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depends

check for mathematical dependence

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

depends(f, x)

Parameters

f

-

expression, or list or set of expressions

x

-

name, or list or set of names

Description

• 

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.

Examples

dependssinx+cosz,x,y

true

(1)

dependssinx+cosz,x,z

true

(2)

dependssinx+cosz,y,z

true

(3)

depends∫abfxⅆx,x

false

(4)

depends∫abfxⅆx,a

true

(5)

dependslimx→01x,x

false

(6)

dependsx=1n1x,x

false

(7)

dependsx=1n1x,n

true

(8)

dependslaplaceft,t,s,t

false

(9)

In some cases f must be simplified before depends is called to get the correct answer.

dependssinx2+cosx2,x

true

(10)

dependssimplifysinx2+cosx2,trig,x

false

(11)

See Also

has

indets

simplify

The depends Modifier

type/dependent

type/freeof

 


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