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<A NAME=NONCOM>

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



<B>NONCOM</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>declaration</B><P>
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<em>noncom</em>declares that already-declared operators are noncommutative 
under multiplication. 
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syntax: </H3>
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<em>noncom</em>&lt;operator&gt;{,&lt;operator&gt;}* 
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&lt;operator&gt; must have been declared an 
<A HREF=r37_0211.html>operator</A>, or a warning 
message is given. 
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examples: </H3>
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operator f,h; 

noncom f; 

f(a)*f(b) - f(b)*f(a); 

  F(A)*F(B) - F(B)*F(A) 


h(a)*h(b) - h(b)*h(a); 

  0 


operator comm; 

for all x,y such that x neq y and ordp(x,y)
        let f(x)*f(y) = f(y)*f(x) + comm(x,y);


f(1)*f(2); 

  F(1)*F(2) 


f(2)*f(1); 

  COMM(2,1) + F(1)*F(2)

</TT></PRE><P>The last example introduces the commutator of f(x) and f(y) 
for all x and y. The equality check is to prevent an infinite loop. The 
operator f can have other functionality attached to it if desired, or it 
can remain an indeterminate operator. 
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