Syntax Reference

Tungsten uses a custom parser that supports a mix of standard LaTeX syntax and intuitive shorthand common in programming or handwritten math.

Variables and Constant## Quick Reference Cheatsheet

Category	Input Example	Notes
Arithmetic	1 + 2 * 3	Standard order of operations applies
Exponents	x^2, e^{x+1}	Use {} to group complex exponents.
Fractions	\frac{a}{b}, a/b	Both LaTeX and inline division are supported.
Grouping	(a + b)c	Parentheses () define scope.
Functions	\sin(x), f(x), \ln x	Standard function calls.
Variables	x, vel, x1	Must start with a letter.
Greek	\alpha, \beta, \pi	Standard LaTeX commands.
Matrices	\begin{pmatrix}...\end{pmatrix}	Supports p, b, and v matrix types.
Vectors	\vec{v}, \mathbf{v}, \begin{pmatrix}...\end{pmatrix}	Symbolic vector notation or as row or column matrix.
Derivatives	\frac{d}{dx} x^2, f', \dot{f}	Multiple notations for differentiation.
Integrals	\int_{0}^{\infty} e^{-x} dx	Definite and indefinite integrals.

1. Variables and Constants

Tungsten uses strict tokenization rules to distinguish between variables, numbers, and commands.

Variable Naming

• Structure: Variable names must begin with a letter (A-Z, a-z).
• Alphanumeric: After the first letter, variables may contain digits or underscores.
  • ✅ Valid: x, y_2, velocity, Area51
  • ❌ Invalid: 1x (starts with digit), _x (starts with underscore)
• Case Sensitivity: x and X are treated as distinct variables.

Greek Letters

Tungsten recognizes standard LaTeX commands for Greek letters. These are treated as symbolic entities distinct from standard variables.

• Syntax: \alpha, \beta, \Gamma, \omega, etc.
• Usage: They can be used anywhere a variable is used: 2\pi, \sin(\theta).

Constants

Certain symbols are reserved or automatically recognized as mathematical constants depending on the backend:

• \pi or pi
• e (Euler's number)
• \infty (Infinity)

2. Operators and Precedence

The parser adheres to standard mathematical precedence rules. When operators share the same precedence, associativity determines the order of evaluation.

Precedence	Operator	Description	Associativity	Syntax Variants
3 (Highest)	^	Exponentiation	Right	x^2, x^{y+1}
2	*	Multiplication	Left	*, \cdot, \times
2	/	Division	Left	/, \frac{num}{den}
1	+	Addition	Left	+
1	-	Subtraction	Left	-
0 (Lowest)	=	Equality	None	=, ==, &=

Important Notes on Operators:

• Right Associativity (^): 2^3^4 is parsed as 2^(3^4), not (2^3)^4.
• Synonyms: The parser treats \cdot (dot) and \times (cross) identically to * in scalar arithmetic contexts. However, in Linear Algebra contexts, they denote Dot Product and Cross Product respectively.

Implicit Multiplication

You can often omit the multiplication operator, just like in handwritten math. The parser infers multiplication in the following cases:

• Number + Variable: 2x becomes 2 * x
• Variable + Variable: x y becomes x * y (Note: xy is parsed as a single variable named "xy". Use a space to separate them.)
• Group + Variable: (a+b)x becomes (a+b) * x
• Number + Greek: 2\pi becomes 2 * \pi
• Function Chains: \sin(x)\cos(y) becomes \sin(x) * \cos(y)

3. Functions and Grouping

Function Syntax

• Standard Calls: name(arg1, arg2)
  • Example: f(x), sin(x)
• LaTeX Style Calls: \command{arg}
  • Example: \sqrt{x}, \frac{1}{2}
• Parenthesis-less Calls: For common log/trig functions, parentheses can sometimes be omitted if the argument is a single token.
  • \ln x is valid.
  • \sin \theta is valid.
  • \cos(x + 1) is valid

Grouping Symbols

• Parentheses (): Used for standard mathematical grouping and function arguments.
• Braces {}: Used strictly for LaTeX command arguments (e.g., x^{2}, \frac{a}{b}).
• Brackets []: Often used for defining lists or specific matrix notations, though () is preferred for arithmetic precedence.

4. Syntax Limitations and Edge Cases

To ensure the parser behaves predictably, certain inputs that might look "okay" to a human are strictly invalid.

1. Decimal Formatting

Numbers must have a leading digit before the decimal point.

• ✅ Correct: 0.5
• ❌ Incorrect: .5 (This will fail to parse as a number)

2. Whitespace and Implicit Multiplication

As noted in section 3, whitespace is semantically significant for variables.

• xy $\rightarrow$ Variable named "xy"
• x y $\rightarrow$ Multiplication x * y

3. LaTeX Environment Closure

All LaTeX environments must be perfectly balanced.

• ❌ \begin{pmatrix} 1 & 2 (Missing end tag)
• ❌ \frac{1}{2 (Unmatched brace)

4. Argument Bracing

LaTeX commands like \frac and \sqrt expect arguments in braces {}.

• ✅ x^{10}
• ⚠️ x^10 (Parses as (x^1) * 0 like it would in standard LaTeX)
• ❌ \frac 1 2 (Arguments must be braced: \frac{1}{2})

5. Multi-line Inputs

For systems of equations or similar you are able to use the standard LaTeX-construction of &= and \\. &= is parsed as = and \\ is parsed as beginning a new expression.

x + y &= 1 \\
x - y &= 2

You are also able to use semi-colons ; between expressions:

x + y = 1;
x - y = 2

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Found syntax that should work but doesn't? The world of mathematical notation is vast. If you encounter valid mathematical notation that Tungsten fails to parse, please file a bug report or feature request.