MATHEMATICA TUTORIAL

# 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.

 full names aliases EscscaEsc - EscsczEsc lowercase script letters EscscAEsc - EscscZEsc uppercase script letters 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.

DifferentialRoot automatically chooses the names for the function arguments.
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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 30Degree.

Note that , , and are all distinct from the ordinary letters (), (\[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.

 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.

 form alias full name ' (keyboard character) \[RawQuote] acute accent Esc \[Prime] acute accent ` (keyboard character) \[RawBackquote] grave accent Esc`Esc \[ReversePrime] grave accent . . (keyboard characters) umlaut or diaeresis ^ (keyboard character) \[RawWedge] circumflex or hat EscesciEsc \[EmptySmallCircle] ring . (keyboard character) \[RawDot] dot ~ (keyboard character) \[RawTilde] tilde _ (keyboard character) \[RawUnderscore] bar or macron EschcEsc \[Hacek] hacek or check EscbvEsc \[Breve] breve EscdbvEsc \[DownBreve] tie accent Esc \[DoublePrime] long umlaut EsccdEsc \[Cedilla] cedilla

Diacritical marks to add to characters.

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