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Optional (:)

is a pattern object which represents an expression of the form p, which, if omitted, should be replaced by v.
  • Optional is used to specify "optional arguments" in functions represented by patterns. The pattern object p gives the form the argument should have, if it is present. The expression v gives the "default value" to use if the argument is absent.
  • The form s_:v is equivalent to Optional[s_, v]. This form is also equivalent to s:_:v. There is no syntactic ambiguity since s must be a symbol in this case.
  • The special form s_. is equivalent to Optional[s_] and can be used to represent function arguments which, if omitted, should be replaced by default values globally specified for the functions in which they occur.
  • Values for Default[f, ...] specify default values to be used when _. appears as an argument of f. Any assignments for Default[f, ...] must be made before_. first appears as an argument of f.
  • Optional[s_h] represents a function which can be omitted, but which, if present, must have head h. There is no simpler syntactic form for this case.
  • Functions with built-in default values include Plus, Times and Power.
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