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Re: Re: significance arithmetic and numeric equation solving

• To: mathgroup at smc.vnet.net
• Subject: [mg61620] Re: [mg61589] Re: [mg61576] significance arithmetic and numeric equation solving
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Mon, 24 Oct 2005 01:44:00 -0400 (EDT)
• References: <200510220911.FAA15007@smc.vnet.net> <200510230945.FAA10713@smc.vnet.net> <acbec1a40510231507n25830ddr733adde7dab78222@mail.gmail.com> <435C4F72.5090404@umbc.edu>
• Sender: owner-wri-mathgroup at wolfram.com

isn't not -> is not
double negative - my bad

On 10/23/05, Pratik Desai <pdesai1 at umbc.edu> wrote:
>
>
> 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
> >
> >
> >
>


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

• References:
  • significance arithmetic and numeric equation solving
    • From: Chris Chiasson <chris.chiasson@gmail.com>
  • Re: significance arithmetic and numeric equation solving
    • From: Pratik Desai <pdesai1@umbc.edu>