Re: [Maxima-discuss] solve() involving sqrt()

[Me S. <vla...@gm...>]

Hello Richard

> These equations (they are not polynomials) can be solved if they are
> converted to polynomials.  For eq1, solve for sqrt(x*y),  then square
> both sides.
> Then lhs-rhs.
> For eq2, do the same.

I'm sorry to revive this, but for a system like this, there are problems:

eq:makelist(0,6)$
eq[1]:(40*sqrt(x3*x4)*y2+40*sqrt(x1*x2)*y1)/41-0.35549$
eq[2]:(40*sqrt(x1*x2)*sqrt(x3*x4)*y1*y2)/41-0.017904$
eq[3]:-(-4*y2-4*y1+20*sqrt(x3*x4)-10*x4-10*x3+20*sqrt(x1*x2)-10*x2-10*x1)/41-2.3362$
eq[4]:-(80*sqrt(x1*x2)*y2-40*x1*y2+x4*(-y2-y1)+x3*(-40*y2-y1)+x2*(-40*y2-1)+2*sqrt(x3*x4)*y1-40*x1*y1)/41-4.4314$
eq[5]:-(x3*(-4*y1*y2-10*x1*y1)+x4*(-10*x2*y2-10*x1*y2-10*x1*y1)-*x2*y1*y2+20*sqrt(x1*x2)*x4*y2+20*x1*sqrt(x3*x4)*y1)/41-2.7884$
eq[6]:(x2*x4*y1*y2+40*x1*x3*y1*y2)/41-2.959$

What I'm trying to do is to solve (symbolically) for sqrt(x1*x2), then
for sqrt(x3*x4), until there are no more radicals, so that I can pass
it on to hompack_polsys(). If it works, it can be made recursively
with the condition to stop as freeof(sqrt()). For the first two
equations, it works, but for the rest, I get strange outputs. This is
what I tried:

solve(eq2[1],sqrt(x1*x2))^2$ solve(%,[sqrt(x3*x4)])^2,expand,numer;  /* works */
solve(eq2[2],sqrt(x1*x2))^2,expand,numer;  /* works */
solve(eq2[3],sqrt(x1*x2))^2$ solve(%,sqrt(x3*x4))^2; num(rhs(%));  /* fails */
solve(eq2[4],sqrt(x1*x2))^2$ solve(%,sqrt(x3*x4))^2; num(rhs(%));
denom(rhs(%th(2)));  /* fails */
solve(eq2[5],sqrt(x1*x2))^2$ solve(%,sqrt(x3*x4))^2; num(rhs(%));
denom(rhs(%th(2)));  /* fails */

Is it because the numbers get very high? keepfloat:true seems to be
ignored by solve(). What's strange is that, without the raise to
power, the second solve() displays a result, as it should. It's a long
result, large numbers, but it is displayed. The raise to power will
make those numbers considerably longer, but even if I append
",expand,numer" at the end, it still fails.


Regards,
Vlad