P.P.S. And thanks to everybody developing Sage :-)
On Apr 9, 2:55 pm, Alex Raichev <tortoise.s...@gmail.com> wrote:
> P.S. Burcin, thanks for all your work on Sage symbolics. I
> appreciate it.
>
> On Apr 8, 11:44 pm, Burcin Erocal <bur...@erocal.org> wrote:
>
> > Hi again Alex,
>
> > Many thanks for the report.
>
> > On Wed, 7 Apr 2010 16:05:09 -0700 (PDT)
>
> > Alex Raichev <tortoise.s...@gmail.com> wrote:
> > > Hi all:
>
> > > I ran into an error trying to evaluate the exponential function at an
> > > algebraic number. Looks like there's a bug in substituting algebraic
> > > numbers for variables; see below. While i was at it, i tried creating
> > > the expression QQbar(sqrt(2))*x and got a not implemented error.
> > > Wasn't symbolics with QQbar working in previous versions of Sage, or
> > > am i mistaken?
>
> > Most structures in Sage coerce to SR, so when you do
>
> > sage: 1 + x
>
> > the result in SR, even though 1 is in ZZ, and x in SR. This is not the
> > case for QQbar and AA. Copying from a comment in
> > sage/symbolic/function.pyx:
>
> > # There is no natural coercion from QQbar to the symbolic ring
> > # in order to support
> > # sage: QQbar(sqrt(2)) + sqrt(3)
> > # 3.146264369941973?
>
> > I wrote that comment to document the current behavior, but I don't
> > necessarily agree with this policy.
>
> > Under these conditions,
>
> > sage: x*QQbar(sqrt(2))
>
> > cannot work. Since we cannot coerce QQbar(sqrt(2)) to SR, we try to
> > coerce x to QQbar.
>
> > I worked around this limitation for evaluating symbolic functions like
> > exp, but didn't think about substituting values. This can be fixed
> > easily by converting QQbar arguments to CC before we coerce them to SR.
>
> > I think we should reconsider the coercion policy though. For example
>
> > > sage: exp(QQbar(sqrt(2)))
> > > 4.11325037878293
>
> > this should remain exact, since QQbar keeps exact values. Then you can
> > evaluate to an arbitrary precision. Since sqrt(2) is converted to CC,
> > an inexact parent, we get a numerical evaluation in this case.
>
> > If we change the coercion policy the examples below will just work.
> > Otherwise
>
> > > sage: exp(x).subs({x:QQbar(sqrt(2))})
>
> > <boom>
>
> > > sage: x.subs({x:QQbar(sqrt(2))})
>
> > <boom>
>
> > These two are bugs, they will be equivalent to
> > sage: x.subs({x:CC(QQbar(sqrt(2)))})
>
> > after the fix.
>
> > This one cannot work with the current coercion direction SR -> QQbar.
>
> > > sage: QQbar(sqrt(2))*x
>
> > <boom>
>
> > Comments?
>
>
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