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MathGroup Archive 2005

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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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