Formula editor

A formula is typed as tokens, built into structures with the toolbar, and read as mathematics as you type. This page says how typing makes a formula, which characters the notation reads, and how to choose what a part of a formula means.

Tokens

What you type goes into tokens, and a token's first character says what it is:

• a letter starts a name: a capital or small Latin letter, a capital or small Greek one, or a modifier letter;
• a decimal digit starts a number;
• any other character starts an operator, such as a math symbol or an arrow.

Characters typed together stay in one token, whatever they are, and a space ends a token. So type a + b with spaces: a+b is one token, which reads as nothing. 2 x is 2 times x, drawn apart, while x2 is one name. Only a parenthesis stands alone, so f(x) is four tokens.

The toolbar changes the token at the caret: Identifier, Number, Operator and Text change what it is, Join joins the two tokens the caret is between, and Split splits the token the caret is in.

Structures

Fractions, roots and scripts come from the toolbar, never from a typed character, so ^ and _ are written as themselves. Fraction, Square root, Root, Superscript and Subscript put the structure at the caret, or around what is selected. Tab and Shift+Tab move between its slots. A superscript or a subscript goes on what comes just before it.

Characters the notation reads

Several characters look alike, and the notation reads one of each:

• 𝟎 and 𝟏 (U+1D7CE and U+1D7CF), the empty type and the unit type, not the double-struck 𝟘 and 𝟙, or the digits 0 and 1;
• 𝒰 (U+1D4B0), the universe;
• ℕ (U+2115), the natural numbers;
• →, which -> also writes, and ×, which * also writes.

A number it reads is written with the digits 0 to 9: other decimal digits start a number that reads as nothing. A name is a letter followed by letters, marks, digits, underscores and primes, such as x₁ or f′. It reads no minus yet: - is the hyphen-minus (dash punctuation), and − (U+2212) the minus sign, a math symbol.

Choosing what a part means

A formula can read more than one way: A + B is a sum of types, or of numbers. The line under the formula says what the part selected is, its role in what holds it, and how many other readings the formula has.

• ⌥↑, Alt+↑ off a Mac, selects the part around the caret, or around the part selected.
• ⌥↓ selects the part inside the part selected, and ⌥← and ⌥→ the part before and after it.
• Tab and Shift+Tab show the part's next reading and the one before, and the line says what each makes the part.
• ↵ chooses the reading shown.
• Esc goes back to the reading the formula had, and puts the caret back where the selection began.

A reading is chosen only of a complete formula: while something is missing, the line says to finish the formula first. An edit drops the reading chosen.

Typing the characters

For now, type a character with your system's own input, such as its character viewer or an input method, or copy it from Unicode. Commands that type them come later.