Re: Is this a bug?
- To: mathgroup at smc.vnet.net
- Subject: [mg90845] Re: Is this a bug?
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Sat, 26 Jul 2008 04:20:49 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <g6c982$brv$1@smc.vnet.net>
mailcwc at gmail.com wrote:
> I tried to solve the following equation with mathematica 6.03
>
> Solve[{Abs[X+Y I]==5,X==3},{X,Y}]
>
> and got the answer
>
> {{X -> 3, Y -> -2 I}, {X -> 3, Y -> 8 I}}
>
> Am I suppose to get {{X -> 3, Y -> 4 I}, {X -> 3, Y -> -4 I}} ?
No. Mathematica is correct. Also, from the online help, "Solve gives
generic solutions only. It discards solutions that are valid only when
the parameters satisfy special conditions. Reduce gives the complete set
of solutions." For instance,
In[1]:=
eqns = {Abs[x + y*I] == 5, x == 3};
sols = Solve[eqns]
eqns /. sols
eqns /. {{x -> 3, y -> 4 I}, {x -> 3, y -> -4 I}}
Reduce[eqns]
Out[2]= {{x -> 3, y -> -2 I}, {x -> 3, y -> 8 I}}
Out[3]= {{True, True}, {True, True}}
Out[4]= {{False, True}, {False, True}}
Out[5]=
2
-2 <= Im[y] <= 8 && (Re[y] == -Sqrt[16 + 6 Im[y] - Im[y] ] ||
2
Re[y] == Sqrt[16 + 6 Im[y] - Im[y] ]) && x == 3
See
http://reference.wolfram.com/mathematica/ref/Solve.html
http://reference.wolfram.com/mathematica/ref/Reduce.html
Regards,
-- Jean-Marc