Subject: Problem with expand in lagrange interpolation
From: Richard Fateman
Date: Thu, 14 Jun 2007 09:42:30 -0700
Because of repeated subexpressions, such an expression would be bulky and
slow to compute (take n! time instead of n^2, I think).
A block (or as robert suggests, a lambda([x], block(....)) ) would be
better, I think
RJF
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Daniel Lakeland
> Sent: Thursday, June 14, 2007 9:23 AM
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] Problem with expand in lagrange interpolation
>
> On Thu, Jun 14, 2007 at 08:53:52AM -0700, Richard Fateman wrote:
> > I think you are doomed if you require that the result is a
> polynomial in
> > expanded form.
> > It doesn't matter how you compute the coefficients if you
> are doing it using
> > floating point arithmetic.
>
> Indeed, I was planning to return an *unexpanded* polynomial. In that
> case, the particular form of the polynomial essentially encodes the
> sequence of operations... it would look like
>
> a(x-x1)(x-x2) + b(x-x1) + c
>
> expanding it will of course eliminate the value of organizing the
> computation along these lines, but having a symbolic expression to
> carry around is more convenient for various purposes than a block
> expression.
>
>
> --
> Daniel Lakeland
> dlakelan at street-artists.org
> http://www.street-artists.org/~dlakelan
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