From mboxrd@z Thu Jan  1 00:00:00 1970
From: Miguel Ruiz <rbenit68@openmailbox.org>
Subject: Two numerical solutions from fsolve inside calc source block
Date: Sun, 26 Jun 2016 15:53:26 +0200
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To: Emacs Orgmode <emacs-orgmode@gnu.org>

Hi,

I have this block which is intended to get the two numerical solutions=20
of the equations system:

#+begin_src calc
fsolve([8.66e10 =3D r * v, -7.51e6 =3D 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=20
manual "It will invent variables n1, n2, =E2=80=A6, which represent indep=
endent=20
arbitrary integers, and s1, s2, =E2=80=A6, which represent independent ar=
bitrary=20
signs (either +1 or -1)."

So I get

#+RESULTS:
: [r =3D 86600000000. / (4621.24711316 - 2517.12631405 s1), v =3D=20
4621.24711316 - 2517.12631405 s1]

Now, to get the two solutions I have to evaluate manually the result=20
expression replacing s1 by "*1" and "*-1"

#+begin_src calc
[r =3D 86600000000. / (4621.24711316 - 2517.12631405 *1), v =3D=20
4621.24711316 - 2517.12631405 *1]
#+end_src

#+RESULTS:
: [r =3D 41157332.8093, v =3D 2104.12079911]

And

#+begin_src calc
[r =3D 86600000000. / (4621.24711316 - 2517.12631405 *-1), v =3D=20
4621.24711316 - 2517.12631405 *-1]
#+end_src

#+RESULTS:
: [r =3D 12131615.2598, v =3D 7138.37342721]

Emacs calc manual states "Note that variables like n1 and s1 are not=20
given any special interpretation in Calc except by the equation solver=20
itself. As usual, you can use the s l (calc-let) command to obtain=20
solutions for various actual values of these variables.", but I cannot=20
figure out a way to call (calc-let) or its algebraic equivalent inside a=20
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.