Working with Operators
You can think of an expression like
as being formed by applying an operator
f to the expression
x. You can think of an expression like
as the result of
composing the operators
f and
g, and applying the result to
x.
Some functional operations.
This represents the composition of the functions
f,
g, and
.
| Out[1]= |  |
You can manipulate compositions of functions symbolically.
| Out[2]= |  |
The composition is evaluated explicitly when you supply a specific argument.
| Out[3]= |  |
You can get the sum of two expressions in
Mathematica just by typing
. Sometimes it is also worthwhile to consider performing operations like addition on
operators.
You can think of this as containing a sum of two operators
f and
g.
| Out[4]= |  |
Using
Through, you can convert the expression to a more explicit form.
| Out[5]= |  |
This corresponds to the mathematical operator
.
| Out[6]= |  |
Mathematica does not automatically apply the separate pieces of the operator to an expression.
| Out[7]= |  |
You can use
Through to apply the operator.
| Out[8]= |  |
Operations for working with operators.
This has a complicated expression as a head.
| Out[9]= |  |
Functions like
Expand do not automatically go inside heads of expressions.
| Out[10]= |  |
| Out[11]= |  |
The replacement operator
does go inside heads of expressions.
| Out[12]= |  |
You can use
Operate to apply a function specifically to the head of an expression.
| Out[13]= |  |
if p is the same as q
