Supported LaTeX Commands

This document provides a reference of all LaTeX commands supported by the texpr library.

Quick Reference

Category	Commands
Arithmetic	+, -, *, /, ^, \times, \cdot, \div
Calculus	\frac, \int, \iint, \iiint, \sum, \prod, \lim, \partial, \nabla
Functions	\sin, \cos, \tan, \log, \ln, \sqrt, \exp, \abs
Greek	\alpha–\omega, \Alpha–\Psi, \varepsilon, \varphi
Matrices	\begin{matrix}, \begin{pmatrix}, \begin{bmatrix}
Special	\binom, \infty, \pi, \text{}, \mathbf{}
Logic	\forall, \exists, \Rightarrow, \Leftarrow, \Leftrightarrow
Sets	\subset, \subseteq, \cup, \cap, \setminus
Decoration	\dot, \ddot, \bar, \overline
Variables	let, f(x) = ...

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Arithmetic Operators

LaTeX	Description	Example
+	Addition	3 + 4 to 7
-	Subtraction	5 - 2 to 3
* or \times	Multiplication	3 \times 4 to 12
/ or \div	Division	8 \div 2 to 4
^	Exponentiation	2^{10} to 1024
\cdot	Dot product / Multiplication	\vec{a} \cdot \vec{b}

Implicit Multiplication: The parser supports implicit multiplication:

2x         to 2 * x
xy         to x * y
2\pi r     to 2 * π * r
\sin x \cos x to sin(x) * cos(x)

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Mathematical Functions

Trigonometric Functions

For more details, see Function Reference.

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

Inverse Trigonometric Functions

LaTeX	Alias	Description
\arcsin{x}	\asin{x}	Inverse sine
\arccos{x}	\acos{x}	Inverse cosine
\arctan{x}	\atan{x}	Inverse tangent
\arccot{x}	\acot{x}	Inverse cotangent
\arcsec{x}	\asec{x}	Inverse secant
\arccsc{x}	\acsc{x}	Inverse cosecant

Hyperbolic Functions

LaTeX	Description	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 Hyperbolic Functions

LaTeX	Description
\asinh{x}	Inverse hyperbolic sine
\acosh{x}	Inverse hyperbolic cosine
\atanh{x}	Inverse hyperbolic tangent
\acoth{x}	Inverse hyperbolic cotangent
\asech{x}	Inverse hyperbolic secant
\acsch{x}	Inverse hyperbolic cosecant

Logarithmic & Exponential Functions

For more details, see Function Reference.

LaTeX	Description	Example
\ln{x}	Natural logarithm	\ln{e} to 1
\log{x}	Logarithm base 10	\log{100} to 2
\log_{b}{x}	Logarithm base b	\log_{2}{8} to 3
\exp{x}	Exponential (e^x)	\exp{1} to e

Power & Root Functions

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

Rounding Functions

LaTeX	Description	Example
\floor{x}	Floor (round down)	\floor{3.7} to 3
\ceil{x}	Ceiling (round up)	\ceil{3.2} to 4
\round{x}	Round to nearest	\round{3.5} to 4

Other Functions

For more details, see Function Reference.

LaTeX	Description	Example
\abs{x} or |x|	Absolute value	\abs{-5} to 5
\sgn{x} or \sign{x}	Sign function	\sgn{-3} to -1
\min{a, b}	Minimum	\min{3, 5} to 3
\max{a, b}	Maximum	\max{3, 5} to 5
\gcd{a, b}	Greatest common divisor	\gcd{12, 8} to 4
\lcm{a, b}	Least common multiple	\lcm{4, 6} to 12
\factorial{n} or n!	Factorial	\factorial{5} to 120
\fibonacci{n}	Fibonacci number	\fibonacci{10} to 55

Decoration Functions (Pass-through)

These functions wrap an expression but return the evaluated value of the argument during numerical computation.

LaTeX	Description	Example
\dot{x}	Time derivative	\dot{5} to 5
\ddot{x}	Second derivative	\ddot{5} to 5
\bar{x}	Bar / Mean	\bar{5} to 5
\overline{x}	Overline	\overline{5} to 5

Complex Number Functions

For more details, see Function Reference.

LaTeX	Description	Example
\Re{z}	Real part	\Re{3 + 4i} to 3
\Im{z}	Imaginary part	\Im{3 + 4i} to 4
\conjugate{z} or \overline{z}	Complex conjugate	\conjugate{3 + 4i} to 3 - 4i

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Calculus Notation

For more details, see Calculus.

Fractions

\frac{numerator}{denominator}

Example: \frac{x^2 + 1}{x - 1}

Derivatives

Syntax	Description
\frac{d}{dx}(f)	First derivative
\frac{d^2}{dx^2}(f)	Second derivative
\frac{d^n}{dx^n}(f)	n-th derivative
\frac{\partial}{\partial x}(f)	Partial derivative
\frac{\partial^2}{\partial x^2}(f)	Second partial derivative

Integrals

LaTeX	Description
\int{f} dx	Indefinite integral
\int_{a}^{b}{f} dx	Definite integral
\iint{f} dx dy	Double integral
\iiint{f} dx dy dz	Triple integral

Example:

\int_{0}^{\pi} \sin{x} dx
\iint{x^2 + y^2} dx dy

Summation & Products

LaTeX	Description	Example
\sum_{i=a}^{b}{f}	Summation	\sum_{i=1}^{10}{i} to 55
\prod_{i=a}^{b}{f}	Product	\prod_{i=1}^{5}{i} to 120

Limits

\lim_{x \to a} f(x)

Example: \lim_{x \to 0} \frac{\sin{x}}{x} to 1

Binomial Coefficient

\binom{n}{k}

Example: \binom{10}{3} to 120

Special Symbols

LaTeX	Description
\partial	Partial derivative symbol (∂)
\nabla	Gradient operator (∇)
\infty	Infinity (∞)
\to or \rightarrow	Arrow (to)
\mapsto	Maps to (↦)
\Rightarrow	Double right arrow (⇒)
\Leftarrow	Double left arrow (⇐)
\Leftrightarrow	Double left-right arrow (⇔)

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Greek Letters

For more details, see standard Greek letter symbols below.

Lowercase Greek

LaTeX	Symbol	LaTeX	Symbol	LaTeX	Symbol
\alpha	α	\iota	ι	\rho	ρ
\beta	β	\kappa	κ	\sigma	σ
\gamma	γ	\lambda	λ	\tau	τ
\delta	δ	\mu	μ	\upsilon	υ
\epsilon	ε	\nu	ν	\phi	φ
\zeta	ζ	\xi	ξ	\chi	χ
\eta	η	\omicron	ο	\psi	ψ
\theta	θ	\pi	π	\omega	ω

Uppercase Greek

LaTeX	Symbol	LaTeX	Symbol	LaTeX	Symbol
\Gamma	Γ	\Lambda	Λ	\Phi	Φ
\Delta	Δ	\Xi	Ξ	\Psi	Ψ
\Theta	Θ	\Pi	Π	\Omega	Ω
\Sigma	Σ	\Upsilon	Υ

Variant Greek Letters

LaTeX	Description
\varepsilon	Variant epsilon (ε)
\varphi	Variant phi (φ)
\varrho	Variant rho (ρ)
\vartheta	Variant theta (θ)
\varpi	Variant pi (ϖ)
\varsigma	Final sigma (ς)

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Variables & Functions

For more details, see Count Environments.

Command	Description	Example
let x = ...	Variable assignment	let x = 5
f(x) = ...	Function definition	f(x) = x^2

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Mathematical Constants

For more details, see Constants.

LaTeX	Value	Description
\pi	3.14159...	Pi
\tau	6.28318...	Tau (2π)
\phi	1.61803...	Golden ratio
e	2.71828...	Euler's number
i	√(-1)	Imaginary unit
\hbar	1.054... * 10⁻³⁴	Reduced Planck constant
\infty	∞	Infinity

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Matrix & Vector Notation

For more details, see matrix and vector sections below.

Matrix Environments

Environment	Description	Delimiters
\begin{matrix}...\end{matrix}	Plain matrix	None
\begin{pmatrix}...\end{pmatrix}	Parenthesized	( )
\begin{bmatrix}...\end{bmatrix}	Bracketed	[ ]
\begin{vmatrix}...\end{vmatrix}	Determinant	| |
\begin{align}...\end{align}	Aligned equations	None

Matrix Syntax

\begin{pmatrix}
  a & b \\
  c & d
\end{pmatrix}

• Use & to separate columns
• Use \\ to separate rows

Matrix Functions

LaTeX	Description
\det{A}	Determinant
\trace{A} or \tr{A}	Trace
A^T	Transpose
A^{-1}	Inverse

Vector Notation

LaTeX	Description
\vec{v}	Vector (arrow notation)
\hat{v}	Unit vector

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Comparison Operators

LaTeX	Symbol	Description
=	=	Equal
\neq	≠	Not equal
<	<	Less than
>	>	Greater than
\leq	≤	Less than or equal
\geq	≥	Greater than or equal
\approx	≈	Approximately equal
\propto	∝	Proportional to

Set Notation & Logic

LaTeX	Symbol	Description
\in	∈	Element of
\subset	⊂	Proper subset
\subseteq	⊆	Subset or equal
\supset	⊃	Proper superset
\supseteq	⊇	Superset or equal
\cup	∪	Union
\cap	∩	Intersection
\setminus	\	Set difference
\forall	∀	For all
\exists	∃	There exists

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Spacing Commands

These commands are recognized but ignored during evaluation (they're for display only):

LaTeX	Description
\,	Thin space
\;	Medium space
\:	Thick space
\!	Negative thin space
\quad	Quad space
\qquad	Double quad space
\thinspace	Thin space (alias)

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Delimiter Sizing

These commands are recognized but ignored during parsing:

LaTeX	Description
\left( ... \right)	Auto-sizing parentheses
\big( ... \big)	Big parentheses
\Big( ... \Big)	Bigger parentheses
\bigg( ... \bigg)	Even bigger
\Bigg( ... \Bigg)	Largest

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Font Commands

Font styling commands wrap content and preserve it for LaTeX round-trip:

LaTeX	Description	Output Variable
\mathbf{E}	Bold	mathbf:E
\mathcal{L}	Calligraphic	mathcal:L
\mathrm{d}	Roman (upright)	mathrm:d
\mathit{x}	Italic	mathit:x
\mathsf{A}	Sans-serif	mathsf:A
\mathtt{x}	Typewriter	mathtt:x
\textbf{text}	Bold text	textbf:text
\boldsymbol{x}	Bold symbol	boldsymbol:x

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Text Mode

\text{some text}

Text within \text{} is treated as a single variable/token.

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Escaped Characters

LaTeX	Result
\{	Literal {
\}	Literal }
\\	Line break (in align)

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Usage Notes

Function Arguments

Functions can take arguments in several ways:

\sin{x}       % Recommended: braces
\sin(x)       % Also works: parentheses
\sin x        % Works with implicit multiplication enabled

Order of Operations

Standard mathematical precedence applies:

1. Parentheses and braces
2. Exponentiation (right-to-left)
3. Unary minus
4. Multiplication and division (left-to-right)
5. Addition and subtraction (left-to-right)
6. Comparisons

Complex Number Support

Use i for the imaginary unit:

3 + 4i
e^{i\pi}
\sqrt{-1}     % Returns i
\sin{1 + 2i} % Complex trigonometry

Textbook Notation Compatibility

The parser supports common textbook notation for copy-paste compatibility:

Function Power Notation:

\sin^2{x} + \cos^2{x}    % Pythagorean identity
\tan^3{\theta}           % Third power of tangent
\sin^{-1}{x}             % Power of -1 on sin

Multi-argument Function Calls:

f(x,y)                   % Function with multiple arguments
g(a,b,c)                 % Function with 3 arguments
\iint_{D} f(x,y) dx dy   % Double integral with function notation