Re: "Assuming"

*To*: mathgroup at smc.vnet.net*Subject*: [mg85858] Re: "Assuming"*From*: "Mariano Suárez-Alvarez" <mariano.suarezalvarez at gmail.com>*Date*: Mon, 25 Feb 2008 07:37:45 -0500 (EST)*References*: <20080221171506.200$2n_-_@newsreader.com> <200802221221.HAA08545@smc.vnet.net>

On Feb 23, 7:34 am, Daniel Lichtblau <d... at wolfram.com> wrote: > Andrzej Kozlowski wrote: > > On 21 Feb 2008, at 23:15, David W. Cantrell wrote: > > >>[Message also posted to: comp.soft-sys.math.mathematica] > > >>Andrzej Kozlowski <a... at mimuw.edu.pl> wrote: > >>[...] > > I intersperse two comments, based on two posts to this thread. > > [From Andrzej Kozlowski:]> Note also one more thing. Suppose we consider a general rational > > function p[x]/q[x], (or even a rational function in several > > variables). Should Mathematica be then required always to try to find > > if p[x] and q[x] do not have common roots in some algebraic (or even > > transcendental inthe case of several variables) extension of the > > rationals? This is far from a trivial problem? [...] > > > Andrzej Kozlowski > > The only removable singularities, in this context, are in fact from > exact divisors. So polynomial gcd extraction (used in, say, Together[]) > suffices to remove them. > > Other cases where numerator and denominator simultaneously vanish will > give points of indeterminacy. These are not removable. > > I'm not sure in what way transcendentals snuck in here. If the > polynomials have common roots, they are describable as an algebraic set. > In particular, isolated common roots will be algebraic numbers. > > [From David Cantrell:] > > > > >>[...] But I do know of a case where > >>Mathematica goes even further, removing a singularity at which the > >>function > >>is defined as a number: > > >>In[17]:= FullSimplify[UnitStep[-x^2]] > >>Out[17]= 0 > > >>despite the fact that correctly > > >>In[18]:= UnitStep[-x^2] /. x -> 0 > >>Out[18]= 1 > > >>Perhaps the simplification above is considered a bug, perhaps not. > > >>David > > A feature, really. That is, it's wrong, but FullSimplify can make > mistakes on measure zero sets. We do not generally regard this > phenomenon as a bug, though we reconsider on case by case basis. How does that `measure zero' allowance work in a context of something like Assuming[Element[x, Integers], FullSimplify[something]] ? -- m

**Follow-Ups**:**Re: Re: "Assuming"***From:*Daniel Lichtblau <danl@wolfram.com>

**References**:**Re: "Assuming"***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>