Module[{x, y, ...}, expr]
specifies that occurrences of the symbols x, y, ... in expr should be treated as local. |
Module[{x=x0, ...}, expr]
defines initial values for x, .... |
- Module allows you to set up local variables with names that are local to the module.
- Module creates new symbols to represent each of its local variables every time it is called.
- Module creates a symbol with name xxx$nnn to represent a local variable with name xxx. The number nnn is the current value of $ModuleNumber.
- The value of $ModuleNumber is incremented every time any module is used.
- Before evaluating expr, Module substitutes new symbols for each of the local variables that appear anywhere in expr except as local variables in scoping constructs.
- Symbols created by Module can be returned from modules.
- You can use Module[{vars}, body/;cond] as the right-hand side of a transformation rule with a condition attached.
- Module constructs can be nested in any way, with inner variables being renamed if necessary.
- Module is a scoping construct that implements lexical scoping.
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EXAMPLES
Basic Examples 
Applications 