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.
is recognized as an infix operator, but has no predefined value.
You can define a value for
is not only recognized as an operator, but can also be evaluated.
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
|x \[name] y||name[x, y]|
|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.
have definite precedences—with
Some two-dimensional forms without built-in meanings.
Subscripts have no built-in meaning in Mathematica
Most superscripts are interpreted as powers by default.
A few special superscripts are not interpreted as powers.