       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[{%[] >= 0, %[] >= 0, %[] >= 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
>
> Thanks,
> V. Stokes
>
Hi Virgil,

In Mathematica, "Everything is an expression." Therefore, you can
manipulate the result made of inequalities as any expression.

In:=
BInv = {{1/4, 1/4, 0}, {-2^(-1), 1/2, 0}, {3/4, -5/4, 1}};
B = Inverse[BInv];
b = {4 + Î´, 8, 10};
FullSimplify[BInv . b];
Reduce[{%[] >= 0, %[] >= 0, %[] >= 0}, {Î´}];
sol = FullSimplify[% /. {Î´ -> b1 - 4}]

Out=
0 <= b1 <= 8

In:=
FullForm[sol]

Out//FullForm=
FullForm[Inequality[0, LessEqual, b1, LessEqual, 8]]

In:=
lowval = First[sol]

Out=
0

In:=
upval = Last[sol]

Out=
8

Regards,
Jean-Marc

```

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