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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- Re: Re: significance arithmetic and numeric equation solving
- From: Chris Chiasson <chris.chiasson@gmail.com>
- Re: Re: significance arithmetic and numeric equation solving
- References:
- significance arithmetic and numeric equation solving
- From: Chris Chiasson <chris.chiasson@gmail.com>
- significance arithmetic and numeric equation solving