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:= "x"^2/"x" Out= "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.