Re: Does Mathematica think Sqrt[2] is rational?

*To*: mathgroup at smc.vnet.net*Subject*: [mg86678] Re: Does Mathematica think Sqrt[2] is rational?*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Tue, 18 Mar 2008 04:49:20 -0500 (EST)

On 3/17/08 at 12:22 AM, maderri2 at gmail.com (magma) wrote: >expr2 = Exists[{x, y}, x^2 == 2 y^2] >Mathematica correctly finds out that expr is true over the reals >Reduce[expr2, {x, y}, Reals] >But gives a wrong answer over the integers or the rationals >Reduce[expr2, {x, y}, Integers] >Reduce[expr2, {x, y}, Rationals] I believe you are overlooking the trivial solution In[5]:= Assuming[x \[Element] Integers && y \[Element] Integers, FindInstance[expr2, {x, y}]] Out[5]= {{x->0,y->0}}