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1.10.8 Other Mathematical Notation

Mathematica supports an extremely wide range of mathematical notation, although often it does not assign a pre-defined meaning to it. Thus, for example, you can enter an expression such as x y, but Mathematica will not initially make any assumption about what you mean by .

Mathematica knows that is an operator, but it does not initially assign any specific meaning to it.

In[1]:= {17 CirclePlus 5, 8 CirclePlus 3}


This gives Mathematica a definition for what the operator does.

In[2]:= x_ CirclePlus y_ := Mod[x + y, 2]

Now Mathematica can evaluate operations.

In[3]:= {17 CirclePlus 5, 8 CirclePlus 3}


A few of the operators whose input is supported by Mathematica.

Mathematica assigns built-in meanings to and , but not to or .

In[4]:= {3 GreaterEqual 4, 3 GreaterSlantEqual 4, 3 GreaterTilde 4, 3 GreaterGreater 4}


There are some forms which look like characters on a standard keyboard, but which are interpreted in a different way by Mathematica. Thus, for example, \[Backslash] or AliasIndicator\AliasIndicator displays as \ but is not interpreted in the same way as a \ typed directly on the keyboard.

The and characters used here are different from the \ and ^ you would type directly on a keyboard.

In[5]:= {a AliasIndicator\AliasIndicator b, a AliasIndicator^AliasIndicator b}


Most operators work like and go in between their operands. But some operators can go in other places. Thus, for example, AliasIndicator<AliasIndicator and AliasIndicator>AliasIndicator or \[LeftAngleBracket] and \[RightAngleBracket] are effectively operators which go around their operand.

The elements of the angle bracket operator go around their operand.

In[6]:= \[LeftAngleBracket] 1 + x \[RightAngleBracket]


Some additional letters and letter-like forms.

You can use letters and letter-like forms anywhere in symbol names.

In[7]:= {GothicCapitalREmptySet, \[Angle]ABC}


is assumed to be a symbol, and so is just multiplied by a and b.

In[8]:= a EmptySet b