Re: More /.{I->-1} craziness
- To: mathgroup at smc.vnet.net
- Subject: [mg106353] Re: More /.{I->-1} craziness
- From: Noqsi <jpd at noqsi.com>
- Date: Sun, 10 Jan 2010 03:29:20 -0500 (EST)
- References: <200912300915.EAA17299@smc.vnet.net> <hhhmn8$o9t$1@smc.vnet.net>
On Jan 8, 2:15 am, Richard Fateman <fate... at cs.berkeley.edu> wrote:
> Noqsi wrote:
>
> > Mathematica has a tool that can do what you want here:
>
> > Reduce[a == Exp[I x] - Exp[-I x] && Exp[I x] == s, {a}, {x}]
> > s != 0 && a == (-1 + s^2)/s
>
> > It's a bit fussier than perhaps you'd like, but that's mathematics for
> > you ;-)
>
> Reduce is a really neat program in Mathematica, one that I especially
> admire since it was improved to work on more than polynomials.
> Unfortunately, it won't work for I->-I, maybe because that is based on a
> decision involving constants represented differently from expressions
> that construct them.
It's more that I==-I makes no sense.
> (David Bailey already pointed this out. Do people
> get instantaneous unfiltered feed from this newsgroup??)
No.
>
> but also..
> Bill Rowe said ...
> "Again, the choice is either understand this behavior and live
> with it or find different software. There isn't any other
> productive choice."
>
> Well, reporting something as a bug and hoping it will be fixed is
> another choice.
But nobody with sense thinks it's a bug.
Remember that nearly all of the expressions evaluated by Mathematica
are also generated by Mathematica, not by human users. Reading human
intent into such expressions would be a grave mistake. Fundamental
facilities like Replace have to perform predictably and regularly to
make it possible for the developers of Mathematica to avoid creating
bugs.
> And writing a version of the facility that does the right thing is
> another choice. (Any takers?)
You cannot even define with adequate rigor what you mean by the "right
thing". How, *in general*, should Mathematica make *mathematical*
sense of a command to replace a constant with a different constant?
>
> Either of these could be "productive".
>
> Are Mathematica design decisions sacred or something?
The design of fundamental functionality like Replace is severely
constrained by the architecture of the system. Balsa wood is a useful
material, but you cannot use it to make the base structure of a
skyscraper.