# [Maxima] complex equation solving

Rogers, Raymond raymond-rogers
Thu Nov 16 10:32:39 CST 2006

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> -----Original Message-----
> From: Seb [mailto:spluque at gmail.com]
> The problem is that I need to estimate u for all t between 0 and 300
> (integers), holding a, b, and x constant.  Additionally, I
> need to repeat
> this procedure for all x between 0.1 and 3 (every 0.1).  I
> was wondering
> if there's some method in maxima to automate this procedure.
> Thanks for
>
Seb,
Considering your goal; can I suggest an alternative?
Solving for t in terms of (u,a,b,x) and varying u ?
Removing the separate zero surface (u-t)^x
And assumes (a*%e^(b*u)+u)^2 >0

Like so:

(%i35) solve(factor((a*%e^(b*u)+u)^2*f1/((u-t)^x)),t);
(%o35) [t=-((a*%e^(b*u)+u)*x-a*b*u*%e^(b*u)-u)/(a*b*%e^(b*u)+1)]

So instead of scanning u(t) you do t(u).
If need be, I have an inversion algorithm to produce
U= Taylor series in t  with a,b,x constant.
But it typically only has a finite radius of convergence around the
expansion point.  If the t(u) a,b,x surface looks smooth then it should work
okay though.

R.Rogers

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