To do this correctly in full generality one needs to get into
"cyclindrical algebraic decomposition" -- a set in R^n has a
cylindrical algebraic
decomposition if it is written as a finite union of sets of the form
{ x : f(x) > 0 } where f is a polynomial. There is an algorithm due
to Tarski
for creating such sets.
Victor
On Dec 10, 5:15 pm, William Stein <wst...@gmail.com> wrote:
> On Thu, Dec 10, 2009 at 1:33 PM, kcrisman <kcris...@gmail.com> wrote:
>
> > On Dec 10, 2:49 pm, William Stein <wst...@gmail.com> wrote:
> >> On Thu, Dec 10, 2009 at 10:32 AM, kcrisman <kcris...@gmail.com> wrote:
>
> >> >> At this point, I'm just throwing some remarks out, not saying that we
> >> >> should
> >> >> do anything in particular.
>
> >> >> I'm curious -- who multiplies equalities by a scalar *except* high
> >> >> school
> >> >> students or college students taking entry level college algebra classes?
>
> >> > Or those in calculus or LP classes who need them to find solution sets
> >> > to various things. But yes.
>
> >> So we should make the semantics be aimed at such people.
>
> > But, although
> > x<y
> > -x>-y
> > what would we do for
> > a*x??a*y
> > situation? I think this was alluded to above - there isn't an answer,
> > per se. That doesn't mean we couldn't check for the 'right' answer if
> > 'a=something numeric' or even if 'a is assumed to be pos. or neg. in
> > assumptions()'. But it's not clear what to do in that case, and we
> > don't want to cause things to happen that are simply wrong. What does
> > Maple do in the symbolic case (the Mma answer, though cryptic, at
> > least is consistent)?
>
> Here is what Maple does:
>
> flat:release_notes wstein$ maple
> |\^/| Maple 13 (APPLE UNIVERSAL OSX)
> ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2009
> \ MAPLE / All rights reserved. Maple is a trademark of
> <____ ____> Waterloo Maple Inc.
> | Type ? for help.> f := x < y;
>
> f := x < y
>
> > f*(-3)
> > ;
>
> -3 y < -3 x
>
> > f*z;
>
> *(x < y, z)
>
> > f*a;
>
> *(x < y, a)
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