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MathGroup Archive 1999

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Re: Re: Re: equaltity of lists

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19283] Re: [mg19243] Re: [mg19162] Re: equaltity of lists
  • From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
  • Date: Thu, 12 Aug 1999 22:34:42 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

The problem is that in Mathematics symbols like x are used in different 
senses. Sometimes x is a "variable", something that can take values. When
you view it in this way than indeed x^2/x and x may no tbe equivalent. This
is what usually happens in analysis. However, there is another way in which
such symbols are used: x can be an "indeterminate". This usually happens in
algebra. For example I frequently deal with the algebra of Laurent series
C[[x,x^(-1)]]. Here x and x^(-1) are indeterminates such that x*(x^(-1))==1.
"Indeterminates" do not take values so there is no question of any
difference between x^2/x and x. Most of computations in abstract algebra are
like this (there is no need to talk of generic solutions here, though there
is a proper context for this too).

I must admit that Mathematica already has another way that could be used for
manipulating symbols which are not meant to be vaiables. Note that you have:

In[11]:=
"x"^2/"x"
Out[11]=
"x"

I don't think anyone can object to this since it is impossible to assign
values to "x". So indeed it might be more consistent to simplify "x"^2/"x"
automatically to "x" and keep x^2/x unchanged unless information about x was
entered. But personally I would find entering these quote marks a nuisance
and I am quite happy with the way things work now.

--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp


----------
>From: "Drago Ganic" <drago.ganic at in2.hr>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg19283] [mg19243] Re: [mg19162] Re: equaltity of lists
>Date: Wed, Aug 11, 1999, 8:06 AM
>

>
> x^2 * x^(-1) = x^(2-1) Equals to x _whenever the expression makes
> sense_. But x makes sense in the point 0 and x^2/x does not. So I
> don't see any difference between function equality and expression
> equality, because an expression _is a function_. When Wolfram says
> "Everything is an expression" he could also say "Everything is a
> function". Isn't the full form of an expression h[x1, x2, ...].
> To me, this looks like a function.


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