This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 2.8.15 Operators without Built-in Meanings When 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. In[1]:= Out[1]//FullForm= In StandardForm, prints as an infix operator. In[2]:= Out[2]= You can define a value for . In[3]:= x_ y_ := Mod[x + y, 2] Now is not only recognized as an operator, but can also be evaluated. In[4]:= 2 3 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. \[Congruent] is displayed as . In[5]:= x \[Congruent] y Out[5]= It corresponds to the function Congruent. In[6]:= FullForm[%] Out[6]//FullForm= 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. SectionÂ A.2.7 lists all the operators recognized by Mathematica, in order of their precedence. The operators and have definite precedenceswith higher than . In[7]:= x y z // FullForm Out[7]//FullForm= Some two-dimensional forms without built-in meanings. Subscripts have no built-in meaning in Mathematica. In[8]:= Out[8]//InputForm= Most superscripts are however interpreted as powers by default. In[9]:= Out[9]//InputForm= A few special superscripts are not interpreted as powers. In[10]:= Out[10]//InputForm= Bar and hat are interpreted as OverBar and OverHat. In[11]:= Out[11]//InputForm=