Solve or LinearSolve or ...?

*To*: mathgroup at smc.vnet.net*Subject*: [mg46347] Solve or LinearSolve or ...?*From*: semorrison_ at hotmail.com (Scott Morrison)*Date*: Mon, 16 Feb 2004 08:59:48 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I'm trying to write a function to calculate coefficients in a basis; for example FindCoefficients[{f[a,a],f[a,b],f[b,a],f[b,b]}, f[a,a]+(1/2)f[b,a], _f] should produce {1,0,1/2,0}. The third argument there means `assuming all objects matching _f are linearly independent'. More difficult, it should produce FindCoefficients[{f[a]+f[b],f[a]-f[b]},f[a], _f] == {1/2,1/2}. And finally, it should work with rational functions as coefficients, not just numbers, and it should run fast enough to be useful with bases with thousands of elements. :-) I've spent quite some time trying to write something like this, and I'm finding it really difficult! I can't seem to use LinearSolve in any way -- it seems to trip up when I use rational functions as coefficients. I've been trying to work around Solve, but the only things that work are glacial in pace! Any ideas or suggestions? I'd be happy to post some of my attempts if they'd be helpful in explaining what I'm trying to do, but mostly I'm too embarrassed by them :-) Scott Morrison

**Follow-Ups**:**Re: Solve or LinearSolve or ...?***From:*Oleksandr Pavlyk <pavlyk@phys.psu.edu>