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Re: RE: question on changing 'type' of numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg69550] Re: [mg69495] RE: [mg69473] question on changing 'type' of numbers
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Fri, 15 Sep 2006 06:45:36 -0400 (EDT)
• References: <200609141055.GAA21466@smc.vnet.net>

On Sep 14, 2006, at 6:55 AM, David Park wrote:

> However, there seem to be cases where this is only partly true. For  
> example
> with complex numbers...
>
> AtomQ[2 + 3 I]
> True
>
> We can't change the Head
>
> Head[List @@ (2 + 3 I)]
> Complex
>
> but we can certainly access the parts
>
> 2 + I 3 /. Complex[a_, b_] -> {a, b}
> {2, 3}
>
> Maybe others will point out other 'in between' objects.

I think this is a side effect of how different atoms are  
represented.  FullForm[9] is 9 but FullForm[9+I] is Complex[9,1], so  
the pattern Complex[a_,b_] will match a complex number but Integer 
[x_] will not match an integer.  I'm too lazy to search for atoms  
whose FullForm contains a pattern that I can match to, but that would  
be the strategy for finding 'in between' objects.

Incidentally though there's no fundamental difference between

2 + I 3 /. Complex[a_, b_] -> {a, b}

and

9/.x_->{x,x}

the head isn't actually changing in either case.

Regards,

Ssezi

• References:
  • RE: question on changing 'type' of numbers
    • From: "David Park" <djmp@earthlink.net>