
<A NAME=Optional_Free_Variable>

<TITLE>Optional_Free_Variable</TITLE></A>
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<B>OPTIONAL FREE VARIABLE</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>type</B><P>
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A variable preceded by a double tilde is considered as 
<em>optional free variable</em><P>
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and stands for an arbitrary part part in an algebraic form during 
pattern matching. In contrast to ordinary 
<A HREF=r37_0061.html>free variable</A>s 
an operator pattern with an <em>optional free variable</em> 
matches also if the operand for the variable is missing. In such 
a case the variable is bound to a neutral value. 
Optional free variables can be used as 
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term in a sum: set to 0 if missing, 
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factor in a product: set to 1 if missing, 
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exponent: set to 1 if missing 
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examples: </H3>
<P><PRE><TT></TT></PRE><P>Optional free variables are allowed only in the left-h
and sides 
of 
<A HREF=r37_0060.html>rule</A>s. 
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