DEPEND _ _ _ _ _ _ _ _ _ _ _ _ declaration

dependdeclares that its first argument depends on the rest of its arguments.

syntax:

<kernel> must be a legal variable name or a prefix operator (see kernel).

examples:

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)

Dependencies can be removed by using the declaration nodepend. The differentiation operator uses this information, as shown in the examples above. Linear operators also use knowledge of dependencies (see linear). 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 DF(Y,X), for example, are expanded when they are displayed again, as shown in the last example. The boolean operator freeof allows you to check the dependency between two algebraic objects.