Re: Re: significance arithmetic and numeric equation solving

• To: mathgroup at smc.vnet.net
• Subject: [mg61627] Re: [mg61589] Re: [mg61576] significance arithmetic and numeric equation solving
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Mon, 24 Oct 2005 01:44:16 -0400 (EDT)
• References: <200510220911.FAA15007@smc.vnet.net> <200510230945.FAA10713@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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.

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,

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
> UMBC
> Department of Mechanical Engineering
> Phone: 410 455 8134
>
>
>

--
http://chrischiasson.com/contact/chris_chiasson

```

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