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.
Out[1]//FullForm= |
| |  |
| Out[2]= |  |
You can define a value for
.
Now
is not only recognized as an operator, but can also be evaluated.
| Out[4]= |  |
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
.
| Out[5]= |  |
Out[6]//FullForm= |
| |  |
| x \[name] y |  |
| \[name] x |  |
| \[Left name] x,y,... \[Right name] |  |
| x \[name] y | name[x, y] |
\ | name[x] |
| 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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| |  |
Some two-dimensional forms without built-in meanings.
Subscripts have no built-in meaning in
Mathematica.
Out[8]//InputForm= |
| |  |
Most superscripts are interpreted as powers by default.
Out[9]//InputForm= |
| |  |
A few special superscripts are not interpreted as powers.
Out[10]//InputForm= |
| |  |
Out[11]//InputForm= |
| |  |
y
y
y
y
x
x
x,y,...
