MATHEMATICA TUTORIAL

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[2, 2], 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

In[3]:=

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, 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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x_y	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]