I thought J already had that: just in library rather than iombedded native
transparent form?
This is one of the sterling characteristics of the gem called J:
It flexes so well.
As to symbolic versus indefinite precision:
I would prefer to use the term "exact" instead of "symbolic".
it would also be useful to kmnow whose opinions lead to voting among J's
designers:
it becomes a little easier to see where the driving motive force of
the next (re)vision of it
actually comes from, and what that actually, if publically explicated.
I use "exact" rather than "symbolic" because it is only when you apply
the step "display the metric" that you then get a value calculated and
displayed:
"exact" is better than "extended" or "indefinite" "precision" because
there is NO error term in "exact".
Unlike that, "indefinite precision' will always have one,
and to be presumtuous enough to presume that this
error term will always deconvolve down to the
nuemrical analysis a la calculus of differentials
functional equivalent of epsilon (All epsilon > 0 as
it in turn approaches zero)
is an unsustainable hope, at least to the extent of
the field of numerical analysis applied to
compuably applied finite extended/indefinite
precision packages of ANY type (I believe provably so),
because of the inherent rho characteristics involved
wiuth the athema of indefinite length or depth of
steps calculations.
Especially when applied against previously scientifically metrified
or mathematically computed results,oftimes of which error estimates
are at best approximate, or worse yet, only ambiguously
procimate
and which, adding to such errorrs, leads to cognitive and
metric distortion that in turn leads to vbvery bad, oftimes unrecoverable,
eigenstate loss, and the resulting demise
of
verifiable meaning
in the computational AND scientific (real world) result.
IMOHO. And some others.
On 12/6/06, Roger Hui <[EMAIL PROTECTED]> wrote:
I was told by a long-time user whose opinions I
respect that it would be more useful to be able
compute to some specified precision than to have symbolic
manipulations. So, some day, Joey will be
able to say in J:
y=: 40 x: 2.5
y
2.5d40
^ y
12.18249396070347343807017595116796618318
1 o. y
0.5984721441039564940518547021861622717035
^. y
0.9162907318741550651835272117680110714501
And there will be no degradation in the speed of
computations on ordinary 64 bit IEEE floating
point numbers.
----- Original Message -----
From: John Randall <[EMAIL PROTECTED]>
Date: Wednesday, December 6, 2006 12:16 pm
Subject: Re: [Jgeneral] Bug? Sin of pi.
> Joey K Tuttle wrote:
> > At 07:18 -0500 2006/12/06, John Randall wrote:
> >>Joey Tuttle writes:
> >>>In any case, I'm happy to sit back and wait for arbitrary
> >>>precision/accuracy facilities to be introduced in J.
> >>
> >>Symbolic languages such as Maple and Mathematica have arbitrary
> >>precision, but you hit a switch to do native floating-point
> >>calculation when you want speed.
> >>
> >
> > Of course, as the case with 123x currently, I presume that a
> > switch to (surely slower) arbitrary precision would continue
> > to be required. That is what I'm happy to wait for...
>
> Fair enough, but you still pay the price for the slower
> simplification/evaluation model anyway. That is why Maple and
> Mathematicaare not used for serious numerical calculation, except
> as front ends to
> standard libraries like LAPACK.
>
> Even with arbitrary precision, pi is not representable exactly,
> since you
> are still limited to rational numbers. If argument reduction is
> used in
> calculating sin, it is quite likely that sin(pi) is not 0: you need
> symbolic representation (or luck) for that.
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