Solving a two equation system yields strange results
Subject: Solving a two equation system yields strange results
From: Raymond Toy
Date: Wed, 9 May 2012 13:24:43 -0700
On Wed, May 9, 2012 at 11:46 AM, 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]);
>
> This seems a bit ill-defined. Since k is the upper limit of the sum, what
do you expect sum(...,i,0,k-1) be when k is not an integer? Do you mean to
take the floor of k-1?
Ray