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Re: pattern test and default value

• To: mathgroup at smc.vnet.net
• Subject: [mg5979] Re: [mg5967] pattern test and default value
• From: Allan Hayes <hay at haystack.demon.co.uk>
• Date: Sat, 8 Feb 1997 22:37:53 -0500
• Sender: owner-wri-mathgroup at wolfram.com

marliesb at sci.kun.nl (Marlies)
[mg5967] pattern test and default value
writes

> It is possible to do the following:
>
> x_h:v (an expression with head h and default value v)
>
> Can anyone tell me whether it is possible to have a pattern test
> like
> _?NumberQ  AND have a certain default value?

Marlies:
Yes to both.
(1)
g[x_h:h[v]]:= x^2          (*default must match x_h*)

g[h[4]]
	    2
	h[4]
g[]
	    2
	h[v]
	
(2)
Use form

p[x:(_?NumberQ): 5] := x^2  (*default must satisfy test*)
p[7]
	49
p[]
	25

Parsing problems with some other problems can be seen with FullForm:

FullForm[x:(_?NumberQ):5]  (*the form that works*)
	Optional[Pattern[x, PatternTest[Blank[], NumberQ]], 5]

FullForm[x:_?NumberQ:5]
	Pattern[x, PatternTest[Blank[], Pattern[NumberQ, 5]]]

FullForm[x_?NumberQ:5]
	PatternTest[Pattern[x, Blank[]], Pattern[NumberQ, 5]]
	
It's sometimes quicker to type in the full form

Allan Hayes
hay at haystack.demon.co.uk
http://haystack.demon.co.uk