       Re: Solve bug !!

• To: mathgroup at smc.vnet.net
• Subject: [mg31220] Re: [mg31196] Solve bug !!
• From: Tomas Garza <tgarza01 at prodigy.net.mx>
• Date: Fri, 19 Oct 2001 03:12:16 -0400 (EDT)
• References: <200110170935.FAA19667@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```It looks as a bug, but in fact the trouble is that *Solve deals primarily
with linear and polynomial equations* (see Help browser). What seems to be
happening here is that there are zeros which have not been detected by
Solve, among them those which you correctly identify with the missing minus
sign. Indeed, we have that

In:=
Simplify[(E^(-c))^2 - A/E^c + 1 /.
c -> -Log[(1/2)*(A + Sqrt[-4 + A^2])]]
Out=
0

i.e., writing the missing minus sign results in a zero of your function. But
it turns out that

In:=
Simplify[(E^(-c))^2 - A/E^c + 1 /.
c -> Log[(1/2)*(A + Sqrt[-4 + A^2])]]
Out=
0

so that the result given by Solve with the missing minus sign is also a
zero. The conclusion is that using Solve with trascendental equations may
provide some, but not necessarily all, of the solutions. Not really a bug.

Tomas Garza
Mexico City

----- Original Message -----
From: "Marcel" <arzo at exp.uji.es>
To: mathgroup at smc.vnet.net
Subject: [mg31220] [mg31196] Solve bug !!

> Where is the minus sign whe must obtain in the second case??
>
> > Solve[(E^c)^2 - A*E^c + 1 == 0, c]
>
> {{c -> Log[(1/2)*(A - Sqrt[-4 + A^2])]},
>   {c -> Log[(1/2)*(A + Sqrt[-4 + A^2])]}}
>
> > Solve[(E^(-c))^2 - A*E^(-c) + 1 == 0, c]
>
> {{c -> Log[(1/2)*(A - Sqrt[-4 + A^2])]},
>   {c -> Log[(1/2)*(A + Sqrt[-4 + A^2])]}}
>
>
> Mathematica 4.1, Windows 2000 SP2, PII400.
>
> Marcel Aguilella
>
>
>

```

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