[Maxima] [newbie] help with simplification
macrakis at alum.mit.edu
Mon Jan 22 12:48:14 CST 2007
As simplified with ratsimp/algebraic, the result is:
(call that qq)
To simplify beyond that, you'll need to decide what form you want, or
what assumptions you make about the values of the parameters. For
example, if R is relatively small, you might try
taylor(qq,r,0,1) => sqrt(c)*sqrt(l)/(c*r)+5*sqrt(c)*sqrt(l)*r/(8*l)+...
which you can simplify further ...
map(factor,taylor(...)) => sqrt(c)*sqrt(l)/(c*r)+5*sqrt(c)*sqrt(l)*r/(8*l)
which it turns out is the same as taylor(qq,[r,l,c],0,3).
If on the other hand R is relatively large,
map(factor,taylor(qq,r,inf,3)) => l/(c*r^2)-sqrt(2)*l^(3/2)/(c^(3/2)*r^3)+1
If L >> C, then try rr:subst(a*c,l,qq) and then
taylor(rr,a,inf,1) => sqrt(a)/r+5*r/(8*sqrt(a))
or if L << C
taylor(rr,a,0,1) => 1+a/r^2
and so on.
Hope this helps.
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