Examples of Functional Operators - Maple Programming Help

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Examples of Functional Operators

A functional operator in Maple is a special form of a procedure. Functional operators are written using arrow notation:

  vars  result

For basic information, see Functional Operators.  The following examples demonstrate the different types of functional operators that you can use in Maple.

Examples

First, define a basic operator on a single variable x and apply it using function notation.

F:=x→sinx

F:=x→sinx

(1.1)

Ft

sint

(1.2)

In this example, empty parentheses denote that the operator returns 1, no matter what the input.

A:=→1

A:=→1

(1.3)

Ax

1

(1.4)

Note that in 1-D Math input, an operator can always be applied by using function notation.  However, in 2-D Math input, when the operator is also of type atomic, you must use the apply command.  This is because 1x is interpreted as multiplication in 2-D math rather than function application.  For more information, including how to change this default behavior, see 2DMathDetails.  

1(x);

1

(1.5)

1x

x

(1.6)

apply1, x

1

(1.7)

Similarly, this multivariate operator returns 3.14, no matter what the input.

B:=→3.14

B:=→3.14

(1.8)

Bx,y

3.14

(1.9)

3.14(x,y);

3.14

(1.10)

apply3.14, x,y

3.14

(1.11)

Operators can be applied without assigning them a name.

x→xt

t

(1.12)

xx24

16

(1.13)

Operators are distributive.

a+bt

at+bt

(1.14)

a+1t

at+1

(1.15)

Use the composition operator @ to perform operator composition.  That is, f@g means fg.

fxx+2;gyy

f:=x→x+2

g:=y→y

(1.16)

f@gt;g@ft

t+2

t+2

(1.17)

xsinx@xarcsinxt

t

(1.18)

Repeated composition is entered with the @@ operator.  Here, a function is composed with itself.

x→lnx+1@@2t

lnlnt+1+1

(1.19)

See Also

@, @@, 2-D Math Details, apply, D, Functional Operators, unapply  

 

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