Default value behaves differently when used in Function and when used with Cases

Question

Consider this example:

 Cases[{4, x, 5 a , 6 x}, x_.*a_ :> x]

(*{1, 1, 5, 6}*)

It is clear that the _. took 1 as a Default value.

Now:

f[x_.] := {x} dose not work and _. Default value has to be user defined first

Default[f] = 0;
f[x_.] := {x}
f[]
(*{0}*)

It is little confusing that _. takes default value in some operation and has to be user defined with default value in other operation.

Any explanations?

Thanks

The functions Times, Plus, Power have built-in default values (1, 0, and 1, respectively). — kglr, Commented Dec 29, 2014 at 0:56
Use DefaultValues[Times], DefaultValues[Plus] etc. to see this. Now try DefaultValues[f] before you have attached any default values to it, and you will see that f has no built-in default values. — C. E., Commented Dec 29, 2014 at 0:57

halirutan · Accepted Answer · 2014-12-29 00:59:51Z

2

The answer is pretty simple and you were very close to seeing this yourself:

Default[Times]

(* Out[9]= 1 *)

As you see, the DefaultValues for Times and Plus are already built in.

answered Dec 29, 2014 at 0:59

halirutan

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$\begingroup$ I was very close yes but I would never seeing it myself before your answer. Thanks :) $\endgroup$
– Basheer Algohi
Commented Dec 29, 2014 at 1:03

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