# [Maxima] Solving a two equation system yields strange results

Jason Filippou jason.filippou at gmail.com
Wed May 9 13:46:17 CDT 2012

```Good afternoon.

I've been using  Maxima 5.21.1 in a Debian GNU / Linux 2.6.32-5-686
system to solve a particular two equation system that I have to. The
system is as follows:

(1): b*(k - 1) = 0.1

(2): exp(-1/b) / sum(i! * b^i, i, 0, k -1) = 0.02

I've been using solve/2 for this, but I've been returned an empty
solution set. Namely:

%i9) solve([b * (k - 1) = 0.1, exp(-1/b) / sum(i! * b^i, i, 0, k -1) =
0.02], [b, k]);

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced -0.02 by -1/50 = -0.02
(%o9)                                 []

Now, normally I would assume that this means that the system doesn't
have a solution, but after substituting beta with its equivalent from
the first equation, i.e 0.1 / (k - 1), I noticed that the evaluation
of the second equation halts after a couple of steps:

(%i5) solve([exp(-(k - 1) / 0.1) * sum(1/(i! * (0.1 / (k-1))^i), i, 0,
k -1) = 0.02], [k]);

rat: replaced -0.02 by -1/50 = -0.02

rat: replaced 0.1 by 1/10 = 0.1

rat: replaced 10.0 by 10/1 = 10.0
%i %pi
------
5
1 - k                %e
(%o5) [%e      = -----------------------------------,
k - 1
====    i        i
1/10  1/5  \     10  (k - 1)  1/10
2     5    ( >    ------------)
/          i!
====
i = 0
2 %i %pi
--------
5
1 - k               %e
%e      = -----------------------------------,
k - 1
====    i        i
1/10  1/5  \     10  (k - 1)  1/10
2     5    ( >    ------------)
/          i!
====
i = 0
3 %i %pi
--------
5
1 - k               %e
%e      = -----------------------------------,
k - 1
====    i        i
1/10  1/5  \     10  (k - 1)  1/10
2     5    ( >    ------------)
/          i!
====
i = 0
4 %i %pi
--------
5
1 - k               %e
%e      = -----------------------------------,
k - 1
====    i        i
1/10  1/5  \     10  (k - 1)  1/10
2     5    ( >    ------------)
/          i!
====
i = 0
1 - k                      1
%e      = - -----------------------------------,
k - 1
====    i        i
1/10  1/5  \     10  (k - 1)  1/10
2     5    ( >    ------------)
/          i!
====
i = 0
5 k - 4 %i %pi - 5
- ------------------
5                             1
%e                     = -----------------------------------,
k - 1
====    i        i
1/10  1/5  \     10  (k - 1)  1/10
2     5    ( >    ------------)
/          i!
====
i = 0
5 k - 3 %i %pi - 5
- ------------------
5                             1
%e                     = -----------------------------------,
k - 1
====    i        i
1/10  1/5  \     10  (k - 1)  1/10
2     5    ( >    ------------)
/          i!
====
i = 0
5 k - 2 %i %pi - 5
- ------------------
5                             1
%e                     = -----------------------------------,
k - 1
====    i        i
1/10  1/5  \     10  (k - 1)  1/10
2     5    ( >    ------------)
/          i!
====
i = 0
5 k - %i %pi - 5
- ----------------
5                            1
%e                   = -----------------------------------,
k - 1
====    i        i
1/10  1/5  \     10  (k - 1)  1/10
2     5    ( >    ------------)
/          i!
====
i = 0
1 - k                    1
%e      = -----------------------------------]
k - 1
====    i        i
1/10  1/5  \     10  (k - 1)  1/10
2     5    ( >    ------------)
/          i!
====
i = 0

And then if I try to "solve" it any further I get no solutions:

(%i6) solve(%, [k]);
(%o6)                                 []

What am I doing wrong here?

Thanks,

Jason

--
Jason Filippou
Research Associate
NCSR Demokritos
NCSR Webpage: http://users.iit.demokritos.gr/~jfilip/
D.I.T Webpage: http://cgi.di.uoa.gr/~std06142/