the composition operator - Maple Help

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@ - the composition operator

@@ - the repeated composition operator

Calling Sequence

f @ g

f @@ n

Parameters

f, g

-

any functions

n

-

integer

Description

• 

 @ is the function composition  operator.

• 

 @@ is the repeated function composition  operator.

• 

If n is negative, the invfunc table is checked to see if it has an entry for f.  That is, if invfuncf=g, then f@@n>g@@n.

• 

Composition also applies to procedures.  However, given two procedures f and g, the composition f@g is of type function, not type procedure.  For more information, see type/function and type/procedure.

Composition Examples

(sin@cos)(x);

sincosx

(1)

(sin@arcsin)(x);

x

(2)

sin@arcsin;

sin@arcsin

(3)

simplify((3));

→args

(4)

sin@@0;

→args

(5)

sin@@1;

sin

(6)

(sin@@2)(x);

sin2x

(7)

cos@@(-1);

arccos

(8)

(D@@2)(ln);

z→1z2

(9)

Thread Safety

• 

The @ and @@ operators are thread-safe as of Maple 15.

• 

For more information on thread safety, see index/threadsafe.

See Also

combinat[composition], invfunc, operator, simplify, type[composition]


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