RE: Simplifying with assumptions

*To*: mathgroup at smc.vnet.net*Subject*: [mg48980] RE: [mg48949] Simplifying with assumptions*From*: "Simons, F.H." <F.H.Simons at tue.nl>*Date*: Fri, 25 Jun 2004 17:52:23 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com*Thread-topic*: [mg48949] Simplifying with assumptions

Mietek, It does not look like a silly question! Maybe an analytical solution for this problem exists, but here are some Mathematica commands that will give you some solutions. I rewrite your problem in the following form: In[1]:= eq = 48 - n^2 + 8*x==m^2 Out[1]= 48 - n^2 + 8*x == m^2 Mathematica can rewrite the equation In[2]:= Reduce[eq,{n,m,x}]//Simplify Out[2]= m^2 + n^2 == 8*(6 + x) So x has to be at least -6. Here are some solutions: In[3]:= Table[{x, Reduce[eq&& m\[GreaterEqual]0&&n\[GreaterEqual]0, {n,m}, Integers]}, {x,-6, 10}]; DeleteCases[%, {_, False}] Out[4]= {{-6, n == 0 && m == 0}, {-4, n == 0 && m == 4 || n == 4 && m == 0}, {-1, n == 2 && m == 6 || n == 6 && m == 2}, {2, n == 0 && m == 8 || n == 8 && m == 0}, {4, n == 4 && m == 8 || n == 8 && m == 4}, {7, n == 2 && m == 10 || n == 10 && m == 2}} Maybe this is of some help for you. Regards, Fred Simons Eindhoven University of Technology > -----Original Message----- > From: Mietek Bak [mailto:mietek at icpnet.pl] To: mathgroup at smc.vnet.net > Sent: vrijdag 25 juni 2004 8:58 > To: mathgroup at smc.vnet.net > Subject: [mg48980] [mg48949] Simplifying with assumptions > > > Hello, > > I'm a complete newcomer to Mathematica, so please excuse this possibly > silly question. > > I'm trying to determine if a formula will ever give an integer result, > assuming that all variables used in it are integer. I've > been searching > through the built-in documentation, but my best guess didn't really do > anything: > > Simplify[Element[Sqrt[48 - n^2 + 8*x],Integers],Element[{n, > x},Integers]] > > It would be best if I could somehow determine the set of > combinations of > variables that would give an integer result -- if there are any. Is > there a way to do that in Mathematica? > > Thanks in advance, > Mietek Bak. > > > -- > desp; > } > >