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Re: significance arithmetic and numeric equation solving

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61589] Re: [mg61576] significance arithmetic and numeric equation solving
  • From: Pratik Desai <pdesai1 at umbc.edu>
  • Date: Sun, 23 Oct 2005 05:45:52 -0400 (EDT)
  • References: <200510220911.FAA15007@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Chris Chiasson wrote:

>Hello MathGroup,
>My last confession was...
>er...
>NSolve seems able to carry through significance arithmetic. FindRoot
>and NDSolve seem inable to do so.
>I would like to be able to solve the following equation for acCap[0]
>assuming cNapRatio->0
>(sorry about the FullForm, but I had to rid the post of the one way
>Notations I made), does anyone know a way to get Mathematica to do
>this?
>
>Equal[Times[Power[Log[10],-1],Log[acCap[cNapRatio]]],
>  Plus[Times[0.6107999999999999999`0.9956786262173576,cNapRatio],
>    Times[-2.0360000000000000001`2.9999999999999996,
>      Plus[Times[-0.0061540230743798795`0.9978339382434933,
>          Power[acCap[cNapRatio],-2],
>          Power[Power[acCap[cNapRatio],2],Rational[1,2]]],
>        Times[Power[2,Rational[-1,2]],
>          Power[Plus[Times[2,cNapRatio],
>              Times[0.0410268204958658633`3.3010299956639817,
>                Power[acCap[cNapRatio],-2],
>                Power[Power[acCap[cNapRatio],2],Rational[1,2]]]],
>            Rational[1,2]],
>          Power[Plus[1,
>              Times[Power[2,Rational[-1,2]],
>                Power[Plus[Times[2,cNapRatio],
>                    Times[0.0410268204958658633`3.3010299956639817,
>                      Power[acCap[cNapRatio],-2],
>                      Power[Power[acCap[cNapRatio],2],Rational[1,2]]]],
>                  Rational[1,2]]]],-1]]]]]]
>
>--
>Chris Chiasson
>http://chrischiasson.com/contact/chris_chiasson
>
>  
>
Hey Chris

Here is my somewhat belabored attempt, hope this is what you are looking 
for


Cell[BoxData[{
    RowBox[{"expr1", "=",
      RowBox[{"Equal", "[",
        RowBox[{
          RowBox[{"Times", "[",
            RowBox[{
              RowBox[{"Power", "[",
                RowBox[{
                  RowBox[{"Log", "[", "10", "]"}], ",",
                  RowBox[{"-", "1"}]}], "]"}], ",",
              RowBox[{"Log", "[",
                RowBox[{"acCap", "[", "cNapRatio", "]"}], "]"}]}], 
"]"}], ",",
          RowBox[{"Plus", "[",
            RowBox[{
              RowBox[{"Times", "[",
                RowBox[{"0.6107999999999999999`0.9956786262173576", ",", 
"cNapRatio"}], "]"}], ",",
              RowBox[{"Times", "[",
                RowBox[{
                  RowBox[{"-", 
"2.0360000000000000001`2.9999999999999996"}], ",",
                  RowBox[{"Plus", "[",
                    RowBox[{
                      RowBox[{"Times", "[",
                        RowBox[{
                          RowBox[{"-", 
"0.0061540230743798795`0.9978339382434933"}], ",",
                          RowBox[{"Power", "[",
                            RowBox[{
                              RowBox[{"acCap", "[", "cNapRatio", "]"}], 
",",
                              RowBox[{"-", "2"}]}], "]"}], ",",
                          RowBox[{"Power", "[",
                            RowBox[{
                              RowBox[{"Power", "[",
                                RowBox[{
                                  RowBox[{"acCap", "[", "cNapRatio", 
"]"}], ",", "2"}], "]"}], ",",
                              RowBox[{"Rational", "[",
                                RowBox[{"1", ",", "2"}], "]"}]}], 
"]"}]}], "]"}], ",",
                      RowBox[{"Times", "[",
                        RowBox[{
                          RowBox[{"Power", "[",
                            RowBox[{"2", ",",
                              RowBox[{"Rational", "[",
                                RowBox[{
                                  RowBox[{"-", "1"}], ",", "2"}], 
"]"}]}], "]"}], ",",
                          RowBox[{"Power", "[",
                            RowBox[{
                              RowBox[{"Plus", "[",
                                RowBox[{
                                  RowBox[{"Times", "[",
                                    RowBox[{"2", ",", "cNapRatio"}], 
"]"}], ",",
                                  RowBox[{"Times", "[",
                                    
RowBox[{"0.0410268204958658633`3.3010299956639817", ",",
                                      RowBox[{"Power", "[",
                                        RowBox[{
                                        RowBox[{"acCap", "[", 
"cNapRatio", "]"}], ",",
                                        RowBox[{"-", "2"}]}], "]"}], ",",
                                      RowBox[{"Power", "[",
                                        RowBox[{
                                        RowBox[{"Power", "[",
                                        RowBox[{
                                        RowBox[{"acCap", "[", 
"cNapRatio", "]"}], ",", "2"}], "]"}], ",",
                                        RowBox[{"Rational", "[",
                                        RowBox[{"1", ",", "2"}], 
"]"}]}], "]"}]}], "]"}]}], "]"}], ",",
                              RowBox[{"Rational", "[",
                                RowBox[{"1", ",", "2"}], "]"}]}], "]"}], 
",",
                          RowBox[{"Power", "[",
                            RowBox[{
                              RowBox[{"Plus", "[",
                                RowBox[{"1", ",",
                                  RowBox[{"Times", "[",
                                    RowBox[{
                                      RowBox[{"Power", "[",
                                        RowBox[{"2", ",",
                                        RowBox[{"Rational", "[",
                                        RowBox[{
                                        RowBox[{"-", "1"}], ",", "2"}], 
"]"}]}], "]"}], ",",
                                      RowBox[{"Power", "[",
                                        RowBox[{
                                        RowBox[{"Plus", "[",
                                        RowBox[{
                                        RowBox[{"Times", "[",
                                        RowBox[{"2", ",", "cNapRatio"}], 
"]"}], ",",
                                        RowBox[{"Times", "[",
                                        
RowBox[{"0.0410268204958658633`3.3010299956639817", ",",
                                        RowBox[{"Power", "[",
                                        RowBox[{
                                        RowBox[{"acCap", "[", 
"cNapRatio", "]"}], ",",
                                        RowBox[{"-", "2"}]}], "]"}], ",",
                                        RowBox[{"Power", "[",
                                        RowBox[{
                                        RowBox[{"Power", "[",
                                        RowBox[{
                                        RowBox[{"acCap", "[", 
"cNapRatio", "]"}], ",", "2"}], "]"}], ",",
                                        RowBox[{"Rational", "[",
                                        RowBox[{"1", ",", "2"}], 
"]"}]}], "]"}]}], "]"}]}], "]"}], ",",
                                        RowBox[{"Rational", "[",
                                        RowBox[{"1", ",", "2"}], 
"]"}]}], "]"}]}], "]"}]}], "]"}], ",",
                              RowBox[{"-", "1"}]}], "]"}]}], "]"}]}], 
"]"}]}], "]"}]}], "]"}]}], "]"}]}], "\[IndentingNewLine]",
    RowBox[{"expr2", "=",
      RowBox[{
        RowBox[{"expr1", "/.",
          RowBox[{"{",
            RowBox[{
              RowBox[{"acCap", "[", "cNapRatio", "]"}], "\[Rule]", 
"\[Lambda]"}], "}"}]}], "//",
        "PowerExpand"}]}], "\[IndentingNewLine]",
    RowBox[{
      RowBox[{"expr4", "=",
        RowBox[{
          RowBox[{
            RowBox[{
              RowBox[{"expr2", "[",
                RowBox[{"[", "1", "]"}], "]"}], "+",
              RowBox[{"2.04", "*",
                RowBox[{
                  RowBox[{
                    RowBox[{"expr2", "[",
                      RowBox[{"[", "2", "]"}], "]"}], "[",
                    RowBox[{"[", "2", "]"}], "]"}], "[",
                  RowBox[{"[", "2", "]"}], "]"}]}]}], "//", 
"Simplify"}], "//", "Chop"}]}],
      "\[IndentingNewLine]"}], "\[IndentingNewLine]",
    RowBox[{"sol11", "=",
      RowBox[{
        RowBox[{"Solve", "[",
          RowBox[{
            RowBox[{"expr4", "==",
              RowBox[{
                RowBox[{"expr2", "[",
                  RowBox[{"[", "2", "]"}], "]"}], "[",
                RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[Lambda]"}], 
"]"}], "//", "First"}]}], "\[IndentingNewLine]",
    RowBox[{
      RowBox[{"acCap", "[", "cNapRatio_", "]"}], "=",
      RowBox[{"\[Lambda]", "/.",
        RowBox[{"sol11", "[",
          RowBox[{"[", "1", "]"}], "]"}]}]}], "\[IndentingNewLine]",
    RowBox[{"Plot", "[",
      RowBox[{
        RowBox[{"acCap", "[", "cNapRatio", "]"}], ",",
        RowBox[{"{",
          RowBox[{"cNapRatio", ",", "0", ",", "1"}], "}"}]}], "]"}], 
"\[IndentingNewLine]",
    RowBox[{"acCap", "[", "0", "]"}]}], "Input"]

Hope this helps

Pratik  .

-- 
Pratik Desai
Graduate Student
UMBC
Department of Mechanical Engineering
Phone: 410 455 8134



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