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FullSimplify interpretation

• To: mathgroup at smc.vnet.net
• Subject: [mg86467] FullSimplify interpretation
• From: Brian Beckage <Brian.Beckage at uvm.edu>
• Date: Wed, 12 Mar 2008 00:10:55 -0500 (EST)

Hi all,

Can anyone provide some guidance on how to interpret the result of  
FullSimplify[ ] given in the Cell Expression copied below?  I'm  
specifically wondering how to interpret the conditional nature of the  
result.

Thanks for your help!

Best wishes,
Brian



Cell[CellGroupData[{Cell[BoxData[
  RowBox[{" ",
   RowBox[{"d1EIGwP", "=",
    RowBox[{"FullSimplify", "[",
     RowBox[{
      RowBox[{
       RowBox[{"d1EIG", "[",
        RowBox[{"[", "3", "]"}], "]"}], "/.", "parmListND1"}], ",",
      RowBox[{
       RowBox[{"c", ">", "0"}], " ", "&&",
       RowBox[{"c", "\[Element]", "Reals"}], "&&",
       RowBox[{
        SubscriptBox["M", "g"], ">", "0"}], " ", "&&",
       RowBox[{
        SubscriptBox["M", "g"], "\[Element]", "Reals"}], "&&",
       RowBox[{
        SubscriptBox["r", "g"], ">", "0"}], "&&",
       RowBox[{
        SubscriptBox["r", "g"], "\[Element]", "Reals"}], "&&",
       RowBox[{
        SubscriptBox["M", "p"], ">", "0"}], "&&",
       RowBox[{
        SubscriptBox["M", "p"], "\[Element]", "Reals"}], "&&",
       RowBox[{
        SubscriptBox["r", "p"], ">", "0"}], "&&",
       RowBox[{
        SubscriptBox["r", "p"], "\[Element]", "Reals"}]}]}], "]"}],
    " "}]}]], "Input",
  CellChangeTimes->{{3.413589871370825*^9, 3.413589953706039*^9},
    3.413589997339566*^9, {3.4135900344682426`*^9,
    3.413590190426937*^9}, {3.414235731209591*^9,
    3.414235759758086*^9}, {3.414236913610442*^9,
    3.4142369526933117`*^9}, {3.4142398465364103`*^9,
    3.4142398469656754`*^9}}],

Cell[BoxData[
  RowBox[{"{",
   RowBox[{
    RowBox[{"\[Piecewise]", GridBox[{
       {
        RowBox[{"-", "1"}],
        RowBox[{
         RowBox[{
          RowBox[{"c", " ",
           SubscriptBox["M", "g"], " ",
           RowBox[{"(",
            RowBox[{
             SubscriptBox["r", "g"], "+",
             SubscriptBox["r", "p"]}], ")"}]}], "+",
          RowBox[{
           SubscriptBox["r", "g"], " ",
           RowBox[{"(",
            RowBox[{
             RowBox[{
              RowBox[{"-", "c"}], " ",
              SubscriptBox["M", "p"]}], "+",
             SubscriptBox["r", "g"], "+",
             SubscriptBox["r", "p"]}], ")"}]}]}], "\[GreaterEqual]",
         "0"}]},
       {
        RowBox[{
         RowBox[{"-",
          FractionBox[
           RowBox[{"c", " ",
            SubscriptBox["M", "p"]}],
           RowBox[{
            RowBox[{"c", " ",
             SubscriptBox["M", "g"]}], "+",
            SubscriptBox["r", "g"]}]]}], "+",
         FractionBox[
          SubscriptBox["r", "p"],
          SubscriptBox["r", "g"]]}],
        TagBox["True",
         "PiecewiseDefault",
         AutoDelete->False,
         DeletionWarning->True]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Left}}, "ColumnsIndexed" -> {},
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxItemSize->{
       "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {},
        "Rows" -> {{1.}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.84]},
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {},
        "Rows" -> {
          Offset[0.2], {
           Offset[0.4]},
          Offset[0.2]}, "RowsIndexed" -> {}}]}], ",",
    RowBox[{"\[Piecewise]", GridBox[{
       {
        RowBox[{"-", "1"}],
        RowBox[{
         RowBox[{
          RowBox[{"c", " ",
           SubscriptBox["M", "g"], " ",
           RowBox[{"(",
            RowBox[{
             SubscriptBox["r", "g"], "+",
             SubscriptBox["r", "p"]}], ")"}]}], "+",
          RowBox[{
           SubscriptBox["r", "g"], " ",
           RowBox[{"(",
            RowBox[{
             RowBox[{
              RowBox[{"-", "c"}], " ",
              SubscriptBox["M", "p"]}], "+",
             SubscriptBox["r", "g"], "+",
             SubscriptBox["r", "p"]}], ")"}]}]}], "<", "0"}]},
       {
        RowBox[{
         RowBox[{"-",
          FractionBox[
           RowBox[{"c", " ",
            SubscriptBox["M", "p"]}],
           RowBox[{
            RowBox[{"c", " ",
             SubscriptBox["M", "g"]}], "+",
            SubscriptBox["r", "g"]}]]}], "+",
         FractionBox[
          SubscriptBox["r", "p"],
          SubscriptBox["r", "g"]]}],
        TagBox["True",
         "PiecewiseDefault",
         AutoDelete->False,
         DeletionWarning->True]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Left}}, "ColumnsIndexed" -> {},
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxItemSize->{
       "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {},
        "Rows" -> {{1.}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.84]},
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {},
        "Rows" -> {
          Offset[0.2], {
           Offset[0.4]},
          Offset[0.2]}, "RowsIndexed" -> {}}]}]}], "}"}]], "Output",
  CellChangeTimes->{3.414236972638122*^9, 3.414239858373014*^9}]
}, Open  ]]

• Follow-Ups:
  • Re: FullSimplify interpretation
    • From: "Matthias Bode" <lvsaba@hotmail.com>