File r37/lisp/csl/html/r37_0187.html artifact d3f7d12db9 part of check-in 3af273af29

<A NAME=ANTISYMMETRIC>

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



<B>ANTISYMMETRIC</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>declaration</B><P>
<P>
 
When an operator is declared <em>antisymmetric</em>, its arguments are 
reordered to conform to the internal ordering of the system. If an odd 
number of argument interchanges are required to do this ordering, 
the sign of the expression is changed. 
<P>
<P>
 <P> <H3> 
syntax: </H3>
<em>antisymmetric</em>&lt;identifier&gt;{<em>,</em>&lt;identifier&gt;}* 
<P>
<P>
<P>
&lt;identifier&gt; is an identifier that has been declared as an operator. 
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
operator m,n; 

antisymmetric m,n; 

m(x,n(1,2)); 

  - M( - N(2,1),X) 


operator p; 

antisymmetric p; 

p(a,b,c); 

  P(A,B,C) 


p(b,a,c); 

  - P(A,B,C)

</TT></PRE><P>If &lt;identifier&gt; has not been declared an operator, the flag 

<em>antisymmetric</em> is still attached to it. When &lt;identifier&gt; is 
subsequently used as an operator, the message <em>Declare</em> &lt;identifier
&gt; 
 <em>operator? (Y or N)</em> is printed. If the user replies <em>y</em>, the 
antisymmetric property of the operator is used. 
<P>
<P>
Note in the first example, identifiers are customarily ordered 
alphabetically, while numbers are ordered from largest to smallest. 
The operators may have any desired number of arguments (less than 128). 
<P>
<P>
<P>