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Re: Replacement Rule with Sqrt in denominator

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114635] Re: Replacement Rule with Sqrt in denominator
  • From: Noqsi <noqsiaerospace at gmail.com>
  • Date: Sat, 11 Dec 2010 01:53:33 -0500 (EST)
  • References: <idl6vd$mkp$1@smc.vnet.net> <idnqq6$q5i$1@smc.vnet.net> <idsku3$6ko$1@smc.vnet.net>

On Dec 10, 12:30 am, AES <sieg... at stanford.edu> wrote:
> In article <idnqq6$q5... at smc.vnet.net>,
>
>  Noqsi <noqsiaerosp... 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.

Oh, come on. This really isn't hard to understand.

>
> But I will offer the following opinion:  However the above rule is to b=
e
> 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.

And this is trivially understandable by looking at FullForm. "I" is
part of the number in this case: it is not a separate symbol. As well
expect 22/.2->1 to yield 11.

>  This behavior is a "gotcha" that
> can be responsible for large and hard to trace difficulties for many
> users

Sure. And if you use a power saw carelessly, you'll cut your fingers
off. That's a worse "gotcha", but it can't be helped in a foolproof
way without crippling the saw. Just as this can't be helped without
crippling Mathematica.

>
> 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?

It's a consequence of two very simple considerations:

1. Pattern matching works on FullForm.

2. Pattern matching can't split atoms.

What's so hard about this? There are only six kinds of atoms.

When using a tool, it's preferable to exploit the way it actually
works, rather than make up some impossible notion and complain that it
should work that way.


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