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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;
> }
>
>
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