
<A NAME=INFIX>

<TITLE>INFIX</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>INFIX</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>declaration</B><P>
<P>
 
 <P>
<P>
<em>infix</em>declares identifiers to be infix operators. 
 <P> <H3> 
syntax: </H3>
<P>
<P>
<em>infix</em>&lt;identifier&gt;{,&lt;identifier&gt;}* 
<P>
<P>
<P>
&lt;identifier&gt; can be any valid REDUCE identifier, which has not already 
been declared an operator, array or matrix, and is not reserved by the 
system. 
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
infix aa; 

for all x,y let aa(x,y) = cos(x)*cos(y) - sin(x)*sin(y); 

x aa y; 

  COS(X)*COS(Y) - SIN(X)*SIN(Y) 


pi/3 aa pi/2; 

    SQRT(3)
  - ------- 
       2


aa(pi,pi); 

  1

</TT></PRE><P>A 
<A HREF=r37_0199.html>let</A> statement must be used to attach functionality to 

the operator. Note that the operator is defined in prefix form in 
the <em>let</em> statement. 
After its definition, the operator may be used in either prefix or infix 
mode. The above operator aa finds the cosine of the sum 
of two angles by the formula 
<P>
<P>
cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y). 
<P>
<P>
Precedence may be attached to infix operators with the 

<A HREF=r37_0213.html>precedence</A> declaration. 
<P>
<P>
User-defined infix operators may be used in prefix form. If they are used 
in infix form, a space must be left on each side of the operator to avoid 
ambiguity. Infix operators are always binary. 
<P>
<P>
<P>
