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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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