On Wed, Jul 9, 2008 at 3:38 PM, Bill Page <[EMAIL PROTECTED]> wrote: >>>> >>>>> *yixin.cao wrote:* -- In the light of polynomial, (2d) is a >>>>> non-zero polynomial, so that it's always safe to write (1/(2d)) >>>>> >>> ... > >> On Wed, Jul 9, 2008 at 10:38 AM, Bill Page wrote: >>> But is computing in the field Q(d) "safe" if we eventually intend to >>> replace d with some non-symbolic value? >> > > On Wed, Jul 9, 2008 at 3:56 PM, Gabriel Dos Reis wrote: >> That is a question separate from whether the polynomial 2*d is >> nonzero or not. There is no doubt it is nonzero. >> > > Call it whatever you like.
Then that is unfortunate, because it seems the solution presented is being dismissed for another proposal, when in fact the other proposal refuses to be careful in its terminology and semantics. > My question is: "Is yixin.cao's original claim true?" His claim was that the polynomial 2d is nonzero -- again, I stress for the casual reader that `d' is the unknown. That such a simple claim could be seen as untrue escapes my understanding. > >>> Isn't there a possibility that >>> such computations could lead to incorrect results due to (for example) >>> implicit divisions by 0? >> >> This is a classic problem of interpretation, discussed by classic volumes >> of algebra books, and classics of symbolic computation. >> > > True. What is your point? That you need to be careful in your arguments. > >> And this is precisely one of the fundamental reasons why I prefer >> a distinct domain Symbolic T, instead of reusing Polynomial or >> similar thing. From my point of view, this is also a good reason >> to reject Union(Variable d, Float). >> > > How will 'Symbolic T' deal with this issue? > How will it be different from Polynomial? Symbolic T is not a Polynomial T, therefore does not use simplification rules from the field of quotients of Polynomial T. > >> ... > > Regards, > Bill Page. > ------------------------------------------------------------------------- Sponsored by: SourceForge.net Community Choice Awards: VOTE NOW! Studies have shown that voting for your favorite open source project, along with a healthy diet, reduces your potential for chronic lameness and boredom. Vote Now at http://www.sourceforge.net/community/cca08 _______________________________________________ open-axiom-devel mailing list open-axiom-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/open-axiom-devel
