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
You can manipulate compositions of functions symbolically.
The composition is evaluated explicitly when you supply a specific argument.
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
, you can convert the expression to a more explicit form.
This corresponds to the mathematical operator
does not automatically apply the separate pieces of the operator to an expression.
You can use Through
to apply the operator.
Operations for working with operators.
This has a complicated expression as a head.
Functions like Expand
do not automatically go inside heads of expressions.
The replacement operator
does go inside heads of expressions.
You can use Operate
to apply a function specifically to the head of an expression.