functions.md

Function Reference

TeXpr provides a wide range of mathematical functions, from basic trigonometry to complex number arithmetic.

Trigonometric Functions

All trigonometric functions expect arguments in radians.

LaTeX	Purpose	Complex Support
\sin{x}	Sine	✅
\cos{x}	Cosine	✅
\tan{x}	Tangent	✅
\cot{x}	Cotangent	✅
\sec{x}	Secant	✅
\csc{x}	Cosecant	✅

Hyperbolic Functions

LaTeX	Purpose	Complex Support
\sinh{x}	Hyperbolic sine	✅
\cosh{x}	Hyperbolic cosine	✅
\tanh{x}	Hyperbolic tangent	✅
\coth{x}	Hyperbolic cotangent	✅
\sech{x}	Hyperbolic secant	✅
\csch{x}	Hyperbolic cosecant	✅

Inverse Functions

LaTeX	Purpose	Alias
\arcsin{x}	Inverse sine	\asin{x}
\arccos{x}	Inverse cosine	\acos{x}
\arctan{x}	Inverse tangent	\atan{x}
\arccot{x}	Inverse cotangent	\acot{x}
\arcsec{x}	Inverse secant	\asec{x}
\arccsc{x}	Inverse cosecant	\acsc{x}
\asinh{x}	Inverse hyperbolic sine	-
\acosh{x}	Inverse hyperbolic cosine	-
\atanh{x}	Inverse hyperbolic tangent	-

---

Logarithmic & Exponential

LaTeX	Purpose	Description
\ln{x}	Natural log	Base $e$
\log{x}	Common log	Base 10
\log_{b}{x}	Arbitrary log	Base $b$
\log2{x}	Base 2 log	Alias: \log_{2}
\exp{x}	Exponential	$e^x$

---

Power & Roots

LaTeX	Purpose	Example
\sqrt{x}	Square root	\sqrt{16} = 4
\sqrt[n]{x}	n-th root	\sqrt[3]{27} = 3

---

Rounding & Absolute Value

LaTeX	Purpose	Example
\abs{x}	Absolute value	\abs{-5} = 5
\floor{x}	Floor	\floor{3.7} = 3
\ceil{x}	Ceiling	\ceil{3.2} = 4
\round{x}	Round	\round{3.5} = 4
\sgn{x}	Sign function	\sgn{-3} = -1

---

Number Theory & Misc

LaTeX	Purpose	Description
\gcd{a, b}	GCD	Greatest Common Divisor
\lcm{a, b}	LCM	Least Common Multiple
\min{a, b}	Minimum	Smaller of two values
\max{a, b}	Maximum	Larger of two values
\factorial{n}	Factorial	$n! = 1 \cdot 2 \cdot ... \cdot n$
\binom{n}{k}	Binomial	"n choose k"
\fibonacci{n}	Fibonacci	n-th Fibonacci number

---

Complex Numbers

Special functions for complex numbers $z = a + bi$.

LaTeX	Purpose	Description
\Re{z}	Real part	Returns $a$
\Im{z}	Imaginary part	Returns $b$
\arg{z}	Argument	Phase angle in radians
\conjugate{z}	Conjugate	Returns $a - bi$
\overline{z}	Conjugate	Alias for \conjugate

---

Implementation Details

Most mathematical functions delegate directly to Dart's dart:math library for real numbers and a custom Complex implementation for complex numbers.

Precision

Calculations use IEEE 754 double-precision floating-point arithmetic. High-order functions like \factorial and \fibonacci return results as doubles and may lose precision for very large inputs (typically $n > 20$ for factorial).

Domain Errors

If a function is called outside its domain (e.g., \ln{-1} with only real support enabled, or \sqrt{-1} without complex results expected), an EvaluatorException is thrown.

try {
  evaluator.evaluate(r'\ln{-1}');
} on EvaluatorException catch (e) {
  print(e.message); // "Domain error: ln() argument must be positive"
}

Piecewise Definition

Support for piecewise functions is available via the \begin{cases} environment. See the Piecewise Functions Guide for full details on syntax and usage.