Letters and Letter-like Forms
Greek Letters
The complete collection of Greek letters in Mathematica.
You can use Greek letters as the names of symbols. The only Greek letter with a built-in meaning in
StandardForm is
, which
Mathematica takes to stand for the symbol
Pi.
Note that even though
on its own is assigned a built-in meaning, combinations such as
or
have no built-in meanings.
The Greek letters
and
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,
is different from the
operator
\[Element], and
is different from
or
\[Micro].
Some capital Greek letters such as
\[CapitalAlpha] look essentially the same as capital English letters.
Mathematica, however, treats them as different characters, and in
TraditionalForm it uses
\[CapitalBeta], for example, to denote the built-in function
Beta.
Following common convention, lowercase Greek letters are rendered slightly slanted in the standard fonts provided with
Mathematica, while capital Greek letters are unslanted. On Greek systems, however,
Mathematica 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
is rare, though it is used to denote the cascade hyperon particles, the grand canonical partition function, and regular language complexity. The capital upsilon
is also rare, though it is used to denote
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
is rare, except in astronomy.
The final sigma
is used for sigmas that appear at the ends of words in written Greek; it is not commonly used in technical notation.
The digamma
, koppa
, stigma
, and sampi
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
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
Mathematica kernel.
Script, gothic, and double-struck characters are, however, treated as fundamentally different from their ordinary forms. This means that even though a
C that is italic or a different size will be considered equivalent to an ordinary
C when fed to the kernel, a double-struck
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.
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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,
conventionally denotes the set of complex numbers, and
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
WeierstrassP.
| | |
| \[ScriptA] - \[ScriptZ] | EscscaEsc - EscsczEsc | lowercase script letters |
|
| EscscAEsc - EscscZEsc | uppercase script letters |
| \[GothicA] - \[GothicZ] | EscgoaEsc - EscgozEsc | lowercase gothic letters |
|
| EscgoAEsc - EscgoZEsc | uppercase gothic letters |
|
| EscdsaEsc - EscdszEsc | lowercase double-struck letters |
|
| EscdsAEsc - EscdsZEsc | uppercase double-struck letters |
|
| Esc$aEsc - Esc$zEsc | lowercase formal letters |
|
| Esc$AEsc - Esc$ZEsc | uppercase formal letters |
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.
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Formal symbols are
Protected, so they cannot be accidentally assigned a value.
Trying to modify a formal symbol fails.
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This means that expressions depending on formal symbols will not be accidentally modified.
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Specific values for formal symbols can be substituted using replacement rules.
Verify that the defining equations hold for cosine.
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Formal symbols can be temporarily modified inside a
Block because
Block clears all definitions associated with a symbol, including
Attributes.
Table works essentially like
Block, thus also allowing temporary changes.
Assign a temporary value to
.
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In most situations modifying formal symbols is not necessary. Since in
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
for
and
for
.
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It is possible to define custom typesetting rules for formal symbols.
Use coloring to highlight formal symbols.
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The formatting rules were attached to
MakeBoxes. Restore the original formatting.
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Hebrew Letters
Hebrew characters.
Hebrew characters are used in mathematics in the theory of transfinite sets;
is for example used to denote the total number of integers.
Units and Letter-like Mathematical Symbols
Units and letter-like mathematical symbols.
Mathematica treats
or
\[Degree] as the symbol
Degree, so that, for example,
is equivalent to
Degree.
Note that
,
, and
are all distinct from the ordinary letters
(
\[Mu]),
(
\[CapitalARing]), and
(
\[CapitalOSlash]).
Mathematica interprets
as
Infinity,
as
E, and both
and
as
I. The characters
,
, and
are provided as alternatives to the usual uppercase letters
E and
I.
and
are not by default assigned meanings in
StandardForm. You can therefore use
to represent a pi that will not automatically be treated as
Pi. In
TraditionalForm,
is interpreted as
EulerGamma.
Operators that look like letters.
is an operator while
,
, and
are ordinary symbols.
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Shapes, Icons, and Geometrical Constructs
Shapes.
Shapes are most often used as "dingbats" to emphasize pieces of text. But
Mathematica treats them as letter-like forms, and also allows them to appear in the names of symbols.
In addition to shapes such as
\[EmptySquare], there are characters such as
\[Square], which are treated by
Mathematica as operators rather than letter-like forms.
Icons.
You can use icon characters just like any other letter-like forms.
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Notation for geometrical constructs.
Since
Mathematica treats characters like
as letter-like forms, constructs like
are treated in
Mathematica 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.
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Extended Latin Letters
Mathematica 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
\[SZ] 
, used in German, and
\[Thorn] 
and
\[Eth] 
, used primarily in Old English.
You can make additional characters by explicitly adding diacritical marks yourself.
| char Ctrl+& mark Ctrl+Space | add a mark above a character |
| char Ctrl++ mark Ctrl+Space | add a mark below a character |
Adding marks above and below characters.
Diacritical marks to add to characters.
