[Maxima] Solving a two equation system yields strange results
Jason Filippou
jason.filippou at gmail.com
Wed May 9 13:47:56 CDT 2012
Pardon, the second equation (2) should read (as is implied by the
output that I typed in):
(%i7) exp(-1/b) * sum(1/(i! * b^i), i, 0, k -1) = 0.02;
k - 1
====
- 1/b \ 1
(%o7) %e > ----- = 0.02
/ i
==== b i!
i = 0
Still no luck though.
Jason
On Wed, May 9, 2012 at 9:46 PM, Jason Filippou <jason.filippou at gmail.com> wrote:
> 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/
> LinkedIn! Profile: http://www.linkedin.com/profile/view?id=132927442&trk=tab_pro
>
>
> --
> Jason Filippou
> Research Associate
> NCSR Demokritos
> NCSR Webpage: http://users.iit.demokritos.gr/~jfilip/
> D.I.T Webpage: http://cgi.di.uoa.gr/~std06142/
> LinkedIn! Profile: http://www.linkedin.com/profile/view?id=132927442&trk=tab_pro
--
Jason Filippou
Research Associate
NCSR Demokritos
NCSR Webpage: http://users.iit.demokritos.gr/~jfilip/
D.I.T Webpage: http://cgi.di.uoa.gr/~std06142/
LinkedIn! Profile: http://www.linkedin.com/profile/view?id=132927442&trk=tab_pro
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