2.9.15 Operators without Built-in MeaningsWhen you enter a piece of input such as 2 + 2, Mathematica first recognizes the + as an operator and constructs the expression Plus[2, 2], then uses the built-in rules for Plus to evaluate the expression and get the result 4. But not all operators recognized by Mathematica are associated with functions that have built-in meanings. Mathematica also supports several hundred additional operators that can be used in constructing expressions, but for which no evaluation rules are initially defined. You can use these operators as a way to build up your own notation within the Mathematica language. The  is recognized as an infix operator, but has no predefined value. | |
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2 3//FullForm
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In StandardForm,  prints as an infix operator. | |
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23
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You can define a value for  . | |
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x_ y_ := Mod[x + y, 2]
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Now  is not only recognized as an operator, but can also be evaluated. | |
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2 3
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x  y | CirclePlus[x, y] | x  y | TildeTilde[x, y] | x  y | Therefore[x, y] | x  y | LeftRightArrow[x, y] |  x | Del[x] |  x | Square[x] |  x,y, ...  | AngleBracket[x, y, ... ] |
A few Mathematica operators corresponding to functions without predefined values. Mathematica follows the general convention that the function associated with a particular operator should have the same name as the special character that represents that operator. \[Congruent] is displayed as  . | |
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| It corresponds to the function Congruent. | |
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| x \[name] y | name[x, y] | | \[name] x | name[x] | | \[Leftname] x, y, ... \[Rightname] | name[x, y, ... ] |
The conventional correspondence in Mathematica between operator names and function names. You should realize that even though the functions CirclePlus and CircleTimes do not have built-in evaluation rules, the operators  and  do have built-in precedences. Section A.2.7 lists all the operators recognized by Mathematica, in order of their precedence.
 | Subscript[x, y] |  | SubPlus[x] |  | SubMinus[x] |  | SubStar[x] |  | SuperPlus[x] |  | SuperMinus[x] |  | SuperStar[x] |  | SuperDagger[x] |
|  | Overscript[x, y] |  | Underscript[x, y] |  | OverBar[x] |  | OverVector[x] |  | OverTilde[x] |  | OverHat[x] |  | OverDot[x] |  | UnderBar[x] |
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Some two-dimensional forms without built-in meanings. | Subscripts have no built-in meaning in Mathematica. | |
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{x} . XMLElement[sub, {}, {2}]+{y} . XMLElement[sub, {}, {2}]//InputForm
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| Most superscripts are however interpreted as powers by default. | |
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| A few special superscripts are not interpreted as powers. | |
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x†+y+//InputForm
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| Bar and hat are interpreted as OverBar and OverHat. | |
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x_+y^//InputForm
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and 
have definite precedences--with 
higher than 
. 
y 
