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Bug report for Reduce

Posted 11 years ago
There is a bug in functionality of "Reduce" in Mathematica 9:
In[10]:= Reduce[3 x^2 + 8 x y + 2 y^2 == 0, {x, y}, Integers]

Out[10]= False
Which is evident that there is a solution, namely:
x == 0 && y == 0

On the other hand:
 In[9]:= Reduce[3 x^2 + 8 x y + 2 y^2 == 0, {x, y}, Rationals]
 
 Out[9]= (x | y) \[Element]
   Rationals && ((x <
       0 && (y == -2 x - Sqrt[5/2] Abs[x] ||
        y == -2 x + Sqrt[5/2] Abs[x])) || (x == 0 &&
      y == 0) || (x >
       0 && (y == -2 x - Sqrt[5/2] Abs[x] ||
        y == -2 x + Sqrt[5/2] Abs[x])))

It is not able to solve such a trivial equation, and it thinks like there may be many solutions, while again x=0, y=0 is the only solution also for Rationals.
POSTED BY: Azer Bajdzan
Thank you for your feedback. In future please send this type of reports to the Technical Support using this form.
POSTED BY: Moderation Team

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