On Wed, Jul 9, 2008 at 10:38 AM, Bill Page <[EMAIL PROTECTED]> wrote: > On Wed, Jul 9, 2008 at 7:29 AM, Gabriel Dos Reis wrote: >> On Wed, Jul 9, 2008 at 12:35 AM, Bill Page 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)) >>> >>> If a value of 0 is subsituted for d in this "non-zero polynomial" >>> then in what sense is '1/(2d)' safe? >> >> This is the classical difference between a function (defined by a >> polynomial) and a polynomial. >> >> There is no doubt that -- if d is the unknown -- then 2d is a non-zero >> polynomial and as such has an inverse in the field Q(d). >> > > But is computing in the field Q(d) "safe" if we eventually intend to > replace d with some non-symbolic value?
That is a question separate from whether the polynomial 2*d is nonzero or not. There is no doubt it is nonzero. > 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. And this is precisely one of the fundamental reasons why I prefer a distinct domin 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). > It seems to me that an inverse in Q(d) might > have no counterpart in Q. > > 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
