How Mathematica does Unicode?

This page explains some tech detail about how Mathematica uses Unicode.

Mathematica supports Unicode, but does not use Unicode when saving to file. 〔➤see Unicode Basics: What's Character Set, Character Encoding, UTF-8?〕

Mathematica files use 7-bits ASCII only. http://www.wolfram.com/technology/nb/

How does it support Unicode if it uses only ASCII?

Mathematica's Named Characters \[Name]

Mathematica has a set of special characters with the syntax \[name]. For example:

Glyph	Syntax
é	\[EAcute]
É	\[CapitalEAcute]
α	\[Alpha]
Δ	\[CapitalDelta]
⊕	\[CirclePlus]
∵	\[Because]
∈	\[Element]
⇔	\[Equivalent]
ℝ	\[DoubleStruckCapitalR]

So, when you type \[Alpha], it is displayed as “α”. (All built-in symbols in Mathematica starts with capital letter.)

You can think of them as HTML's “named character entities”. 〔➤see Character Sets and Encoding in HTML〕 There are about 900 named chars. http://reference.wolfram.com/mathematica/guide/ListingOfNamedCharacters.html

Many of the named chars are also in Unicode, but not all. Similarly, many Math Symbols in Unicode are not in this list. Also, Unicode's Chinese chars, Arabic alphabets etc, are not in Mathematica's named chars.

Map Between Unicode and Named Chars

When you paste a Unicode char into Mathematica, Mathematica will try to interpret the Unicode as one of the named char.

So, for example, if you paste “α” (GREEK SMALL LETTER ALPHA; “U+x3b1”), it automatically becomes Mathematica's \[Alpha], and displayed as “α”.

Syntax for Arbitrary Unicode Char

For any Unicode that's not one of Mathematica's named char (such as Chinese chars), their syntax is this: \:xxxx, where the xxxx is Unicode's 4 digit hexidecimal representation of the char. For example, the Chinese char “水” (water), Unicode hex is “6c34”, in Mathematica is: \:6c34.

The above roughly summarize how Mathematica takes Unicode as input.

Some Named Chars has Built-in Meaning

Of the named chars, many has special meaning in Mathematica. For example, π \[Pi] is automatically considered identical to the built-in symbol Pi, which means the mathematical constant. (So, if you type \[Pi] or \:03c0, they are displayed as π with meaning of Pi.). Here's some examples of special meaning named chars.

Glyph	Mathematica's name	Unicode name	Unicode hexidecimal	Default Interpretation
≥	\[GreaterEqual]	GREATER-THAN OR EQUAL TO	2265	GreaterThan
π	\[Pi]	GREEK SMALL LETTER PI	03c0	Pi
∞	\[Infinity]	INFINITY	221e	Infinity
∫	\[Integral]	INTEGRAL	222b	Integrate
⋂	\[Intersection]	N-ARY INTERSECTION	22c2	Union
∑	\[Sum]	N-ARY SUMMATION	2211	Sum
√	\[Sqrt]	SQUARE ROOT	221a	Sqrt
⊕	\[CirclePlus]	CIRCLED PLUS	2295	CirclePlus

Note: it appears that it is possible to over-ride the default interpretation of named char to built-in symbol (function, constant), for all or some of the named char. (i haven't investigated on how yet.)

• http://reference.wolfram.com/mathematica/ref/MakeExpression.html
• http://reference.wolfram.com/mathematica/tutorial/Operators.html

Alias Shortcut for Named Chars

Some of the named char has one or more aliases for ease of input. For example, to enter α, you can type 【EscaEsc】 or 【EscalphaEsc】. Here's some examples:

Glyph	Common Alias
α	a
π	p
∞	inf
≤	<=
°	deg
Δ	D
∈	el
→	->

• http://reference.wolfram.com/mathematica/tutorial/Introduction-ListingOfNamedCharacters.html
• http://reference.wolfram.com/mathematica/guide/SpecialCharacters.html

Inputting Special Chars

You can input a special character by:

• Use one of the graphical palettes.
• Type Esc, then the char's alias name, then Esc again.
• Copy the Unicode char somewhere and pasting it in Mathematica.
• Type it like this: \[Name].
• Type the Unicode hexadecimal like this: \:xxxx