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Re: Bug in Reduce?


This does indeed like a bug.

The documentation states:

When expr involves only polynomial conditions, Reduce[expr, vars,  
Reals] gives a cylindrical algebraic decomposition of expr.

However


FullSimplify[CylindricalDecomposition[
    {a*c - b*d == 0, a*d + b*c == 0}, {a, b, c, d}]]


(a == 0 && b == 0) || (c == 0 && d == 0)

so something is definitely fishy, particularly that if you call  
Reduce without explicit variables you get the same correct answer as  
above


FullSimplify[Reduce[{a*c - b*d == 0, a*d + b*c == 0},
    Reals]]


(c == 0 && d == 0) || (a == 0 && b == 0)

Andrzej Kozlowski




On 15 Sep 2005, at 18:16, Kennedy wrote:

> The source of this apparent bug could be my misunderstanding of the  
> middle,
> "vars" parameter of Reduce, but it sure seems like the following  
> output
> indicates that  c  must be  0  for my two equations to be  
> satisfied, when in
> fact if  a  and  b  are both  0,  c  does not need to be  0.
>
> Regards,
> Jack
>
> In[1]:=
> Reduce[{a c - b d == 0, a d + b c == 0}, {a, b, c, d}, Reals] //
> FullSimplify
>
> Out[1]=
> c == 0 && (d == 0 || (a == 0 && b == 0))
>
> (version 5.1 for Windows)
>
>


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