What does @#(%=<[!} et cetera mean? Mathematica has a very extensive set of characters used as its syntax. I will try to list most (all?) of them here. Non-standard characters If the symbol appears to be a non-standard character one can wrap the symbol in quotes and perform FullForm on it to get the name of the symbol. Example: gives: "\[Function]" Brackets These syntax elements all appear in pairs: -
(...) Circumfix. Used to group expressions such that it has higher precedence, not used to enclose arguments of a function -
{...} List doc. Circumfix. Used to describe lists of any depth, e.g.: {a,b,...} . Known as arrays, vectors, matrices, tensors, in other languages -
[...] Circumfix. Used to enclose arguments of a function, e.g.: f[a] -
[[...]] Part doc. Post/circumfix. a[[b]] = Part[a,b] . Used to extract parts of an expression. Can also be typeset as a single character: \[LeftDoubleBracket] and \[RightDoubleBracket] , and can also be typeset as a subscript -
<|...|> Association doc. Circumfix. Used to describe a list of key-value pairs. Known as associative arrays, dictionaries, hashmaps. Can also be typeset as a single character: \[LeftAssociation] and \[RightAssociation] . -
(*...*) Circumfix. Used for making comments in code, can be anywhere in the code except inside strings, then it will be taken literal. -
<*...*> TemplateExpression doc. Circumfix. Expression inside a string template. -
\[LeftFloor]...\[RightFloor] Floor doc. Circumfix. Mathematical Floor function. \[LeftFloor]a\[RightFloor] = Floor[a] . Can be typeset using \[LeftFloor] and \[RightFloor] . -
\[LeftCeiling]...\[RightCeiling] Ceiling doc. Circumfix. Mathematical Ceiling function. \[LeftCeiling]a\[RightCeiling] = Ceiling[a] . Can be typeset using \[LeftCeiling] and \[RightCeiling] . Applying functions -
@ doc. Infix. Used to apply a function to a single argument: f@x = f[x] (related to Prefix doc) -
// doc. Infix. Used to apply a function to a single argument: x // f = f[x] (related to Postfix doc) -
~ Infix. Works on two arguments: a ~ f ~ b = f[a,b] (related to Infix doc) -
@* Composition doc. Infix. f@*g = Composition[f,g] Used to compose two or more functions. @* is the infix operator form of Composition -
/* RightComposition doc. Infix. f/*g = RightComposition[f,g] Used to compose two or more functions. /* in the infix operator form of RightComposition -
/@ Map doc. Infix. f/@ a = Map[f,a] Used to apply a function to all elements of a -
//@ MapAll doc. Infix. f//@ a = MapAll[f,a] Used to apply a function to every subexpression of a -
@@ Apply doc. Infix. f @@ a = Apply[f,a] Used to replace the head of a by f -
@@@ Apply doc. Infix. f @@@ a = Apply[f,a,{1}] Used to replace the heads at level 1 of a by f. Pure function, slots, and slot sequences -
& Function doc. Used to define a pure function where the arguments are given by #1 (short: # ), #2 , #3 , et cetera. Also known as lambda function, anonymous functions, function literal, lambda abstraction... -
# Slot doc. represents the first argument supplied to a pure function -
#1 , #2 , #n Slot doc. represents the nth argument supplied to a pure function -
#0 Slot doc. represents the pure function itself. -
#name Slot doc. represents the value associated with the key name in an association in the first argument -
## SlotSequence doc. represents a sequence of all the arguments -
##n SlotSequence doc. represents a sequence of arguments starting from the nth -
\[Function] Function doc. Infix operator of Function. x \[Function] body = Function[x,body] Assignments -
= Set doc. Infix. a=b = Set[a,b] -
:= SetDelayed doc. Infix. a:=b = SetDelayed[a,b] -
=. Unset doc. Postfix. a=. = Unset[a] -
^= UpSet doc. Infix. a[b]^=c = Upset[a[b],c] -
^:= UpsetDelayed doc. Infix. a[b]^:=c = UpSetDelayed[a[b], c] -
/: = TagSet doc. Compound infix. a /: b[a] = c = TagSet[a, b[a], c] -
/: := TagSetDelayed doc. Compound infix. a /: b[a] := c = TagSetDelayed[a, b[a], c] -
/: =. TagUnset doc. Compound infix. a /: b[a] =. = TagUnset[a, b[a]] -
+= AddTo doc. Infix. a+=b = AddTo[a, b] Adds b to a and stores the value in a. -
-= SubtractFrom doc. Infix. a-=b = SubtractFrom[a, b] Subtracts b from a and stores the value in a. -
*= TimesBy doc. Infix. a*=b = TimesBy[a, b] Multiplies a by b and stores the value in a. -
/= DivideBy doc. Infix. a/=b = DivideBy[a,b] Divides a by b and stores the value in a. -
//= ApplyTo doc. Infix. a//=f = ApplyTo[a,f] . Applies function f to a and stores the value in a. -
++ used as a prefix operator is PreIncrement doc. ++a = PreIncrement[a] Adds 1 to a and stores the value in a, returns the new a -
++ used as a postfix operator is Increment doc. a++ = Increment[a] Adds 1 to a and stores the value in a, returns the old a -
-- used as a prefix operator is PreDecrement doc. --a = PreDecrement[a] Subtracts 1 from a and stores the value in a, returns the new a -
-- used as a postfix operator is Decrement doc. a-- = Decrement[a] Subtracts 1 from a and stores the value in a, returns the old a Number related -
*^ Infix. Equivalent to *10^ sometimes 'e' in other languages. 3*^4 = 30000 - ` related to Precision doc. Postfix. Define number to be a machine precision number. It denotes context when it is written between symbols. Also appears in pairs inside strings for TemplateSlot doc where they denote an argument
- `
n related to Precision doc. Infix. Defines number to have precision n. It denotes context when it is written between symbols - ``
n related to Accuracy doc. Infix. Supposed to be written between 2 numbers. Defines number to have accuracy n -
^^ related to BaseForm doc. Infix. 3^^1212 represents 1212 written in base 3. Up to base 36 can be specified in this notation (using letters a through z, in either lower of upper case, to denote 10 through 35). Use FromDigits doc for higher bases. Base conversion is done using IntegerDigits doc or RealDigits doc -
\[ImplicitPlus] ImplicitPlus doc. Infix. An invisible character used for e.g. fractions: 5\[ImplicitPlus](3/4) = Plus[5,3/4] = 23/4 where 3/4 is then typed as a fraction Relational operators -
== Equal doc. Infix. a==b = Equal[a,b] . Used to test if a and b are equal. Also used to define an equation -
\[Equal] Equal doc. Infix. a==b = Equal[a,b] . Used to test if a and b are equal -
!= UnEqual doc. Infix a!=b = UnEqual[a,b] . Used to test if a and b are not equal -
? UnEqual doc. Infix a!=b = UnEqual[a,b] . Used to test if a and b are not equal -
> Greater doc. Infix. a>b = Greater[a,b] . Used to test if a is greater than b -
< Less doc. Infix. a<b = Less[a,b] . Used to test if a is less than b -
>= GreaterEqual doc. Infix. a>=b = GreaterEqual[a,b] . Used to test if a is great than or equal to b -
<= LessEqual doc. Infix. a<=b = LessEqual[a,b] . Used to test if a is less than or equal to b -
=== SameQ doc. Infix. a===b = SameQ[a,b] . Used to test if a and b are identical -
=!= UnsameQ doc. Infix. a=!=b = UnsameQ[a,b] . Used to test if a and b are not identical Note: All the above operator can remain unevaluated, except for SameQ and UnsameQ, these always evaluate to either True or False. Even when a or b is symbolic. All operator can be used multiple times in a row e.g.: a == b == c (all have to be equal) or a > b > c (strictly decreasing numbers) or a != b != c (all unequal). The functions have arbitrary arity, e.g. Equal[] = True . -
\[Element] Element doc. Infix. a \[Element] b = Element[a,b] . Asserts that a is an element of b Logical operators -
&& , \[And] And doc. Infix. Logical And operator. a && b = a \[And] b = And[a,b] Executes in order and has lazy evaluation -
|| , \[Or] Or doc. Infix. Logical Or operator. a || b = a \[Or] b = Or[a,b] Executes in order and has lazy evaluation -
\[Nand] Nand doc. Infix. Logical Nand operator a \[Nand] b = Nand[a,b] Executes in order and has lazy evaluation -
\[Nor] Nor doc. Infix. Logical Nor operator a \[Nor] b = Nor[a,b] Executes in order and has lazy evaluation -
! Not doc. Prefix. Logical negation !a = Not[a] . Not to be confused with Factorial doc (postfix operator) -
¬ Not doc. Prefix. Logical negation ¬a = Not[a] . -
\[Xor] Xor doc. Infix. Logical Xor operator a \[Xor] b = Xor[a,b] -
\[Implies] Implies doc. Infix. Logical implication. a \[Implies] b = Implied[a,b] -
\[Equivalent] Equivalent doc. Infix. Logical equivalence testing. a \[Equivalent] b = Equivalent[a,b] Note: And, Or, Nand, Nor, and Xor have arbitrary arity. Patterns and rules -
_ Blank doc. Prefix. _ = Blank[] -
_a Blank doc. Prefix. _a = Blank[a] -
__ BlankSequence doc. Prefix. __ = BlankSequence[] -
__a BlankSequence doc. Prefix. __a = BlankSequence[a] -
___ BlankNullSequence doc. Prefix. ___ = BlankNullSequence[] -
___a BlankNullSequence doc. Prefix. ___a = BlankNullSequence[a] -
a_ Pattern doc. Postfix/infix. a_ = Pattern[a, Blank[]] -
a:_ Pattern doc. Postfix/infix. a:_ = Pattern[a, Blank[]] -
a__ Pattern doc. Postfix/infix. a__ = Pattern[a, BlankSequence[]] -
a:__ Pattern doc. Postfix/infix. a:__ = Pattern[a, BlankSequence[]] -
a___ Pattern doc. Postfix/infix. a__ = Pattern[a, BlankNullSequence[]] -
a:___ Pattern doc. Postfix/infix. a:__ = Pattern[a, BlankNullSequence[]] -
_. Optional doc. Postfix. _. = Optional[Blank[]] also related to Default doc -
_:a Optional doc. Postfix. _:a = Optional[Blank[],a] also related to Default doc -
__. Optional doc. Postfix. __. = Optional[BlankSequence[]] also related to Default doc -
__:a Optional doc. Postfix. __:a = Optional[BlankSequence[],a] also related to Default doc -
___. Optional doc. Postfix. ___. = Optional[BlankNullSequence[]] also related to Default doc -
___:a Optional doc. Postfix. ___:a = Optional[BlankNullSequence[],a] also related to Default doc -
/; Condition doc. Infix. a /; b = Condition[a, b] -
? PatternTest doc. Infix. a ? b = PatternTest[a,b] -
-> Rule doc. Infix. a -> b = Rule[a,b] -
\[Rule] Rule doc. Infix. a \[Rule] b = Rule[a,b] -
:> RuleDelayed doc. Infix. a :> b = RuleDelayed[a,b] -
\[RuleDelayed] RuleDelayed doc. Infix. a \[RuleDelayed] b = RuleDelayed[a,b] -
/. ReplaceAll doc. Infix. a /. b = ReplaceAll[a, b] -
//. ReplaceRepeated doc. Infix. a //. b = ReplaceRepeated[a,b] -
.. Repeated doc. Postfix. a.. = Repeated[a] -
... RepeatedNull doc. Postfix. a... = RepeatedNull[a] -
| Alternatives doc. Infix. a | b = Alternatives[a, b] . Not to be confused with || Or doc String related -
<> StringJoin doc. Infix. a<>b = StringJoin[a,b] -
~~ StringExpression doc. Infix. a~~b = StringExpression[a,b] Note: both have arbitrary arity. Graph related -
<-> UndirectedEdge doc. Infix. a<->b = UndirectedEdge[a,b] -
\[UndirectedEdge] UndirectedEdge doc. Infix. a\[UndirectedEdge]b = UndirectedEdge[a,b] -
\[DirectedEdge] DirectedEdge doc. Infix. a\[DirectedEdge]b = DirectedEdge[a,b] Other -
\[Application] Application doc a\[Application]b Performs Application[a,b]. -
. Dot doc a.b Performs the dot product of a and b -
, Used to separate arguments in a function call, e.g.: f[a,b] -
% Out doc. % = Out[$Line - 1] = Out[] . Gives the last result generated -
%% Out doc. %% = Out[-2] . Gives the penultimate result -
%..% (k repetitions of %) Out doc. %...% = Out[-k] . Gives the k-th last result -
%n Out doc. Gives the result of line n -
\[PartialD] D doc. Postfix. Use in combination with a subscript to denote a partial derivate -
\[DifferentialD] Integrate doc. Compound match fix. \[Integral]a\[DifferentialD]b = Integrate[f,b] -
! as a postfix operator means Factorial doc a! = Factorial[a] . Mathematical factorial function -
!! as a postfix operator means Factorial2 doc a!! = Factorial2[a] . Mathematical double factorial function -
; CompoundExpression doc. Infix. a=1;a=2 = CompoundExpression[a=1,b=2] Though it might look like a postfix operator, it is not: a=1;a=2; = CompoundExpression[a=1,b=2,Null] -
;; Span doc. Infix. a ;; b = Span[a,b] and a ;; b ;; c= Span[a,b,c] Note that more than 2 infix operator in a row will give (most likely) unexpected results -
:: MessageName doc. Infix. a::b = MessageName[a,b] -
? Information doc. Prefix. ?a = Information[f, LongForm -> False] . Print some information about symbol a -
?? Information doc. Prefix. ??a = Information[f] . Print information about symbol a -
<< Get doc. Prefix. << a = Get["a"] . Reads in file a, evaluating each expression in it and returning the last one. Not to be confused with left bit shift operators in other languages (BitShiftLeft doc) -
>> Putt doc. Infix. a >> b = Put[a,b] . Write a to file b. Not to be confused with right bit shift operators in other languages (BitShiftRight doc) -
>>> PutAppend doc. Infix. a >>> b = PutAppend[a,b] . Appends a to file b. In case some symbol(s) is(are) missing, let me know! |
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