Re: On Reduce
- To: mathgroup at smc.vnet.net
- Subject: [mg72046] Re: On Reduce
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Sat, 9 Dec 2006 06:09:55 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <elbi51$k23$1@smc.vnet.net>
Virgil Stokes wrote:
> I have the following small piece of Mathematica code that works fine for
> my purposes.
>
> BInv = {{ 1/4, 1/4, 0},
> {-1/2, 1/2, 0},
> { 3/4, -5/4, 1}}
> B = Inverse[BInv]
> b = {4 + \[Delta], 8, 10};
> BInv.b // FullSimplify
> Reduce[{%[[1]] >= 0, %[[2]] >= 0, %[[3]] >= 0}, {\[Delta]}]
> % /. {\[Delta] -> b1 - 4} // FullSimplify
>
> which gives
>
> 0 <= b1 <= 8
>
> which is of course correct. But, how can I use (access) the values 0 and 8?
> That is, I would like to now use these values in some expressions that
> would follow this.
>
> Thanks,
> V. Stokes
>
Hi Virgil,
In Mathematica, "Everything is an expression." Therefore, you can
manipulate the result made of inequalities as any expression.
In[1]:=
BInv = {{1/4, 1/4, 0}, {-2^(-1), 1/2, 0}, {3/4, -5/4, 1}};
B = Inverse[BInv];
b = {4 + δ, 8, 10};
FullSimplify[BInv . b];
Reduce[{%[[1]] >= 0, %[[2]] >= 0, %[[3]] >= 0}, {δ}];
sol = FullSimplify[% /. {δ -> b1 - 4}]
Out[6]=
0 <= b1 <= 8
In[7]:=
FullForm[sol]
Out[7]//FullForm=
FullForm[Inequality[0, LessEqual, b1, LessEqual, 8]]
In[8]:=
lowval = First[sol]
Out[8]=
0
In[9]:=
upval = Last[sol]
Out[9]=
8
Regards,
Jean-Marc