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MathGroup Archive 2005

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Solve yields unreal solutions, NSolve yields real solutions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58278] Solve yields unreal solutions, NSolve yields real solutions
  • From: "Mukhtar Bekkali" <mbekkali at gmail.com>
  • Date: Sat, 25 Jun 2005 01:56:40 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I thought NSolve is the same as Solve just numeric. The below code
gives real answers, replacing NSolve with Solve in the last line
generates Unreal results.  I do not understand why.

\!\(\*
  RowBox[{\(Clear["\<Global`*\>"]\), "\n", \(Remove["\<Global`*\>"]\),
    "\[IndentingNewLine]", \(Needs["\<Miscellaneous`RealOnly`\>"]\),
    "\[IndentingNewLine]",
    RowBox[{
      RowBox[{
        RowBox[{
          StyleBox["{",
            FontColor->RGBColor[1, 0, 1]],
          StyleBox[\(\[Lambda], \[Gamma], k\),
            FontColor->RGBColor[1, 0, 1]],
          StyleBox["}",
            FontColor->RGBColor[1, 0, 0]]}],
        StyleBox["=",
          FontColor->RGBColor[1, 0, 0]],
        RowBox[{
          StyleBox["{",
            FontColor->RGBColor[1, 0, 0]],
          RowBox[{"1",
            StyleBox[",",
              FontColor->RGBColor[1, 0, 0]], \(2\/3\), ",", "0"}],
"}"}]}],
      ";"}], "\[IndentingNewLine]", \(Table[h\_i = \[Gamma], {i, 1,
k}];\),
    "\[IndentingNewLine]", \(Table[h\_i = 1 - \[Gamma], {i, k + 1,
2}];\),
    "\[IndentingNewLine]", \(Table[{p\_i, b\_i} = {p\_i, b\_i}, {i, 1,
2}];\),
     "\[IndentingNewLine]", \(T\_p = Table[p\_i, {i, 1, 2}];\),
    "\[IndentingNewLine]", \(T\_b = Table[b\_i, {i, 1, 2}];\),
    "\[IndentingNewLine]", \(T\_u =
        Table[u\_i = 1 - \[Lambda] \((b\_i - \[Beta])\)\^2 - p\_i, {i,
1,
            2}];\), "\[IndentingNewLine]", \({I\_0, I\_1,
          I\_2} = {0, \[Beta] /. \(Solve[
                u\_1 \[Equal] u\_2, \[Beta]]\)[\([1]\)], 1};\),
    "\[IndentingNewLine]", \(T\_m =
        Table[m\_i = I\_i - I\_\(i - 1\), {i, 1, 2}];\),
    "\[IndentingNewLine]", \(T\_R =
        Table[R\_i = \(p\_i\)
                m\_i - \((\(h\_i\)
                    b\_i\^2\/2 + \((1 - h\_i)\) \((1 -
b\_i)\)\^2\/2)\), {i,
            1, 2}];\),
    "\[IndentingNewLine]", \(FOCP = Table[D[R\_i, p\_i], {i, 1, 2}];\),

    "\[IndentingNewLine]", \(T\_p =
        T\_p /. \(Solve[FOCP \[Equal] 0, T\_p]\)[\([1]\)];\),
    "\[IndentingNewLine]", \(Table[p\_i = T\_p[\([i]\)], {i, 1, 2}];\),

    "\[IndentingNewLine]", \(FOCB = Table[D[R\_i, b\_i], {i, 1, 2}];\),

    "\[IndentingNewLine]", \(NSolve[FOCB \[Equal] 0, T\_b]\)}]\)


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