BUILT-IN MATHEMATICA SYMBOL

With

specifies that in expr occurrences of the symbols x, y, ... should be replaced by

,

, ....

With replaces symbols in expr only when they do not occur as local variables inside scoping constructs.

You can use With as the right-hand side of a transformation rule with a condition attached.

With constructs can be nested in any way, with inner variables being renamed if necessary.

Out[2]=

Use With to insert values into held expressions:

The variable names can be the same:

Use a constant for a value that is needed more than once:

With allows inserting values into unevaluated expressions:

Module introduces local variables to which you can assign values:

With is faster than Module:

Block localizes values only; it does not substitute values. Module creates new symbols:

With allows substitution inside an unevaluated expression, preserving nested scopes:

Ordinary substitution does not preserve scoping:

With is a scoping construct; variables are renamed in nested scopes:

Build the function from its elements to avoid the renaming:

Find a zero of an arbitrary function using Newton's method:

Find a fixed point:

A version of With where the initializer is within the scope of the local variable:

Here the f inside the function definition is not inside its own scope: