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

```

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