On Mon, 25 Jan 2010, Leo wrote:
< Hello,
<
< I have maxima 5.20.1 thanks to help from this mailing list ;)
<
< How to make maxima give me some meaningful result in the following:
<
< eq1: I/(e*V) - Nw*(1-h)/t_w2 + NQ*h/t_2w - Nw/t_wR=0;
< eq2: Nw*(1-h)/t_w2 - NQ*h/t_2w + NQ*h*(1-f)/t_21 + NQ*f*(1-h)/t_12=0;
< eq3: NQ*h*(1-f)/t_21 - NQ*f*(1-h)/t_12 - NQ*f*f/t_1R - g*P/(sigma*hbar*omega)=0;
< eq4: g = gmax*(2*f-1);
<
< Nw, h, f are variables, the rest are real numbers. How to solve these
< eqs to get the expression of Nw, h and f? Thanks in advance.
This is overdetermined, and both solve and to_poly_solve don't obtain a
solution.
First, I would note that eq4 and eq2 are both linear in f, and eq4 is
independent of h,Nw so use that solution as a consistency condition at
the end.
Solve eq2 for f=f(h,Nw).
Since eq1 is linear in h and independent of f, solve eq1 for h=h(Nw).
Substitute h,f into eq3, to get a solution for Nw in terms of the
parameters. Back substitute to get f and h. Finally, check your answer
for f with that for eq4.
Unfortunately, the expressions grow rapidly in size. I would suggest rethinking
why you've put so many parameters into these equations. For example,
I think you can 'remove' 3 or 4 parameters from eq1 by rewriting it like
a - Nw*(1-h) + NQ*h - Nw*b = 0
Finally, since your system is quadratic in f,h,Nw, maybe it would make
sense to solve the linearised system.
I should have said earlier: Welcome to Maxima.
HTH
Leo
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