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 Case-insensitive dynamic search of latex as plain text: XOR

The operation ID links to a page where you can edit the operation

dict_of_expressions_that_use_operation:
{'0002222764': [{'name_latex': 'MacLaurin series with expanded terms', 'reference_latex': 'https://en.wikipedia.org/wiki/Taylor_series', 'latex_condition': '{\\rm the\\ function\\ is\\ infinitely\\ differentiable\\ at\\ x = 0.}', 'latex_rhs': "f(0)+f'(x)\\ x + \\frac{f''(x)\\ x^2}{2!} + \\frac{f'''(x)\\ x^3}{3!} + ...", 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'description_latex': 'a Maclaurin series is a special case of a Taylor series where the expansion point is always x=0.', 'id': '9605409442', 'created_datetime': '2026-03-01_14-13-41-223833', 'latex_lhs': 'f(x)', 'latex_relation': '='}, {'sympy_lhs': "Add(Mul(Rational(1, 2), exp(Mul(Symbol('pdg0001464'), Symbol('pdg0004621')))), Mul(Rational(1, 2), exp(Mul(Integer(-1), Symbol('pdg0001464'), Symbol('pdg0004621')))))", 'name_latex': '', 'reference_latex': '', 'latex_condition': '', 'lean': '', 'latex_rhs': '\\cos(x)', 'sympy_rhs': "cos(Symbol('pdg0001464'))", 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'description_latex': '', 'id': '3829492824', 'latex_lhs': '\\frac{1}{2}\\left(\\exp(i x)+\\exp(-i x) \\right)', 'latex_relation': '='}], '0002222427': [{'name_latex': 'Taylor series as summation', 'reference_latex': 'https://en.wikipedia.org/wiki/Taylor_series', 'latex_condition': '{\\rm the\\ function\\ is\\ infinitely\\ differentiable\\ at}\\ x = a.', 'latex_rhs': '\\sum_{n=0}^{\\infty} \\frac{f^n(a)}{n!} (x-a)^n', 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'description_latex': '', 'id': '7764834870', 'created_datetime': '2026-03-01_15-05-53-683114', 'latex_lhs': 'f(x)', 'latex_relation': '='}], '0002222348': [{'name_latex': 'Taylor series as summation', 'reference_latex': 'https://en.wikipedia.org/wiki/Taylor_series', 'latex_condition': '{\\rm the\\ function\\ is\\ infinitely\\ differentiable\\ at}\\ x = a.', 'latex_rhs': '\\sum_{n=0}^{\\infty} \\frac{f^n(a)}{n!} (x-a)^n', 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'description_latex': '', 'id': '7764834870', 'created_datetime': '2026-03-01_15-05-53-683114', 'latex_lhs': 'f(x)', 'latex_relation': '='}, {'name_latex': 'MacLaurin series as summation', 'reference_latex': 'https://en.wikipedia.org/wiki/Taylor_series', 'latex_condition': '{\\rm the\\ function\\ is\\ infinitely\\ differentiable\\ at\\ x = 0.}', 'latex_rhs': '\\sum_{n=0}^{\\infty} \\frac{f^n(0)}{n!} x^n', 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'description_latex': 'a Maclaurin series is a special case of a Taylor series where the expansion point is always x=0.', 'id': '8637447837', 'created_datetime': '2026-03-01_14-18-02-534007', 'latex_lhs': 'f(x)', 'latex_relation': '='}], '0002495151': [{'name_latex': 'Taylor series as summation', 'reference_latex': 'https://en.wikipedia.org/wiki/Taylor_series', 'latex_condition': '{\\rm the\\ function\\ is\\ infinitely\\ differentiable\\ at}\\ x = a.', 'latex_rhs': '\\sum_{n=0}^{\\infty} \\frac{f^n(a)}{n!} (x-a)^n', 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'description_latex': '', 'id': '7764834870', 'created_datetime': '2026-03-01_15-05-53-683114', 'latex_lhs': 'f(x)', 'latex_relation': '='}, {'name_latex': 'MacLaurin series with expanded terms', 'reference_latex': 'https://en.wikipedia.org/wiki/Taylor_series', 'latex_condition': '{\\rm the\\ function\\ is\\ infinitely\\ differentiable\\ at\\ x = 0.}', 'latex_rhs': "f(0)+f'(x)\\ x + \\frac{f''(x)\\ x^2}{2!} + \\frac{f'''(x)\\ x^3}{3!} + ...", 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'description_latex': 'a Maclaurin series is a special case of a Taylor series where the expansion point is always x=0.', 'id': '9605409442', 'created_datetime': '2026-03-01_14-13-41-223833', 'latex_lhs': 'f(x)', 'latex_relation': '='}, {'name_latex': 'MacLaurin series as summation', 'reference_latex': 'https://en.wikipedia.org/wiki/Taylor_series', 'latex_condition': '{\\rm the\\ function\\ is\\ infinitely\\ differentiable\\ at\\ x = 0.}', 'latex_rhs': '\\sum_{n=0}^{\\infty} \\frac{f^n(0)}{n!} x^n', 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'description_latex': 'a Maclaurin series is a special case of a Taylor series where the expansion point is always x=0.', 'id': '8637447837', 'created_datetime': '2026-03-01_14-18-02-534007', 'latex_lhs': 'f(x)', 'latex_relation': '='}]}

dict_of_derivations_that_use_operation:
{'0002222764': [{'name_latex': "Euler's equation from MacLaurin series", 'abstract_latex': '', 'reference_latex': 'https://fermatslasttheorem.blogspot.com/2006/02/eulers-formula.html', 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'id': '6470318827', 'created_datetime': '2026-03-01_14-06-23-459141'}, {'name_latex': 'Euler equation: trigonometric relations', 'abstract_latex': '', 'reference_latex': '', 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'id': '0000000003'}], '0002222427': [{'name_latex': "Euler's equation from MacLaurin series", 'abstract_latex': '', 'reference_latex': 'https://fermatslasttheorem.blogspot.com/2006/02/eulers-formula.html', 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'id': '6470318827', 'created_datetime': '2026-03-01_14-06-23-459141'}], '0002222348': [{'name_latex': "Euler's equation from MacLaurin series", 'abstract_latex': '', 'reference_latex': 'https://fermatslasttheorem.blogspot.com/2006/02/eulers-formula.html', 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'id': '6470318827', 'created_datetime': '2026-03-01_14-06-23-459141'}], '0002495151': [{'name_latex': "Euler's equation from MacLaurin series", 'abstract_latex': '', 'reference_latex': 'https://fermatslasttheorem.blogspot.com/2006/02/eulers-formula.html', 'author_name_latex': 'a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba', 'id': '6470318827', 'created_datetime': '2026-03-01_14-06-23-459141'}]}

ID latex name argument count description used in expression used in derivation reference
0001094924 \(\cdot\)
\cdot		 multiplication 2 multiply two terms
0001130211 \(\arctan\)
\arctan		 arc tangent 1
https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
0001299288 \(\det\)
\det		 determinant 1
https://en.wikipedia.org/wiki/Determinant
0002090103 \(\coth\)
\coth		 hyperbolic cotangent 1
https://en.wikipedia.org/wiki/Hyperbolic_function
0002222105 \(\vec{\nabla}\)
\vec{\nabla}		 gradient 1
0002222144 \(\sin\)
\sin		 sine 1
0002222278 \(\times\)
\times		 cross product 2
0002222280 \(\int\)
\int		 definite integral 4
0002222329 \(f\)
f		 function 1
0002222348 \(\sum\)
\sum		 summation 4
  • 7764834870
    \(f(x)=\sum_{n=0}^{\infty} \frac{f^n(a)}{n!} (x-a)^n\)
  • 8637447837
    \(f(x)=\sum_{n=0}^{\infty} \frac{f^n(0)}{n!} x^n\)
0002222427 \(-\)
-		 subtraction 2
  • 7764834870
    \(f(x)=\sum_{n=0}^{\infty} \frac{f^n(a)}{n!} (x-a)^n\)
0002222435 \(+\)
+		 element-wise addition 2
0002222439 \(\vec{\nabla}\)
\vec{\nabla}		 spatial vector differential 2
0002222455 \(\circ\)
\circ		 dot product 2
0002222591 \(\vec{\nabla} \cdot\)
\vec{\nabla} \cdot		 divergence 1
0002222657 \(\int\)
\int		 indefinite intergral 2
0002222764 \(+\)
+		 addition 2
  • 9605409442
    \(f(x)=f(0)+f'(x)\ x + \frac{f''(x)\ x^2}{2!} + \frac{f'''(x)\ x^3}{3!} + ...\)
  • 3829492824
    \(\frac{1}{2}\left(\exp(i x)+\exp(-i x) \right)=\cos(x)\)
0002222829 \(*\)
*		 multiplication 2
0002222891 \(/\)
/		 division 2
0002222896 \(\vec{\nabla} \times\)
\vec{\nabla} \times		 curl 1
0002222940 \(\cos\)
\cos		 cosine 1
0002495151 \(!\)
!		 factorial 1
  • 7764834870
    \(f(x)=\sum_{n=0}^{\infty} \frac{f^n(a)}{n!} (x-a)^n\)
  • 9605409442
    \(f(x)=f(0)+f'(x)\ x + \frac{f''(x)\ x^2}{2!} + \frac{f'''(x)\ x^3}{3!} + ...\)
  • 8637447837
    \(f(x)=\sum_{n=0}^{\infty} \frac{f^n(0)}{n!} x^n\)
https://en.wikipedia.org/wiki/Factorial
0002532789 \(\tan\)
\tan		 tangent 1
https://en.wikipedia.org/wiki/Trigonometric_functions
0002841881 \(\sinh\)
\sinh		 hyperbolic sine 1
https://en.wikipedia.org/wiki/Hyperbolic_function
0003382639 \(\cot\)
\cot		 cotangent 1
https://en.wikipedia.org/wiki/Trigonometric_functions
0003403771 \(\log\)
\log		 log, arbitrary base 2 default base 10
0003530844 \(\mod{}\)
\mod{}		 modulo 2
0004352752 \(\tanh\)
\tanh		 hyperbolic tangent 1
https://en.wikipedia.org/wiki/Hyperbolic_function
0004426238 \(\div\)
\div		 divide 2 division
0004958131 \(\max\)
\max		 maximum 1
0005560743 \(\arcsin\)
\arcsin		 arc sine 1
https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
0005818852 \(\cosh\)
\cosh		 hyperbolic cosine 1
https://en.wikipedia.org/wiki/Hyperbolic_function
0006151818 \(\arccos\)
\arccos		 arc cosine 1
https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
0006521282 \(\ln\)
\ln		 natural logarithm 1
0006739965 \(\sec\)
\sec		 secant 1
https://en.wikipedia.org/wiki/Trigonometric_functions
0007843744 \(\sqrt{}\)
\sqrt{}		 square root 1
https://en.wikipedia.org/wiki/Square_root
0008632687 \(\exp\)
\exp		 exponential function 1
https://en.wikipedia.org/wiki/Exponential_function
0008940007 \(\oint\)
\oint		 indefinite surface integral 2
0009780858 \(\csc\)
\csc		 cosecant 1
https://en.wikipedia.org/wiki/Trigonometric_functions
0009993766 \(\min\)
\min		 minimum 1

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