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Re: Re: significance arithmetic and numeric equation solving
- To: mathgroup at smc.vnet.net
- Subject: [mg61633] Re: [mg61589] Re: [mg61576] significance arithmetic and numeric equation solving
- From: Pratik Desai <pdesai1 at umbc.edu>
- Date: Mon, 24 Oct 2005 01:44:34 -0400 (EDT)
- References: <200510220911.FAA15007@smc.vnet.net> <200510230945.FAA10713@smc.vnet.net> <acbec1a40510231507n25830ddr733adde7dab78222@mail.gmail.com>
- Sender: owner-wri-mathgroup at wolfram.com
Chris Chiasson wrote:
>Pratik,
>
>You changed the equation with expr4=expr2[[1]] + 2.04*expr2[[2]][[2]][[2]]
>
>How could you possibly expect that to work? Also the machine precision
>2.04 you supplied completely eliminates all significance tracking,
>which was the entire point of my post.
>
>
Why not ?? algebraic rules still work inspite of your concern about
significance tracking . Not e that I had used Solve instead of NSolve. I
think if you have a close look at your expression it is a simple
algebraic expression.
>acCap is between 0 and 1 because it is an activity coefficient; it
>isn't not greater than one...
>
>Thank you for trying to help me,
>
>
No problem
>On 10/23/05, Pratik Desai <pdesai1 at umbc.edu> wrote:
>
>
>>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
>>
>>
>>
>>
>>
>
>
>--
>http://chrischiasson.com/contact/chris_chiasson
>
>
>
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