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[O] Two numerical solutions from fsolve inside calc source block


From: Miguel Ruiz
Subject: [O] Two numerical solutions from fsolve inside calc source block
Date: Sun, 26 Jun 2016 15:53:26 +0200
User-agent: Roundcube Webmail/1.0.6

Hi,

I have this block which is intended to get the two numerical solutions of the equations system:

#+begin_src calc
fsolve([8.66e10 = r * v, -7.51e6 = 0.5*v^2 - 6.67e-11*6e24/r],[r,v])
#+end_src

This way I get the generic form of a multiple solution, and citing the manual "It will invent variables n1, n2, …, which represent independent arbitrary integers, and s1, s2, …, which represent independent arbitrary signs (either +1 or -1)."

So I get

#+RESULTS:
: [r = 86600000000. / (4621.24711316 - 2517.12631405 s1), v = 4621.24711316 - 2517.12631405 s1]

Now, to get the two solutions I have to evaluate manually the result expression replacing s1 by "*1" and "*-1"

#+begin_src calc
[r = 86600000000. / (4621.24711316 - 2517.12631405 *1), v = 4621.24711316 - 2517.12631405 *1]
#+end_src

#+RESULTS:
: [r = 41157332.8093, v = 2104.12079911]

And

#+begin_src calc
[r = 86600000000. / (4621.24711316 - 2517.12631405 *-1), v = 4621.24711316 - 2517.12631405 *-1]
#+end_src

#+RESULTS:
: [r = 12131615.2598, v = 7138.37342721]

Emacs calc manual states "Note that variables like n1 and s1 are not given any special interpretation in Calc except by the equation solver itself. As usual, you can use the s l (calc-let) command to obtain solutions for various actual values of these variables.", but I cannot figure out a way to call (calc-let) or its algebraic equivalent inside a calc source block.

I can accept a only-elisp workaround if it is more convenient.

Any hint to do everything commented without user interaction?

Regards.



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