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 > > >
- 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>
- significance arithmetic and numeric equation solving