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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.



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