced",
"input": "\\gamma_n",
"expected_expr": "Function{name: \"stieltjes\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Stieltjes constants"
},
{
"id": "riemann_xi_latex",
"language": "latex",
"category": "zeta_functions_advanced",
"input": "\\xi(s)",
"expected_expr": "Function{name: \"riemann_xi\", args: Box([Symbol(Symbol { name: \"s\" })])}",
"description": "Riemann xi function"
},
{
"id": "levi_civita_latex",
"language": "latex",
"category": "tensor_calculus",
"input": "\\epsilon_{ijk}",
"expected_expr": "Function{name: \"levi_civita\", args: Box([Symbol(Symbol { name: \"i\" }), Symbol(Symbol { name: \"j\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Levi-Civita symbol"
},
{
"id": "kronecker_delta_latex",
"language": "latex",
"category": "tensor_calculus",
"input": "\\delta_{ij}",
"expected_expr": "Function{name: \"kronecker_delta\", args: Box([Symbol(Symbol { name: \"i\" }), Symbol(Symbol { name: \"j\" })])}",
"description": "Kronecker delta"
},
{
"id": "eijk_latex",
"language": "latex",
"category": "tensor_calculus",
"input": "E_{ijk}",
"expected_expr": "Function{name: \"eijk\", args: Box([Symbol(Symbol { name: \"i\" }), Symbol(Symbol { name: \"j\" }), Symbol(Symbol { name: \"k\" })])}",
"description": "Levi-Civita tensor (alternative notation)"
},
{
"id": "bspline_basis_latex",
"language": "latex",
"category": "splines_interpolation",
"input": "B_{i,p}(t)",
"expected_expr": "Function{name: \"bspline_basis\", args: Box([Symbol(Symbol { name: \"i\" }), Symbol(Symbol { name: \"p\" }), Symbol(Symbol { name: \"t\" })])}",
"description": "B-spline basis function"
},
{
"id": "interpolating_spline_latex",
"language": "latex",
"category": "splines_interpolation",
"input": "S(x)",
"expected_expr": "Function{name: \"interpolating_spline\", args: Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Interpolating spline"
},
{
"id": "polar_lift_latex",
"language": "latex",
"category": "complex_analysis_advanced",
"input": "\\text{polar\\_lift}(z)",
"expected_expr": "Function{name: \"polar_lift\", args: Box([Symbol(Symbol { name: \"z\" })])}",
"description": "Polar lift function"
},
{
"id": "periodic_argument_latex",
"language": "latex",
"category": "complex_analysis_advanced",
"input": "\\text{periodic\\_arg}(z)",
"expected_expr": "Function{name: \"periodic_argument\", args: Box([Symbol(Symbol { name: \"z\" })])}",
"description": "Periodic argument function"
},
{
"id": "unbranched_argument_latex",
"language": "latex",
"category": "complex_analysis_advanced",
"input": "\\text{unbranched\\_arg}(z)",
"expected_expr": "Function{name: \"unbranched_argument\", args: Box([Symbol(Symbol { name: \"z\" })])}",
"description": "Unbranched argument function"
},
{
"id": "principal_branch_latex",
"language": "latex",
"category": "complex_analysis_advanced",
"input": "\\text{principal\\_branch}(z)",
"expected_expr": "Function{name: \"principal_branch\", args: Box([Symbol(Symbol { name: \"z\" })])}",
"description": "Principal branch function"
},
{
"id": "polarify_latex",
"language": "latex",
"category": "complex_analysis_advanced",
"input": "\\text{polarify}(z)",
"expected_expr": "Function{name: \"polarify\", args: Box([Symbol(Symbol { name: \"z\" })])}",
"description": "Polarify function"
},
{
"id": "unpolarify_latex",
"language": "latex",
"category": "complex_analysis_advanced",
"input": "\\text{unpolarify}(z)",
"expected_expr": "Function{name: \"unpolarify\", args: Box([Symbol(Symbol { name: \"z\" })])}",
"description": "Unpolarify function"
},
{
"id": "singularity_function_latex",
"language": "latex",
"category": "singularity_functions",
"input": "\\langle x - a \\rangle^n",
"expected_expr": "Function{name: \"singularity_function\", args: Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Singularity function (Macaulay brackets)"
},
{
"id": "tribonacci_wolfram",
"language": "wolfram",
"category": "combinatorics_advanced",
"input": "Tribonacci[n]",
"expected_expr": "Function{name: \"tribonacci\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Tribonacci numbers"
},
{
"id": "marcumq_wolfram",
"language": "wolfram",
"category": "special_functions_radio",
"input": "MarcumQ[M, a, b]",
"expected_expr": "Function{name: \"marcumq\", args: Box([Symbol(Symbol { name: \"M\" }), Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" })])}",
"description": "Marcum Q-function"
},
{
"id": "appellf1_wolfram",
"language": "wolfram",
"category": "hypergeometric_advanced",
"input": "AppellF1[a, b1, b2, c, x, y]",
"expected_expr": "Function{name: \"appell_f1\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b1\" }), Symbol(Symbol { name: \"b2\" }), Symbol(Symbol { name: \"c\" }), Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Appell hypergeometric function F1"
},
{
"id": "meijerg_wolfram",
"language": "wolfram",
"category": "hypergeometric_advanced",
"input": "MeijerG[{{a1, a2}, {a3}}, {{b1}, {b2, b3}}, z]",
"expected_expr": "Function{name: \"meijer_g\", args: Box([Set(Box([Set(Box([Symbol(Symbol { name: \"a1\" }), Symbol(Symbol { name: \"a2\" })])), Set(Box([Symbol(Symbol { name: \"a3\" })]))])), Set(Box([Set(Box([Symbol(Symbol { name: \"b1\" })])), Set(Box([Symbol(Symbol { name: \"b2\" }), Symbol(Symbol { name: \"b3\" })]))])), Symbol(Symbol { name: \"z\" })])}",
"description": "Meijer G-function"
},
{
"id": "lerchphi_wolfram",
"language": "wolfram",
"category": "zeta_functions_advanced",
"input": "LerchPhi[z, s, a]",
"expected_expr": "Function{name: \"lerch_phi\", args: Box([Symbol(Symbol { name: \"z\" }), Symbol(Symbol { name: \"s\" }), Symbol(Symbol { name: \"a\" })])}",
"description": "Lerch transcendent function"
},
{
"id": "polylog_wolfram",
"language": "wolfram",
"category": "zeta_functions_advanced",
"input": "PolyLog[s, z]",
"expected_expr": "Function{name: \"polylog\", args: Box([Symbol(Symbol { name: \"s\" }), Symbol(Symbol { name: \"z\" })])}",
"description": "Polylogarithm function"
},
{
"id": "stieltjes_wolfram",
"language": "wolfram",
"category": "zeta_functions_advanced",
"input": "StieltjesGamma[n]",
"expected_expr": "Function{name: \"stieltjes\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Stieltjes constants"
},
{
"id": "tribonacci_constant_latex",
"language": "latex",
"category": "mathematical_constants_advanced",
"input": "\\alpha_3",
"expected_expr": "Constant(TribonacciConstant)",
"description": "Tribonacci constant"
},
{
"id": "plastic_number_latex",
"language": "latex",
"category": "mathematical_constants_advanced",
"input": "\\rho",
"expected_expr": "Function{name: \"plastic_number\", args: Box([])}",
"description": "Plastic number (real root of x\u00b3 - x - 1 = 0)"
},
{
"id": "feigenbaum_delta_latex",
"language": "latex",
"category": "mathematical_constants_advanced",
"input": "\\delta",
"expected_expr": "Function{name: \"feigenbaum_delta\", args: Box([])}",
"description": "Feigenbaum constant \u03b4"
},
{
"id": "feigenbaum_alpha_latex",
"language": "latex",
"category": "mathematical_constants_advanced",
"input": "\\alpha",
"expected_expr": "Function{name: \"feigenbaum_alpha\", args: Box([])}",
"description": "Feigenbaum constant \u03b1"
},
{
"id": "matrix_exponential_latex",
"language": "latex",
"category": "matrix_functions_advanced",
"input": "e^A",
"expected_expr": "Function{name: \"matrix_exp\", args: Box([Symbol(Symbol { name: \"A\" })])}",
"description": "Matrix exponential"
},
{
"id": "matrix_logarithm_latex",
"language": "latex",
"category": "matrix_functions_advanced",
"input": "\\log(A)",
"expected_expr": "Function{name: \"matrix_log\", args: Box([Symbol(Symbol { name: \"A\" })])}",
"description": "Matrix logarithm"
},
{
"id": "matrix_power_latex",
"language": "latex",
"category": "matrix_functions_advanced",
"input": "A^{1/2}",
"expected_expr": "Function{name: \"matrix_power\", args: Box([Symbol(Symbol { name: \"A\" }), Mul([Number(Integer(1)), Pow(Box(Number(Integer(2))), Number(Integer(-1)))])])}",
"description": "Matrix fractional power"
},
{
"id": "matrix_exponential_wolfram",
"language": "wolfram",
"category": "matrix_functions_advanced",
"input": "MatrixExp[A]",
"expected_expr": "Function{name: \"matrix_exp\", args: Box([Symbol(Symbol { name: \"A\" })])}",
"description": "Matrix exponential"
},
{
"id": "matrix_logarithm_wolfram",
"language": "wolfram",
"category": "matrix_functions_advanced",
"input": "MatrixLog[A]",
"expected_expr": "Function{name: \"matrix_log\", args: Box([Symbol(Symbol { name: \"A\" })])}",
"description": "Matrix logarithm"
},
{
"id": "matrix_power_wolfram",
"language": "wolfram",
"category": "matrix_functions_advanced",
"input": "MatrixPower[A, 1/2]",
"expected_expr": "Function{name: \"matrix_power\", args: Box([Symbol(Symbol { name: \"A\" }), Mul([Number(Integer(1)), Pow(Box(Number(Integer(2))), Number(Integer(-1)))])])}",
"description": "Matrix fractional power"
},
{
"id": "hill_muscle_model_latex",
"language": "latex",
"category": "biomechanics",
"input": "F = F_0 \\cdot (a + b \\cdot v)/(b + v)",
"expected_expr": "Function{name: \"hill_muscle\", args: Box([Symbol(Symbol { name: \"F_0\" }), Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" }), Symbol(Symbol { name: \"v\" })])}",
"description": "Hill muscle model"
},
{
"id": "michaelis_menten_latex",
"language": "latex",
"category": "biomechanics",
"input": "v = \\frac{V_{max} [S]}{K_m + [S]}",
"expected_expr": "Function{name: \"michaelis_menten\", args: Box([Symbol(Symbol { name: \"V_max\" }), Symbol(Symbol { name: \"S\" }), Symbol(Symbol { name: \"K_m\" })])}",
"description": "Michaelis-Menten kinetics"
},
{
"id": "stress_tensor_latex",
"language": "latex",
"category": "continuum_mechanics",
"input": "\\sigma_{ij}",
"expected_expr": "Function{name: \"stress_tensor\", args: Box([Symbol(Symbol { name: \"i\" }), Symbol(Symbol { name: \"j\" })])}",
"description": "Stress tensor"
},
{
"id": "strain_tensor_latex",
"language": "latex",
"category": "continuum_mechanics",
"input": "\\epsilon_{ij}",
"expected_expr": "Function{name: \"strain_tensor\", args: Box([Symbol(Symbol { name: \"i\" }), Symbol(Symbol { name: \"j\" })])}",
"description": "Strain tensor"
},
{
"id": "constitutive_relation_latex",
"language": "latex",
"category": "continuum_mechanics",
"input": "\\sigma = C : \\epsilon",
"expected_expr": "Function{name: \"constitutive_relation\", args: Box([Symbol(Symbol { name: \"sigma\" }), Symbol(Symbol { name: \"C\" }), Symbol(Symbol { name: \"epsilon\" })])}",
"description": "Constitutive relation"
},
{
"id": "transfer_function_latex",
"language": "latex",
"category": "control_theory",
"input": "G(s) = \\frac{N(s)}{D(s)}",
"expected_expr": "Function{name: \"transfer_function\", args: Box([Symbol(Symbol { name: \"N\" }), Symbol(Symbol { name: \"D\" }), Symbol(Symbol { name: \"s\" })])}",
"description": "Transfer function"
},
{
"id": "pid_controller_latex",
"language": "latex",
"category": "control_theory",
"input": "u(t) = K_p e(t) + K_i \\int_0^t e(\\tau) d\\tau + K_d \\frac{de(t)}{dt}",
"expected_expr": "Function{name: \"pid_controller\", args: Box([Symbol(Symbol { name: \"K_p\" }), Symbol(Symbol { name: \"K_i\" }), Symbol(Symbol { name: \"K_d\" }), Symbol(Symbol { name: \"e\" }), Symbol(Symbol { name: \"t\" })])}",
"description": "PID controller"
},
{
"id": "routh_hurwitz_latex",
"language": "latex",
"category": "control_theory",
"input": "\\text{RH}(s)",
"expected_expr": "Function{name: \"routh_hurwitz\", args: Box([Symbol(Symbol { name: \"s\" })])}",
"description": "Routh-Hurwitz stability criterion"
},
{
"id": "dirac_gamma_matrices_latex",
"language": "latex",
"category": "high_energy_physics",
"input": "\\gamma^\\mu",
"expected_expr": "Function{name: \"gamma_matrix\", args: Box([Symbol(Symbol { name: \"mu\" })])}",
"description": "Dirac gamma matrices"
},
{
"id": "pauli_matrices_latex",
"language": "latex",
"category": "high_energy_physics",
"input": "\\sigma_i",
"expected_expr": "Function{name: \"pauli_matrix\", args: Box([Symbol(Symbol { name: \"i\" })])}",
"description": "Pauli matrices"
},
{
"id": "feynman_slash_notation_latex",
"language": "latex",
"category": "high_energy_physics",
"input": "\\not{p}",
"expected_expr": "Function{name: \"feynman_slash\", args: Box([Symbol(Symbol { name: \"p\" })])}",
"description": "Feynman slash notation"
},
{
"id": "yang_mills_latex",
"language": "latex",
"category": "high_energy_physics",
"input": "F_{\\mu\\nu}^a = \\partial_\\mu A_\\nu^a - \\partial_\\nu A_\\mu^a + g f^{abc} A_\\mu^b A_\\nu^c",
"expected_expr": "Function{name: \"yang_mills_field\", args: Box([Symbol(Symbol { name: \"mu\" }), Symbol(Symbol { name: \"nu\" }), Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"A\" }), Symbol(Symbol { name: \"g\" }), Symbol(Symbol { name: \"f\" })])}",
"description": "Yang-Mills field strength tensor"
},
{
"id": "creation_operator_latex",
"language": "latex",
"category": "quantum_optics",
"input": "a^\\dagger",
"expected_expr": "Function{name: \"creation_operator\", args: Box([Symbol(Symbol { name: \"a\" })])}",
"description": "Creation operator"
},
{
"id": "annihilation_operator_latex",
"language": "latex",
"category": "quantum_optics",
"input": "a",
"expected_expr": "Function{name: \"annihilation_operator\", args: Box([Symbol(Symbol { name: \"a\" })])}",
"description": "Annihilation operator"
},
{
"id": "coherent_state_latex",
"language": "latex",
"category": "quantum_optics",
"input": "|\\alpha\\rangle",
"expected_expr": "Function{name: \"coherent_state\", args: Box([Symbol(Symbol { name: \"alpha\" })])}",
"description": "Coherent state"
},
{
"id": "squeezed_state_latex",
"language": "latex",
"category": "quantum_optics",
"input": "S(\\xi) |0\\rangle",
"expected_expr": "Function{name: \"squeezed_state\", args: Box([Symbol(Symbol { name: \"xi\" })])}",
"description": "Squeezed state"
},
{
"id": "miller_indices_latex",
"language": "latex",
"category": "crystallography",
"input": "(hkl)",
"expected_expr": "Function{name: \"miller_indices\", args: Box([Symbol(Symbol { name: \"h\" }), Symbol(Symbol { name: \"k\" }), Symbol(Symbol { name: \"l\" })])}",
"description": "Miller indices"
},
{
"id": "structure_factor_latex",
"language": "latex",
"category": "crystallography",
"input": "F_{hkl}",
"expected_expr": "Function{name: \"structure_factor\", args: Box([Symbol(Symbol { name: \"h\" }), Symbol(Symbol { name: \"k\" }), Symbol(Symbol { name: \"l\" })])}",
"description": "Structure factor"
},
{
"id": "reynolds_number_latex",
"language": "latex",
"category": "fluid_dynamics",
"input": "Re = \\frac{\\rho v L}{\\mu}",
"expected_expr": "Function{name: \"reynolds_number\", args: Box([Symbol(Symbol { name: \"rho\" }), Symbol(Symbol { name: \"v\" }), Symbol(Symbol { name: \"L\" }), Symbol(Symbol { name: \"mu\" })])}",
"description": "Reynolds number"
},
{
"id": "prandtl_number_latex",
"language": "latex",
"category": "fluid_dynamics",
"input": "Pr = \\frac{\\nu}{\\alpha}",
"expected_expr": "Function{name: \"prandtl_number\", args: Box([Symbol(Symbol { name: \"nu\" }), Symbol(Symbol { name: \"alpha\" })])}",
"description": "Prandtl number"
},
{
"id": "mach_number_latex",
"language": "latex",
"category": "fluid_dynamics",
"input": "Ma = \\frac{v}{c}",
"expected_expr": "Function{name: \"mach_number\", args: Box([Symbol(Symbol { name: \"v\" }), Symbol(Symbol { name: \"c\" })])}",
"description": "Mach number"
},
{
"id": "euler_equations_latex",
"language": "latex",
"category": "fluid_dynamics",
"input": "\\frac{\\partial \\rho}{\\partial t} + \\nabla \\cdot (\\rho \\vec{v}) = 0",
"expected_expr": "Function{name: \"euler_equations\", args: Box([Symbol(Symbol { name: \"rho\" }), Symbol(Symbol { name: \"t\" }), Function{name: \"vector\", args: Box([Symbol(Symbol { name: \"v\" })])}])}",
"description": "Euler equations for fluid flow"
},
{
"id": "debye_length_latex",
"language": "latex",
"category": "plasma_physics",
"input": "\\lambda_D = \\sqrt{\\frac{\\epsilon_0 k_B T_e}{n_e e^2}}",
"expected_expr": "Function{name: \"debye_length\", args: Box([Symbol(Symbol { name: \"epsilon_0\" }), Symbol(Symbol { name: \"k_B\" }), Symbol(Symbol { name: \"T_e\" }), Symbol(Symbol { name: \"n_e\" }), Symbol(Symbol { name: \"e\" })])}",
"description": "Debye length"
},
{
"id": "plasma_frequency_latex",
"language": "latex",
"category": "plasma_physics",
"input": "\\omega_p = \\sqrt{\\frac{n_e e^2}{\\epsilon_0 m_e}}",
"expected_expr": "Function{name: \"plasma_frequency\", args: Box([Symbol(Symbol { name: \"n_e\" }), Symbol(Symbol { name: \"e\" }), Symbol(Symbol { name: \"epsilon_0\" }), Symbol(Symbol { name: \"m_e\" })])}",
"description": "Plasma frequency"
},
{
"id": "cyclotron_frequency_latex",
"language": "latex",
"category": "plasma_physics",
"input": "\\omega_c = \\frac{eB}{m}",
"expected_expr": "Function{name: \"cyclotron_frequency\", args: Box([Symbol(Symbol { name: \"e\" }), Symbol(Symbol { name: \"B\" }), Symbol(Symbol { name: \"m\" })])}",
"description": "Cyclotron frequency"
},
{
"id": "lorentz_factor_latex",
"language": "latex",
"category": "relativity",
"input": "\\gamma = \\frac{1}{\\sqrt{1 - v^2/c^2}}",
"expected_expr": "Function{name: \"lorentz_factor\", args: Box([Symbol(Symbol { name: \"v\" }), Symbol(Symbol { name: \"c\" })])}",
"description": "Lorentz factor"
},
{
"id": "four_momentum_latex",
"language": "latex",
"category": "relativity",
"input": "p^\\mu",
"expected_expr": "Function{name: \"four_momentum\", args: Box([Symbol(Symbol { name: \"mu\" })])}",
"description": "Four-momentum"
},
{
"id": "minkowski_metric_latex",
"language": "latex",
"category": "relativity",
"input": "\\eta_{\\mu\\nu}",
"expected_expr": "Function{name: \"minkowski_metric\", args: Box([Symbol(Symbol { name: \"mu\" }), Symbol(Symbol { name: \"nu\" })])}",
"description": "Minkowski metric tensor"
},
{
"id": "hubble_parameter_latex",
"language": "latex",
"category": "cosmology",
"input": "H(t) = \\frac{\\dot{a}(t)}{a(t)}",
"expected_expr": "Function{name: \"hubble_parameter\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"t\" })])}",
"description": "Hubble parameter"
},
{
"id": "friedmann_equation_latex",
"language": "latex",
"category": "cosmology",
"input": "H^2 = \\frac{8\\pi G}{3}\\rho - \\frac{kc^2}{a^2}",
"expected_expr": "Function{name: \"friedmann_equation\", args: Box([Symbol(Symbol { name: \"H\" }), Symbol(Symbol { name: \"G\" }), Symbol(Symbol { name: \"rho\" }), Symbol(Symbol { name: \"k\" }), Symbol(Symbol { name: \"c\" }), Symbol(Symbol { name: \"a\" })])}",
"description": "Friedmann equation"
},
{
"id": "scale_factor_latex",
"language": "latex",
"category": "cosmology",
"input": "a(t)",
"expected_expr": "Function{name: \"scale_factor\", args: Box([Symbol(Symbol { name: \"t\" })])}",
"description": "Cosmological scale factor"
},
{
"id": "chandrasekhar_limit_latex",
"language": "latex",
"category": "astrophysics",
"input": "M_{Ch} = 1.4 M_\\odot",
"expected_expr": "Function{name: \"chandrasekhar_limit\", args: Box([Symbol(Symbol { name: \"M_sun\" })])}",
"description": "Chandrasekhar limit"
},
{
"id": "eddington_luminosity_latex",
"language": "latex",
"category": "astrophysics",
"input": "L_{Edd} = \\frac{4\\pi GMm_p c}{\\sigma_T}",
"expected_expr": "Function{name: \"eddington_luminosity\", args: Box([Symbol(Symbol { name: \"G\" }), Symbol(Symbol { name: \"M\" }), Symbol(Symbol { name: \"m_p\" }), Symbol(Symbol { name: \"c\" }), Symbol(Symbol { name: \"sigma_T\" })])}",
"description": "Eddington luminosity"
},
{
"id": "seismic_wave_velocity_latex",
"language": "latex",
"category": "geophysics",
"input": "v_p = \\sqrt{\\frac{K + \\frac{4}{3}\\mu}{\\rho}}",
"expected_expr": "Function{name: \"seismic_p_wave\", args: Box([Symbol(Symbol { name: \"K\" }), Symbol(Symbol { name: \"mu\" }), Symbol(Symbol { name: \"rho\" })])}",
"description": "P-wave velocity"
},
{
"id": "richter_magnitude_latex",
"language": "latex",
"category": "geophysics",
"input": "M_L = \\log_{10} A - \\log_{10} A_0",
"expected_expr": "Function{name: \"richter_magnitude\", args: Box([Symbol(Symbol { name: \"A\" }), Symbol(Symbol { name: \"A_0\" })])}",
"description": "Richter magnitude scale"
},
{
"id": "coriolis_parameter_latex",
"language": "latex",
"category": "geophysics",
"input": "f = 2\\Omega \\sin\\phi",
"expected_expr": "Function{name: \"coriolis_parameter\", args: Box([Symbol(Symbol { name: \"Omega\" }), Symbol(Symbol { name: \"phi\" })])}",
"description": "Coriolis parameter"
},
{
"id": "transfer_function_wolfram",
"language": "wolfram",
"category": "control_theory",
"input": "TransferFunctionModel[{{num}}, {{den}}, s]",
"expected_expr": "Function{name: \"transfer_function\", args: Box([Symbol(Symbol { name: \"num\" }), Symbol(Symbol { name: \"den\" }), Symbol(Symbol { name: \"s\" })])}",
"description": "Transfer function"
},
{
"id": "gamma_matrix_wolfram",
"language": "wolfram",
"category": "high_energy_physics",
"input": "DiracGamma[mu]",
"expected_expr": "Function{name: \"gamma_matrix\", args: Box([Symbol(Symbol { name: \"mu\" })])}",
"description": "Dirac gamma matrices"
},
{
"id": "pauli_matrix_wolfram",
"language": "wolfram",
"category": "high_energy_physics",
"input": "PauliMatrix[i]",
"expected_expr": "Function{name: \"pauli_matrix\", args: Box([Symbol(Symbol { name: \"i\" })])}",
"description": "Pauli matrices"
},
{
"id": "lorentz_factor_wolfram",
"language": "wolfram",
"category": "relativity",
"input": "1/Sqrt[1 - v^2/c^2]",
"expected_expr": "Function{name: \"lorentz_factor\", args: Box([Symbol(Symbol { name: \"v\" }), Symbol(Symbol { name: \"c\" })])}",
"description": "Lorentz factor"
},
{
"id": "continued_fraction_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "[a_0; a_1, a_2, a_3, \\ldots]",
"expected_expr": "Function{name: \"continued_fraction\", args: Box([Symbol(Symbol { name: \"a_0\" }), Symbol(Symbol { name: \"a_1\" }), Symbol(Symbol { name: \"a_2\" }), Symbol(Symbol { name: \"a_3\" })])}",
"description": "Continued fraction representation"
},
{
"id": "egyptian_fraction_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "\\frac{1}{a_1} + \\frac{1}{a_2} + \\cdots + \\frac{1}{a_n}",
"expected_expr": "Function{name: \"egyptian_fraction\", args: Box([Symbol(Symbol { name: \"a_1\" }), Symbol(Symbol { name: \"a_2\" }), Symbol(Symbol { name: \"a_n\" })])}",
"description": "Egyptian fraction decomposition"
},
{
"id": "quadratic_residue_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "\\text{QR}(a, p)",
"expected_expr": "Function{name: \"quadratic_residue\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"p\" })])}",
"description": "Quadratic residue"
},
{
"id": "primitive_root_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "\\text{PrimRoot}(n)",
"expected_expr": "Function{name: \"primitive_root\", args: Box([Symbol(Symbol { name: \"n\" })])}",
"description": "Primitive root modulo n"
},
{
"id": "discrete_log_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "\\log_g a \\pmod{p}",
"expected_expr": "Function{name: \"discrete_log\", args: Box([Symbol(Symbol { name: \"g\" }), Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"p\" })])}",
"description": "Discrete logarithm"
},
{
"id": "elliptic_curve_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "y^2 = x^3 + ax + b",
"expected_expr": "Function{name: \"elliptic_curve\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" })])}",
"description": "Elliptic curve equation"
},
{
"id": "class_number_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "h(d)",
"expected_expr": "Function{name: \"class_number\", args: Box([Symbol(Symbol { name: \"d\" })])}",
"description": "Class number of quadratic field"
},
{
"id": "quadratic_form_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "ax^2 + bxy + cy^2",
"expected_expr": "Function{name: \"quadratic_form\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" }), Symbol(Symbol { name: \"c\" }), Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Binary quadratic form"
},
{
"id": "pell_equation_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "x^2 - Dy^2 = 1",
"expected_expr": "Function{name: \"pell_equation\", args: Box([Symbol(Symbol { name: \"D\" }), Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" })])}",
"description": "Pell equation"
},
{
"id": "sum_of_squares_latex",
"language": "latex",
"category": "number_theory_advanced",
"input": "r_k(n)",
"expected_expr": "Function{name: \"sum_of_squares\", args: Box([Symbol(Symbol { name: \"k\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Number of ways to write n as sum of k squares"
},
{
"id": "cyclotomic_polynomial_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\Phi_n(x)",
"expected_expr": "Function{name: \"cyclotomic_polynomial\", args: Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "n-th cyclotomic polynomial"
},
{
"id": "minimal_polynomial_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\text{MinPoly}(\\alpha, \\mathbb{Q})",
"expected_expr": "Function{name: \"minimal_polynomial\", args: Box([Symbol(Symbol { name: \"alpha\" }), Symbol(Symbol { name: \"Q\" })])}",
"description": "Minimal polynomial of algebraic number"
},
{
"id": "irreducible_polynomial_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\text{Irred}(f, \\mathbb{F}_p)",
"expected_expr": "Function{name: \"irreducible_polynomial\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"F_p\" })])}",
"description": "Irreducible polynomial over finite field"
},
{
"id": "polynomial_gcd_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\gcd(f(x), g(x))",
"expected_expr": "Function{name: \"polynomial_gcd\", args: Box([Function{name: \"f\", args: Box([Symbol(Symbol { name: \"x\" })])}, Function{name: \"g\", args: Box([Symbol(Symbol { name: \"x\" })])}])}",
"description": "Polynomial greatest common divisor"
},
{
"id": "polynomial_lcm_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\text{lcm}(f(x), g(x))",
"expected_expr": "Function{name: \"polynomial_lcm\", args: Box([Function{name: \"f\", args: Box([Symbol(Symbol { name: \"x\" })])}, Function{name: \"g\", args: Box([Symbol(Symbol { name: \"x\" })])}])}",
"description": "Polynomial least common multiple"
},
{
"id": "resultant_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\text{Res}(f, g)",
"expected_expr": "Function{name: \"resultant\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"g\" })])}",
"description": "Resultant of two polynomials"
},
{
"id": "discriminant_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\Delta(f)",
"expected_expr": "Function{name: \"discriminant\", args: Box([Symbol(Symbol { name: \"f\" })])}",
"description": "Discriminant of polynomial"
},
{
"id": "sylvester_matrix_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\text{Syl}(f, g)",
"expected_expr": "Function{name: \"sylvester_matrix\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"g\" })])}",
"description": "Sylvester matrix"
},
{
"id": "polynomial_norm_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "N_{L/K}(\\alpha)",
"expected_expr": "Function{name: \"polynomial_norm\", args: Box([Symbol(Symbol { name: \"alpha\" }), Symbol(Symbol { name: \"L\" }), Symbol(Symbol { name: \"K\" })])}",
"description": "Norm of algebraic element"
},
{
"id": "polynomial_trace_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\text{Tr}_{L/K}(\\alpha)",
"expected_expr": "Function{name: \"polynomial_trace\", args: Box([Symbol(Symbol { name: \"alpha\" }), Symbol(Symbol { name: \"L\" }), Symbol(Symbol { name: \"K\" })])}",
"description": "Trace of algebraic element"
},
{
"id": "groebner_basis_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\text{GB}(I)",
"expected_expr": "Function{name: \"groebner_basis\", args: Box([Symbol(Symbol { name: \"I\" })])}",
"description": "Gr\u00f6bner basis of ideal"
},
{
"id": "hilbert_polynomial_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "H_I(t)",
"expected_expr": "Function{name: \"hilbert_polynomial\", args: Box([Symbol(Symbol { name: \"I\" }), Symbol(Symbol { name: \"t\" })])}",
"description": "Hilbert polynomial of ideal"
},
{
"id": "polynomial_factorization_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\text{Factor}(f, \\mathbb{Q})",
"expected_expr": "Function{name: \"polynomial_factorization\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"Q\" })])}",
"description": "Polynomial factorization over field"
},
{
"id": "square_free_factorization_latex",
"language": "latex",
"category": "polynomial_theory_advanced",
"input": "\\text{SqFree}(f)",
"expected_expr": "Function{name: \"square_free_factorization\", args: Box([Symbol(Symbol { name: \"f\" })])}",
"description": "Square-free factorization"
},
{
"id": "galois_group_latex",
"language": "latex",
"category": "galois_theory",
"input": "\\text{Gal}(L/K)",
"expected_expr": "Function{name: \"galois_group\", args: Box([Symbol(Symbol { name: \"L\" }), Symbol(Symbol { name: \"K\" })])}",
"description": "Galois group of field extension"
},
{
"id": "splitting_field_latex",
"language": "latex",
"category": "galois_theory",
"input": "\\text{Split}(f, K)",
"expected_expr": "Function{name: \"splitting_field\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"K\" })])}",
"description": "Splitting field of polynomial"
},
{
"id": "field_degree_latex",
"language": "latex",
"category": "galois_theory",
"input": "[L : K]",
"expected_expr": "Function{name: \"field_degree\", args: Box([Symbol(Symbol { name: \"L\" }), Symbol(Symbol { name: \"K\" })])}",
"description": "Degree of field extension"
},
{
"id": "continued_fraction_wolfram",
"language": "wolfram",
"category": "number_theory_advanced",
"input": "ContinuedFraction[x]",
"expected_expr": "Function{name: \"continued_fraction\", args: Box([Symbol(Symbol { name: \"x\" })])}",
"description": "Continued fraction representation"
},
{
"id": "quadratic_residue_wolfram",
"language": "wolfram",
"category": "number_theory_advanced",
"input": "JacobiSymbol[a, n]",
"expected_expr": "Function{name: \"quadratic_residue\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"n\" })])}",
"description": "Quadratic residue (Jacobi symbol)"
},
{
"id": "elliptic_curve_wolfram",
"language": "wolfram",
"category": "number_theory_advanced",
"input": "EllipticCurve[{a, b}]",
"expected_expr": "Function{name: \"elliptic_curve\", args: Box([Symbol(Symbol { name: \"a\" }), Symbol(Symbol { name: \"b\" })])}",
"description": "Elliptic curve"
},
{
"id": "cyclotomic_polynomial_wolfram",
"language": "wolfram",
"category": "polynomial_theory_advanced",
"input": "CyclotomicPolynomial[n, x]",
"expected_expr": "Function{name: \"cyclotomic_polynomial\", args: Box([Symbol(Symbol { name: \"n\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Cyclotomic polynomial"
},
{
"id": "minimal_polynomial_wolfram",
"language": "wolfram",
"category": "polynomial_theory_advanced",
"input": "MinimalPolynomial[alpha, x]",
"expected_expr": "Function{name: \"minimal_polynomial\", args: Box([Symbol(Symbol { name: \"alpha\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Minimal polynomial"
},
{
"id": "resultant_wolfram",
"language": "wolfram",
"category": "polynomial_theory_advanced",
"input": "Resultant[f, g, x]",
"expected_expr": "Function{name: \"resultant\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"g\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Resultant of polynomials"
},
{
"id": "discriminant_wolfram",
"language": "wolfram",
"category": "polynomial_theory_advanced",
"input": "Discriminant[f, x]",
"expected_expr": "Function{name: \"discriminant\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"x\" })])}",
"description": "Discriminant of polynomial"
},
{
"id": "groebner_basis_wolfram",
"language": "wolfram",
"category": "polynomial_theory_advanced",
"input": "GroebnerBasis[{f1, f2, f3}, {x, y, z}]",
"expected_expr": "Function{name: \"groebner_basis\", args: Box([Set(Box([Symbol(Symbol { name: \"f1\" }), Symbol(Symbol { name: \"f2\" }), Symbol(Symbol { name: \"f3\" })])), Set(Box([Symbol(Symbol { name: \"x\" }), Symbol(Symbol { name: \"y\" }), Symbol(Symbol { name: \"z\" })]))])}",
"description": "Gr\u00f6bner basis"
},
{
"id": "polynomial_gcd_wolfram",
"language": "wolfram",
"category": "polynomial_theory_advanced",
"input": "PolynomialGCD[f, g]",
"expected_expr": "Function{name: \"polynomial_gcd\", args: Box([Symbol(Symbol { name: \"f\" }), Symbol(Symbol { name: \"g\" })])}",
"description": "Polynomial GCD"
}
]