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RE: Problems with SIMPLIFY and SOLVE

• To: mathgroup at smc.vnet.net
• Subject: [mg34150] RE: [mg34111] Problems with SIMPLIFY and SOLVE
• From: "Higinio Ramos" <higra at usal.es>
• Date: Tue, 7 May 2002 03:53:42 -0400 (EDT)
• References: <200205040828.EAA01722@smc.vnet.net>
• Reply-to: "Higinio Ramos" <higra at usal.es>
• Sender: owner-wri-mathgroup at wolfram.com

You may do a substitution, solving for m ,and then doing the substitution
backwards.


Copy and paste in a mathematica notebook from here:
***************

Notebook[{

Cell[CellGroupData[{
Cell[BoxData[
    \(a/\((a\  + \ b\  + \ n)\)\  == \
        m^\((\(-1\)\  + \ a\  + \ b\  + \
                n)\)*\((a/\((a\  + \ b\  + \ n)\))\)^
            a\n*\((\((b\  + \ n)\)/\((a\  + \ b\  + \
                    n)\))\)^\((b\  + \ n)\)*\((a\  + \ b\  + \
              n)\) /. {a + b + n \[Rule] z}\)], "Input"],

Cell[BoxData[
    \(a\/z ==
      m\^\(\(-1\) + z\)\ \((a\/z)\)\^a\ \((\(b + n\)\/z)\)\^\(b + n\)\
\ z\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    StyleBox[\(Solve[
        a\/z ==
          m\^\(\(-1\) + z\)\ \((a\/z)\)\^a\ \((\(b + n\)\/z)\)\^\(b + \
n\)\ z, \ m]\),
      FormatType->StandardForm]], "Input"],

Cell[BoxData[
    \({{m \[Rule] \((\(a\ \((a\/z)\)\^\(-a\)\ \((\(b + \
n\)\/z)\)\^\(\(-b\) - n\)\)\/z\^2)\)\^\(1\/\(\(-1\) + z\)\)}}\)], \
"Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \({{m \[Rule] \((\(a\ \((a\/z)\)\^\(-a\)\ \((\(b + \
n\)\/z)\)\^\(\(-b\) - n\)\)\/z\^2)\)\^\(1\/\(\(-1\) + z\)\)}} /. {z ->
          a + b + n}\)], "Input"],

Cell[BoxData[
    \({{m \[Rule] \((\(a\ \((a\/\(a + b + n\))\)\^\(-a\)\ \((\(b + \
n\)\/\(a + b + n\))\)\^\(\(-b\) - n\)\)\/\((a + b + n)\)\^2)\)\^\(1\/\
\(\(-1\) + a + b + n\)\)}}\)], "Output"]
}, Open  ]]
},
FrontEndVersion->"4.1 for Microsoft Windows",
ScreenRectangle->{{0, 800}, {0, 527}},
WindowSize->{792, 500},
WindowMargins->{{0, Automatic}, {Automatic, 0}}
]

**************
Higinio

----- Original Message -----
From: Hannes Egli <hannes.egli at uni-greifswald.de>
To: mathgroup at smc.vnet.net
Subject: [mg34150] [mg34111] Problems with SIMPLIFY and SOLVE


> Hello
>
> 1)
> After the following input, I would expect the output TRUE, since after
> my mathematical understanding, the expression is unambiguously
> negative. Mathematica, however, only restates the expression.
>
> Element[{a, b, n, m}, Reals]
>
> Simplify[-m^(-2 + a + b + n)*(-1 + a + b + n)*(a/(a + b + n))^a
> *((b + n)/(a + b + n))^(b + n)*(a + b + n) < 0, {a > 0, b > 0, n > 0,
> a + b + n > 1}]
>
>
> 2)
> The second problem may be similar. Given the restriction on the
> parameter values, the following equation should can be solved for m:
>
> Element[{a, b, n, m}, Reals]
>
> Solve[a/(a + b + n) - m^(-1 + a + b + n)*(a/(a + b + n))^a
> *((b + n)/(a + b + n))^(b + n)*(a + b + n) == 0, m]
>
> Does somebody see what I am doing wrong?
>
> Thanks
>
> Hannes
>
>

• References:
  • Problems with SIMPLIFY and SOLVE
    • From: hannes.egli@uni-greifswald.de (Hannes Egli)