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>
- significance arithmetic and numeric equation solving