On Wed, Jul 9, 2008 at 7:04 PM, Bill Page <[EMAIL PROTECTED]> wrote: > On Wed, Jul 9, 2008 at 6:39 PM, Gabriel Dos Reis wrote: >> 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. >> > > I do not recall any solution being presented. I did not intend to > dismiss anything. > >>> My question is: "Is yixin.cao's original claim true?" >> >> His claim was that the polynomial 2d is nonzero > > The part of his claim that interests me is this: > > " ... so that it's always safe to write (1/(2d))"
And that claim is correct since 2*d is a polynomial, where d is the indeterminate. That polynomial has degree 1 with coefficient 2. Last time I checked my algebra, any polynomial of nonzero degree is nonzero. I do not expect that to change soon. > >> -- 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. >> > > 'd' is unknown so it can take any value - including zero, right? Again, you have to be careful about the domain of interpretation. In the field of fraction of polynomial, the fact that 1/(2d) is well define seals no doubt. It does not matter whether d can take on the value zero. That is just a simple fact. That is one of reasons why simplification of expressions that assume fraction of polynomials prove inadequate some times. Have a look at this wonderful paper by James Davenport. "Equality in Computer Algebra and Beyond" http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WM7-46WF0D7-3&_user=952835&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000049198&_version=1&_urlVersion=0&_userid=952835&md5=25ebbe3169a0c167d94835bce649864b ------------------------------------------------------------------------- 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
