check for mathematical dependence
expression, or list or set of expressions
name, or list or set of names
The function depends returns true if any of the expressions contained in f are mathematically dependent on any of the names contained in x.
The expression f is mathematically dependent on the name x if it contains at least one instance of x which is not simply a dummy variable. Examples of dummy variables are index variables in sums, products, integrals, and limits. Dummy variables also appear in integral transforms.
If f is a complicated expression, then depends may not be able to determine that it is independent of x. In such cases, f should simplified before depends is called.
There is a facility for the user to add additional functions to depends. If the function depends/myfunc is defined, then depends will use this function to check for dependence whenever it encounters myfunc. The function depends/myfunc should accept as its parameters the arguments that myfunc expects in the same order, followed by a final parameter which will be a set containing all the names that dependence is being checked against. Note that myfunc may be either a user-defined function or a standard library function.
Unrelated to the above, there is also a procedure parameter modifier, depends, that can be used in declaration to indicate that a parameter's type depends on the value of another parameter.
In some cases f must be simplified before depends is called to get the correct answer.
The depends Modifier
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