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Re: Question on Rescale[]

• To: mathgroup at smc.vnet.net
• Subject: [mg103329] Re: Question on Rescale[]
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Tue, 15 Sep 2009 06:54:19 -0400 (EDT)
• References: <200909141110.HAA08833@smc.vnet.net> <h8nj13$cej$1@smc.vnet.net>

Well, probably either Indeterminate or an error message.  :-)

It does seem curious that the system comes up with such an irrational 
number, doesn't it?  I looked at the available part of the source code 
by removing the ReadProtected attribute, but it doesn't contain the code 
responsible for this result.

However, I found it quite shocking that the code is written with bad 
practices and I immediately noticed a bug.  Among others, it contains 
the following definition:

Rescale[
     System`Dump`x_,
     {DirectedInfinity[System`Dump`d_], System`Dump`a_},
     {DirectedInfinity[D], System`Dump`A_}
   ] :=
   Rescale[
     System`Dump`x,
     {System`Dump`a, DirectedInfinity[System`Dump`d]},
     {System`Dump`A, DirectedInfinity[D]}
   ]

It has been noted several times on this list that it is a bad practice 
to use private symbols starting with capital letters, because it may 
lead to accidental collisions with built-in symbols.  The capital D 
(which also happens to be the function computing the derivative) is used 
throughout the code, and since D is in System`, of course it did not 
become part of the private context System`Dump` (as can be seen in the 
code above).

Furthermore, in this paricular defintion, D is used instead of the 
pattern D_, which is simply a bug.

Now, it is true that I don't see how this (most likely accidental) 
re-use of System`D as a private symbol could cause any problems *in this 
specific code*, but nevertheless I find it discomforting.

On 2009.09.15. 10:25, DrMajorBob wrote:
> What did you expect?
>
> Bobby
>
> On Mon, 14 Sep 2009 06:10:05 -0500, Alexey<lehin.p at gmail.com>  wrote:
>
>> Hello,
>> Consider the following:
>>
>> In[1]:= r=Rescale[x,{min,max}]
>> Rescale[2,{-Infinity,Infinity}]
>> r/.{x->2,min->-Infinity,max->Infinity}
>> Out[1]= -(min/(max-min))+x/(max-min)
>> Out[2]= 1/Sqrt[2]
>> During evaluation of In[1]:= \[Infinity]::indet: Indeterminate
>> expression 0 (-\[Infinity]) encountered.>>
>> Out[3]= Indeterminate
>>
>> At this moment I can not imagine why Rescale[2,{-Infinity,Infinity}]
>> gives 1/Sqrt[2]. Is this behavior correct?
>>

• References:
  • Question on Rescale[]
    • From: Alexey <lehin.p@gmail.com>