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

[Richard F. <fa...@cs...>]

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.
    You may think that this introduces extraneous roots, but maybe not.
After all sqrt(x*y)  has two values, + and -.
Anyway, after   these transformations, the expressions are
(%i23)    [eq1x,eq2x,eq3]
     ;
(%o23)    [(x*y-97594641/(951814872100*z^2))*z^2, 
x*y-(97561*z+243900*y+243900*x-985060)^2/237948840000, 
0.02439*y*z+0.97561*x*z-0.90247]

which can be solved by solve in 0.28 seconds on my computer.


(%i22)    solve([eq1x,eq2x,eq3],[x,y,z]);

rat: replaced -0.90247 by -90247/100000 = -0.90247
rat: replaced 0.97561 by 97561/100000 = 0.97561
rat: replaced 0.02439 by 2439/100000 = 0.02439
(%o22) 
[[x=3.857950974230044,y=4.622955406728833*10^-4,z=0.2397720333808264],
[x=0.09384399438540204,y=1.124525992213461*10^-5,z=9.857090374724468],[x=1.51153204485603*10^-7-2.451968450417641*10^-7*%i,y=2.018288378565508-3.274015555891547*%i,z=8.189435454935102*%i+5.04843123789219],[x=2.451968450417641*10^-7*%i+1.51153204485603*10^-7,y=3.274015555891547*%i+2.018288378565507,z=5.048431237892189-8.189435454935102*%i],[x=4.034937888198757,y=4.835037908040265*10^-4,z=0.2292547568710359],[x=0.09374397222400822,y=1.123327481017417*10^-5,z=9.867608120035305],[x=1.513187556171237*10^-7-2.452800239005231*10^-7*%i,y=2.02049891671416-3.275126209976234*%i,z=8.183250844485642*%i+5.04843123789219],[x=2.452800239005231*10^-7*%i+1.513187556171237*10^-7,y=3.275126209976235*%i+2.02049891671416,z=5.048431237892189-8.183250844485642*%i]]


There are 8 solutions there.
The first two are real.




On 9/14/2020 8:42 AM, Raymond Toy wrote:
>
>
> On Mon, Sep 14, 2020 at 8:32 AM Me Self <vla...@gm... 
> <mailto:vla...@gm...>> wrote:
>
>     > What starting points did you use?
>     >
>     > I got:
>     >
>     > minpack_solve([eq1,eq2,eq3],[x,y,z], [1,1,1]);
>     > Evaluation took 0.0100 seconds (0.0100 elapsed) using 942.305 KB.
>     >
>     > [[5.740409864561979,-1.755503737103853,0.1624466869294288],
>     >  0.01024886625263842,4]$
>
>     So do I, now. In fact, with a bit of tuning, it solves it just fine. I
>     think this happened because of the previous actions, I probably should
>     have used kill() before switching to minpack_solve(). I apologize for
>     the noise.
>
>
> If you can reproduce the issue, it would be nice to know; maybe some 
> check can be added to give a much better answer than just some random 
> lisp type error.
>
>
>
>     Regards,
>     Vlad
>
>
>
> -- 
> Ray
>
>
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