Re: GramSchmidt problem
- To: mathgroup at smc.vnet.net
- Subject: [mg57035] Re: GramSchmidt problem
- From: David Bailey <dave at Remove_Thisdbailey.co.uk>
- Date: Thu, 12 May 2005 22:44:18 -0400 (EDT)
- References: <d5uvda$9at$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Heath Gerhardt wrote:
> Does anyone know if there are any know problems with GramSchmidt
> crashing Mathematica? When I run it on these 4 25-dimensional vectors it
> crashes on my system:
>
> \!\({1\/2\ \((3 + \@5)\), 1\/2\ \((\(-3\) - \@5)\), 1\/2\ \((1 + \@5)\), 0,
> 1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((\(-3\) - \@5)\), 1\/2\ \((3 + \@5)\),
> 1\/2\ \((\(-1\) - \@5)\), 0, 1\/2\ \((1 + \@5)\), 1\/2\ \((1 + \@5)\),
> 1\/2\ \((\(-1\) - \@5)\), 1, 0, \(-1\), 0, 0, 0, 0, 0,
> 1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((1 + \@5)\), \(-1\), 0, 1}\)
>
> \!\({1\/2\ \((1 + \@5)\), 1\/2\ \((\(-3\) - \@5)\), 1\/2\ \((3 + \@5)\),
> 1\/2\ \((\(-1\) - \@5)\), 0, 1\/2\ \((\(-1\) - \@5)\),
> 1\/2\ \((3 + \@5)\), 1\/2\ \((\(-3\) - \@5)\), 1\/2\ \((1 + \@5)\), 0,
> 1,
> 1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((1 + \@5)\), \(-1\), 0, 0, 0, 0, 0,
> 0, \(-1\), 1\/2\ \((1 + \@5)\), 1\/2\ \((\(-1\) - \@5)\), 1, 0}\)
>
> \!\({1\/2\ \((1 + \@5)\), 1\/2\ \((\(-1\) - \@5)\), 1, 0, \(-1\),
> 1\/2\ \((\(-3\) - \@5)\), 1\/2\ \((3 + \@5)\), 1\/2\ \((\(-1\) - \@5)\),
> 0, 1\/2\ \((1 + \@5)\), 1\/2\ \((3 + \@5)\), 1\/2\ \((\(-3\) - \@5)\),
> 1\/2\ \((1 + \@5)\), 0, 1\/2\ \((\(-1\) - \@5)\),
> 1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((1 + \@5)\), \(-1\), 0, 1, 0, 0, 0, 0,
> 0}\)
>
> \!\({1, 1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((1 + \@5)\), \(-1\), 0,
> 1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((3 + \@5)\), 1\/2\ \((\(-3\) - \@5)\),
> 1\/2\ \((1 + \@5)\), 0, 1\/2\ \((1 + \@5)\), 1\/2\ \((\(-3\) - \@5)\),
> 1\/2\ \((3 + \@5)\), 1\/2\ \((\(-1\) - \@5)\), 0, \(-1\),
> 1\/2\ \((1 + \@5)\), 1\/2\ \((\(-1\) - \@5)\), 1, 0, 0, 0, 0, 0, 0}\)
>
>
> thanks in advance
> Heath
>
Like many Mathematica operations, GramSchmidt can operate with exact
quantities (Integers, Fractions, Roots, etc.) yielding an exact result,
or with real numbers yielding a real (inexact) result. All Your numbers
are exact, so it will try to give you an exact answer. Unfortunately,
the size of the numerators/denominators of the terms will explode. Just
apply N to your vectors before you start, and you will obtain an answer
easily.
BTW, please use InputForm when submitting examples - reading box form is
a bit like reading punched paper tape!
David Bailey
http://www.dbaileyconsultancy.co.uk