Re: cannot solve *trivial* equation
- To: mathgroup at smc.vnet.net
- Subject: [mg34391] Re: [mg34380] cannot solve *trivial* equation
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Sat, 18 May 2002 03:50:50 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Friday, May 17, 2002, at 07:31 PM, Marco Manfredini wrote:
> Hi,
>
> I just tried a friend's Mathematica 4.0.0.0:
>
> Solve[{A == S + Q, Q == 2*S}, A]
>
> => {A->3*S}
>
> Solve[{A == S + Q, Q == 2*S}, S]
>
> => {}
>
> Can somebody explain this to me? (ie. "bug","you stupid")
>
> Marco
>
>
>
>
>
>
Read the documentation, you stupid. (Sorry, but you yourself asked for
it).
Solve only finds generic solutions, that is those that hold without any
restrictions on the parameters. But in your case there are no such
solutions: take A=Q=1 and you get incompatible equations. In other
words you need restrictions on the parameters. The function to use in
such cases is Reduce:
In[1]:=
Reduce[{A == S + Q, Q == 2*S}, S]
Out[1]=
2*A == 3*Q && S == Q/2
This tells you that a solution, S=Q/2 exists only if the condition
2*A == 3*Q is satisifed. That is why Solve did not find a generic
solution, there aren't any.
Andrzej
PS. You didn't really think that a bug of this kind would have survived
long enough for you to discover it, did you?
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/