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# Operators without Built-in Meanings

When you enter a piece of input such as , Mathematica first recognizes the as an operator and constructs the expression Plus, then uses the built-in rules for Plus to evaluate the expression and get the result .
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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In StandardForm, prints as an infix operator.
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You can define a value for .
Now is not only recognized as an operator, but can also be evaluated.
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 xy CirclePlus[x,y] xy TildeTilde[x,y] xy Therefore[x,y] xy 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.
is displayed as .
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It corresponds to the function Congruent.
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 x \[name] y \[name] x \[Left name] x,y,... \[Right name]
 x \[name] y name[x, y] \ name[x] \[Leftname] x,y,... \[Right name] 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. "Operator Input Forms" lists all the operators recognized by Mathematica, in order of their precedence.
The operators and have definite precedences—with higher than .
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 xy Subscript[x,y] x+ SubPlus[x] x- SubMinus[x] x* SubStar[x] x+ SuperPlus[x] x- SuperMinus[x] x* SuperStar[x] x† SuperDagger[x] Overscript[x,y] Underscript[x,y] OverBar[x] OverVector[x] OverTilde[x] OverHat[x] OverDot[x] UnderBar[x]

Some two-dimensional forms without built-in meanings.

Subscripts have no built-in meaning in Mathematica.
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Most superscripts are interpreted as powers by default.
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A few special superscripts are not interpreted as powers.
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Bar and hat are interpreted as OverBar and OverHat.
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