Letters and Letter-like Forms

Greek Letters

The complete collection of Greek letters in the Wolfram Language.

You can use Greek letters as the names of symbols. The only Greek letter with a built-in meaning in (RefLink[StandardForm, paclet:ref/StandardForm]) is π, which the Wolfram Language takes to stand for the symbol (RefLink[Pi, paclet:ref/Pi]).

Note that even though π on its own is assigned a built-in meaning, combinations such as π2 or xπ have no built-in meanings.

The Greek letters Σ and Π look very much like the operators for sum and product. But as discussed above, these operators are different characters, entered as ∖[Sum] and ∖[Product], respectively.

Similarly, ϵ is different from the ∈ operator ∖[Element], and μ is different from µ or ∖[Micro].

Some capital Greek letters such as ∖[CapitalAlpha] look essentially the same as capital English letters. The Wolfram Language, however, treats them as different characters, and in (RefLink[TraditionalForm, paclet:ref/TraditionalForm]) it uses ∖[CapitalBeta], for example, to denote the built-in function (RefLink[Beta, paclet:ref/Beta]).

Following common convention, lowercase Greek letters are rendered slightly slanted in the standard fonts provided with the Wolfram System, while capital Greek letters are unslanted. On Greek systems, however, the Wolfram System will render all Greek letters unslanted so that standard Greek fonts can be used.

Almost all Greek letters that do not look similar to English letters are widely used in science and mathematics. The capital xi Ξ is rare, though it is used to denote the cascade hyperon particles, the grand canonical partition function, and regular language complexity. The capital upsilon Υ is also rare, though it is used to denote b(OverBar[b]) particles, as well as the vernal equinox.

Curly Greek letters are often assumed to have different meanings from their ordinary counterparts. Indeed, in pure mathematics a single formula can sometimes contain both curly and ordinary forms of a particular letter. The curly pi ϖ is rare, except in astronomy.

The final sigma ς is used for sigmas that appear at the ends of words in written Greek; it is not commonly used in technical notation.

The digamma ϝ, koppa ϟ, stigma ϛ, and sampi ϡ are archaic Greek letters. These letters provide a convenient extension to the usual set of Greek letters. They are sometimes needed in making correspondences with English letters. The digamma corresponds to an English w, and koppa to an English q. Digamma is occasionally used to denote the digamma function (RefLink[PolyGamma, paclet:ref/PolyGamma])[x].

Variants of English Letters

Some commonly used variants of English letters.

By using menu items in the notebook front end, you can make changes in the font and style of ordinary text. However, such changes are usually discarded whenever you send input to the Wolfram Language kernel.

Script, gothic, and double-struck characters are, however, treated as fundamentally different from their ordinary forms. This means that even though a (RefLink[C, paclet:ref/C]) that is italic or a different size will be considered equivalent to an ordinary (RefLink[C, paclet:ref/C]) when fed to the kernel, a double-struck ℂ will not.

Different styles and sizes of C are treated as the same by the kernel. But gothic and double-struck characters are treated as different:

C+C+C+ℭ+ℂ

In standard mathematical notation, capital script and gothic letters are sometimes used interchangeably. The double-struck letters, sometimes called blackboard or openface letters, are conventionally used to denote specific sets. Thus, for example, ℂ conventionally denotes the set of complex numbers, and ℤ the set of integers.

Dotless i and j are not usually taken to be different in meaning from ordinary i and j; they are simply used when overscripts are being placed on the ordinary characters.

∖[WeierstrassP] is a notation specifically used for the Weierstrass P function (RefLink[WeierstrassP, paclet:ref/WeierstrassP]).

Complete alphabets of variant English letters.

Formal Symbols

Symbols represented by formal letters, or formal symbols, appear in the output of certain functions. They are indicated by gray dots above and below the English letter.

(RefLink[DifferentialRoot, paclet:ref/DifferentialRoot]) automatically chooses the names for the function arguments:

root=DifferentialRootReduce[Cos]

Formal symbols are (RefLink[Protected, paclet:ref/Protected]), so they cannot be accidentally assigned a value.

Trying to modify a formal symbol fails:

\[FormalY]=0

\[FormalY]

This means that expressions depending on formal symbols will not be accidentally modified:

root[[1,2]]

Specific values for formal symbols can be substituted using replacement rules.

Verify that the defining equations hold for cosine:

root[[1,2]]/.\[FormalY]->Cos

Formal symbols can be temporarily modified inside a (RefLink[Block, paclet:ref/Block]) because (RefLink[Block, paclet:ref/Block]) clears all definitions associated with a symbol, including (RefLink[Attributes, paclet:ref/Attributes]). (RefLink[Table, paclet:ref/Table]) works essentially like (RefLink[Block, paclet:ref/Block]), thus also allowing temporary changes.

Assign a temporary value to \[FormalY]:

Block[{\[FormalY]=Cos},root[[1,2]]]

In most situations modifying formal symbols is not necessary. Since in (RefLink[DifferentialRoot, paclet:ref/DifferentialRoot]) formal symbols are used as names for the formal parameters of a function, the function should simply be evaluated for the actual values of arguments.

Evaluating the function substitutes x for \[FormalX] and y for \[FormalY]:

root[[1]][y,x]

It is possible to define custom typesetting rules for formal symbols.

Use coloring to highlight formal symbols:

MakeBoxes[\[FormalX],_]:=TagBox["x",\[FormalX]&,AutoDelete->True,BaseStyle->{FontColor->RGBColor[.6,.4,.2],ShowSyntaxStyles->False}]
MakeBoxes[\[FormalY],_]:=TagBox["y",\[FormalY]&,AutoDelete->True,BaseStyle->{FontColor->RGBColor[.6,.4,.2],ShowSyntaxStyles->False}]

root

The formatting rules were attached to (RefLink[MakeBoxes, paclet:ref/MakeBoxes]). Restore the original formatting:

FormatValues@MakeBoxes={};

root

Hebrew Letters

Hebrew characters.

Hebrew characters are used in mathematics in the theory of transfinite sets; (Subscript[ℵ, 0]) is for example used to denote the total number of integers.

Units and Letter-like Mathematical Symbols

Units and letter-like mathematical symbols.

The Wolfram Language treats ° or (RefLink[\[Degree], paclet:ref/character/Degree]) as the symbol (RefLink[Degree, paclet:ref/Degree]), so that, for example, 30° is equivalent to 30(RefLink[Degree, paclet:ref/Degree]).

Note that µ, Å, and ∅ are all distinct from the ordinary letters μ ((RefLink[\[Mu], paclet:ref/character/Mu])), Å ((RefLink[\[CapitalARing], paclet:ref/character/CapitalARing])), and Ø ((RefLink[\[CapitalOSlash], paclet:ref/character/CapitalOSlash])).

The Wolfram Language interprets ∞ as (RefLink[Infinity, paclet:ref/Infinity]), e as (RefLink[E, paclet:ref/E]), and both i and j as (RefLink[I, paclet:ref/I]). The characters e, i, and j are provided as alternatives to the usual uppercase letters (RefLink[E, paclet:ref/E]) and (RefLink[I, paclet:ref/I]).

ℼ and ℽ are not by default assigned meanings in (RefLink[StandardForm, paclet:ref/StandardForm]). You can therefore use ℼ to represent a pi that will not automatically be treated as (RefLink[Pi, paclet:ref/Pi]). In (RefLink[TraditionalForm, paclet:ref/TraditionalForm]), ℽ is interpreted as (RefLink[EulerGamma, paclet:ref/EulerGamma]).

Operators that look like letters.

∇ is an operator while ℏ, °, and ¥ are ordinary symbols:

{∇ f,ℏ^2,45°,5000¥}//FullForm

Shapes, Icons, and Geometrical Constructs

Shapes.

Shapes are most often used as "dingbats" to emphasize pieces of text. But the Wolfram Language treats them as letter-like forms, and also allows them to appear in the names of symbols.

In addition to shapes such as (RefLink[\[EmptySquare], paclet:ref/character/EmptySquare]), there are characters such as (RefLink[\[Square], paclet:ref/character/Square]), which are treated by the Wolfram Language as operators rather than letter-like forms.

Icons.

You can use icon characters just like any other letter-like forms:

Expand[(☺+🐺)^4]

Notation for geometrical constructs.

Since the Wolfram Language treats characters like ∠ as letter-like forms, constructs like ∠BC are treated in the Wolfram Language as single symbols.

Textual Elements

Characters used for punctuation and annotation.

Other characters used in text.

Characters used in building sequences and arrays.

The under and over braces grow to enclose the whole expression:

Underoverscript[Expand[(1+x)^4],⏟,⏞]

Extended Latin Letters

The Wolfram Language supports all the characters commonly used in Western European languages based on Latin scripts.

Variants of English letters.

Most of the characters shown are formed by adding diacritical marks to ordinary English letters. Exceptions include (RefLink[\[SZ], paclet:ref/character/SZ]) ß, used in German, and (RefLink[\[Thorn], paclet:ref/character/Thorn]) þ and (RefLink[\[Eth], paclet:ref/character/Eth]) ð, used primarily in Old English.

You can make additional characters by explicitly adding diacritical marks yourself.

Adding marks above and below characters.

Diacritical marks to add to characters.