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Re: refining expression in terms of real numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg58837] Re: refining expression in terms of real numbers
• From: "Mukhtar Bekkali" <mbekkali at gmail.com>
• Date: Wed, 20 Jul 2005 00:29:38 -0400 (EDT)
• References: <dba4l5$elr$1@smc.vnet.net><dbd0ll$2pm$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Thanks Peter.  This follow up question pertains to your remark
regarding Mathematica changing the order of solutions.  For example, in
this code

\!\(\(γ = 5\/7;\)\[IndentingNewLine]
  \(T = \(Root[243\ γ - 54\ λ + 432\ γ\ λ +
    54\ γ\^2\ λ -
          96\ λ\^2 + 108\ γ\ λ\^2 - 10\ λ\^3 - 243\ #1 - 540\ λ\
#1 - 324\ γ\
                λ\ #1 - 252\ λ\^2\ #1 - 216\ γ\ λ\^2\ #1 - 24\
                λ\^3\ #1 + 216\ λ\ #1\^2 + 216\ λ\^2\ #1\^2 + 72\
λ\^3\ #1\^2 \
+ 48\ λ\^2\ #1\^3 + 32\ λ\^3\ #1\^3 &, #] &\) /@ Range[3];\)\
\[IndentingNewLine]
  \(TR := Refine[ToRadicals[T[\([i]\)]], {1\/2 � \ γ � \
                1 - λ\/4, 2 > λ > 0}];\)\[IndentingNewLine]
  \(Table[Plot[Evaluate[{TR, T[\([i]\)]}], {λ, 1\/2,
                3\/2}, PlotStyle \[Rule] {Hue[0], Hue[ .7]}], {i, 1,
3}];\)\
\[IndentingNewLine]
  \)

function TR looks nothing like T.  Something weird is happening behind
the scenes. Mukhtar Bekkali