
<A NAME=DEPEND>

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



<B>DEPEND</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>declaration</B><P>
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<em>depend</em>declares that its first argument depends on the rest of its 
arguments. 
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 <P> <H3> 
syntax: </H3>
<em>depend</em>&lt;kernel&gt;{<em>,</em>&lt;kernel&gt;}+ 
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&lt;kernel&gt; must be a legal variable name or a prefix operator (see 

<A HREF=r37_0002.html>kernel</A>). 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>

depend y,x; 


df(y**2,x); 

  2*DF(Y,X)*Y 



depend z,cos(x),y; 


df(sin(z),cos(x)); 

  COS(Z)*DF(Z,COS(X)) 



df(z**2,x); 

  2*DF(Z,X)*Z 



nodepend z,y; 


df(z**2,x); 

  2*DF(Z,X)*Z 



cc := df(y**2,x); 

  CC := 2*DF(Y,X)*Y 



y := tan x; 

  Y := TAN(X); 



cc; 

                  2
  2*TAN(X)*(TAN(X)   + 1)

</TT></PRE><P>Dependencies can be removed by using the declaration 
<A HREF=r37_0204.html>nodepend</A>. 
The differentiation operator uses this information, as shown in the 
examples above. Linear operators also use knowledge of dependencies 
(see 
<A HREF=r37_0200.html>linear</A>). Note that dependencies can be nested: Having 

declared y to depend on x, and z 
to depend on y, we 
see that the chain rule was applied to the derivative of a function of 
z with respect to x. If the explicit function of the 
dependency is later entered into the system, terms with <em>DF(Y,X)</em>, 
for example, are expanded when they are displayed again, as shown in the 
last example. The boolean operator 
<A HREF=r37_0113.html>freeof</A> allows you to 
check the dependency between two algebraic objects. 
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