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

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

Hello Everyone


This system of polynomials involves sqrt():

eq1 : 0.97561*sqrt(x*y)*z-0.009879$
eq2 : 0.097561*z-0.4878*sqrt(x*y)+0.2439*y+0.2439*x-0.98506$
eq3 : 0.02439*y*z+0.97561*x*z-0.90247$

But solve() seems to fail, to_poly_solve() takes ages without results,
while minpack_solve aborts with:

 The value
   ((MEQUAL SIMP) 0.97561 0.009879)
 is not of type
   REAL

I found this post:
https://math.stackexchange.com/questions/174021/complex-equation-in-maxima
and I tried to monkey-see-monkey-do, but it doesn't seem to work:

(algebraic:true, tellrat(M^2=x*y));
rat([0.97561*M*z=0.009879,0.097561*z-0.4878*M+0.2439*y+0.2439*x=0.98506,0.02439*y*z+0.97561*x*z=0.90247]);
solve(%,[M,z]);  /* result is empty [] */
/* solve(%);  /* error: "solve: more unknowns than equations." */
rat(%);
solve(%,[x,y,z]);

I think it's because there's both sqrt(x*y) and x+y in the 3rd
equation. Is there any workaround for this? The hompack version that
Raymond Toy is working on seems to accept non-integer powers for the
coefficients, but it's not in Maxima (yet?). If it matters, the
equations are the result of a (2nd order) transfer function involving
coupled inductors.


Regards,
Vlad