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.