- 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: <email@example.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
> >>is defined as a number:
> >>In:= FullSimplify[UnitStep[-x^2]]
> >>Out= 0
> >>despite the fact that correctly
> >>In:= UnitStep[-x^2] /. x -> 0
> >>Out= 1
> >>Perhaps the simplification above is considered a bug, perhaps not.
> 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]]
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