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Re: Replacement Rule with Sqrt in denominator

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114611] Re: Replacement Rule with Sqrt in denominator
  • From: AES <siegman at stanford.edu>
  • Date: Fri, 10 Dec 2010 02:30:09 -0500 (EST)
  • References: <idl6vd$mkp$1@smc.vnet.net> <idnqq6$q5i$1@smc.vnet.net>

In article <idnqq6$q5i$1 at smc.vnet.net>,
 Noqsi <noqsiaerospace at gmail.com> wrote:

> It is easy to see the kind of chaos the vague and ambiguous "rules
> should be interpreted semantically in a way that makes mathematical
> sense" would cause. How should
> 
> a + b I /. I->-I
> 
> be interpreted *semantically*?

I do not possess anything like the depth of knowledge of symbolic 
algebra or the understanding of the principles of semantics that would 
embolden me to offer any answer to the preceding question.

But I will offer the following opinion:  However the above rule is to be 
interpreted, in any decent symbolic algebra system, assuming a and b 
have not yet been assigned any values, the symbol I should be 
interpreted (i.e., modified) identically -- i.e., in *exactly* the same 
fashion -- for either of the inputs

   a + b I /. I->-I      OR     a + 2 b I /. I->-I

This is NOT the case in Mathematica.  This behavior is a "gotcha" that 
can be responsible for large and hard to trace difficulties for many 
users

Furthermore, I believe that Mathematica WILL interpret (i.e. , modify) 
the two inputs above in exactly the same fashion if the character I in 
thee two expressions is replaced by ANY OTHER single upper or lower case 
letter in the alphabet.  Does anyone else find this not to be true?


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