A54 == How can I (vertically) align several Plots (graphs) in theGraphicsArray to have y axis in the same x position?Somehing like plots = Table[Plot[Sin[i x], {x, 1, [Pi]}], {i, 1, 3}];Show[GraphicsArray[Partition[plots, 1], GraphicsSpacing -> {1, -0.1}]]And how can I impose the AspectRatio of the individual graphs to havex axis spanning the whole x resolution and y axis only one third of yresolution?Cyril FischerReply-To: kuska@informatik.uni-leipzig.de ==== Hi,andresult = Solve[{a == 1/(1/r2 + 1/50), 50 == 1/(1/(a + r1) + 1/r2)}, r1,a]Plot[Evaluate[r1 /. result], {r2, -25, 25}]works fine. Jens I'd sure like to find out how to clean up a process I do a lot. Namely, get> a solution to some set of equations and then plot the result. For example,> I recently did result = Solve[{a == 1/(1/r2 + 1/50), 50 == 1/(1/(a + r1) + 1/r2)}, r1, a] This gives {{r1 -> (a function of r2) }} Then, I plot it by> Plot[ (this function of r2), {r2, startvalue, stopvalue}] where I carefully type in this function. I feel sure you Mathematica pros> don't have to do that so I have made several feeble attempts to automate> this over the years. They fail because I still don't have a clue how Mathematica works. Here's my last attempt:> Plot[ result /. %]> a thing to me. Surely there is a way to get this plot without having to type the Solve[] result> into Plot[]. Any hints would be appreciated, as usual. Rob ==== I have a complex-valued function f(z).If z = x + I y, suppose f(z) has a finite number of simple zerosin the rectangle a < x < b, c < y < d. (and no poles).I can start FindRoot somewhere and it will likely find a root.But, my question is:is there a (best?) systematic way to use Mathematica to findall the roots in the region? ==== Dear MathGroup,I am working on an application where I define a number of graphical objects,which can then be used like graphical primitives. I also want to definegraphical primitives that will control the color, position and size of someof these objects. The use of color is slightly complicated because the colorthat is set may be used for lines, or in SurfaceColor or in EdgeForm and itmay be lightened or darkened.My basic approach is to store the value of the directives in internalvariables and then the graphical primitives use these values.But it is difficult to make it all behave just like regular Mathematicagraphical directives.1) The list of primitives must be HoldFirst. Premature evaluation will causethe last instance of a programmed directive to be used for all cases.2) The default values of any primitives must be set before the primitivesare evaluated else whatever is left over from the last plot will be used.I can pretty much handle those problems. The last problem is more difficultand is the core of my question.3) Regular graphics directives are nested in the sense that if one is setinside brackets, {directive,... }, then, after exiting the brackets, thedirective reverts to the value existing before the brackets were entered.Is it possible to program that behavior?Here is an example. It could be done with regular Mathematica directives,but it was picked to be a simple example. In my actual cases I have to useprogramming. The extra graphical primitive is a ColoredLine. The color to beLineColor. The value is stored in currentcolor.Needs[Graphics`Colors`]currentcolor = Black;ColoredLine[start_, end_] := {currentcolor, Line[{start, end}]}LineColor[color_] := (currentcolor = color; Sequence[]) Show[Graphics[ {LineColor[Black], Sequence @@ primitives}], opts]In the following use everything works. {ColoredLine[{0, 0}, {1, 0}], LineColor[Red], ColoredLine[{0, 1}, {1, 1}], LineColor[Blue], Coloredline[{0, 2}, {1, 2}]}, Background -> Linen, ImageSize -> 400];But if I use nesting it, of course, doesn't work like regular Mathematicadirectives. The color does not revert to Black. {ColoredLine[{0, 0}, {1, 0}], {LineColor[Red], ColoredLine[{0, 1}, {1, 1}]}, Coloredline[{0, 2}, {1, 2}]}, Background -> Linen, ImageSize -> 400];It appears that I need to somehow implement a recursive evaluation of theprimitives list. Any ideas on how I could do that.David Parkdjmp@earthlink.nethttp://home.earthlink.net/~djmp/ Reply-To: kuska@informatik.uni-leipzig.de ==== Hi,try FullForm to see all digits of a ßoating point numberthat is truncated by the Print/Output functions. Jens I tried some of my Mathematica3.01 programs on a computer with> Mathematica4.1,> there where some differences that I could not explain. Regarding N[]: consider for example:> with version 4.1 I got: N[Sqrt[2.],16]->1.4142> and> N[Sqrt[2.],17]->1.4142135623730950 and in version 3.01: N[Sqrt[2.],16]->1.414213562373095> and> N[Sqrt[2.],17]->1.4142135623730950 Using SetPrecision[Sqrt[2.],16] I could make Mathematica4.1 give me 16> digits precision.> Ideas? Peter WReply-To: kuska@informatik.uni-leipzig.de ==== Hi,a interpolation gives for the data x[i], y[i] at everypoint x[i] the original y[i], a fit must not do that. Jens > Another in a series of potentially simple questions: What is the difference between using Fit and Interpolation?> f[x_]=Fit[data, {1,x},x]> -or-> f[x_]=Interpolation[data][x] I do know that Fit can take arguments for the independant variables> form like:> f[x_]=Fit[data, {1,x},x]> f[x_]=Fit[data, {1,x,x^2},x]> but that's a bit of guesswork if you have a limited set of points, no? Also, is there a function in Mathematica that allows me to swap> dependent and independent variables? e.g. x=2.5y --> y=x/2.5 > David Seruyange> Student ==== >What is the difference between using Fit and Interpolation?>f[x_]=Fit[data, {1,x},x] -or- f[x_]=Interpolation[data][x]There are several differences between the expressions aboveFirst, Interpolation[data][x] isn't correct syntax. It should be Interpolation[data]. Interpolation returns a pure function of data. By default that is a 3rd order polynominal that passes through each of the points specified by the variable data.In contrast, Fit[data,{1,x},x] returns a best fit *line* for the points specified by data. The result is not a pure function but an expression. The result is a least squares fit to the data and will not pass through the points specified unless they lie exactly on a line.The two functions, Interpolation and Fit, are intended for different purposes.Suppose you had a list of data points that were known to be accurate to the precesion specified and wanted to estimate the value of the unknown function at an intermediate point. For this you would use interpolation since you want the result to pass through each of the data points you started with.Now suppose you had a list of data points where each data point you have is really the sum of a true value and a random error. The best result would ideally subtract out the error and yeild the true values. So, you would definitely not want the result to pass through the points with error. For this problem you would use Fit. ==== Hi group:When loading Combinatorica with < Calculus, Graphics, Statistics, and Personal (this with some private utilities).Emilio Martin-Serrano___________________________________Reply-To: kuska@informatik.uni-leipzig.de ==== Hi,can you explain how you simple example was obtained ? Jens I want to make a matrix of derivations, so I will be able to multiply> it by a matrix of functions and get the result matrix> simple example: |d/dx 0 | |xy x| |y 1|> | |.| |=| |> |d/dy d/dx| |x+y 3| |x+1 0| thank you ==== When your first matrix is a matrix of functions, then the dot productresults in a matrix of sums of products of arguments and functions. A simplesubstitution then will give you the result you are looking for.In[1]:=mat1 = {{D[#1, x] & , 0 & }, {D[#1, y] & , D[#1, x] & }}Out[1]={{D[#1, x] & , 0 & }, {D[#1, y] & , D[#1, x] & }}In[2]:=mat2 = {{x*y, x}, {x + y, 3}}Out[2]={{x*y, x}, {x + y, 3}}In[3]:=mat1 . mat2 /. a_.*b_Function -> b[a]Out[3]={{y, 1}, {1 + x, 0}}Fred SimonsEindhoven University of Technology> -----Original Message-----> Sent: maandag 3 februari 2003 7:08> To: mathgroup@smc.vnet.net > I want to make a matrix of derivations, so I will be able to multiply> it by a matrix of functions and get the result matrix> simple example: |d/dx 0 | |xy x| |y 1|> | |.| |=| |> |d/dy d/dx| |x+y 3| |x+1 0| thank you> ==== > I want to make a matrix of derivations, so I will be able to multiply> it by a matrix of functions and get the result matrix> simple example:>> |d/dx 0 | |xy x| |y 1|> | |.| |=| |> |d/dy d/dx| |x+y 3| |x+1 0|>> thank you>Inner[#1[#2]&, {{D[#, x]&, #*0&},{D[#, y]&, D[#, x]&}}, {{x*y, x}, {x + y, 3}}, Plus]{{y, 1}, {1 + x, 0}}orInner[D[#2,#1]&, {{x, Unique[]},{y, x}}, {{x*y, x},{x + y, 3}}, Plus]{{y, 1}, {1 + x, 0}}Bob Hanlon ==== Dear all,Suppose I create a function f[x_,opts___]with optionsShape in {Circle, Ellipsis} and Diameter in R+, DiameterLong in R+,DiameterShort in R+Say that the defaults areOptions[x]={Shape->Circle, Diameter->1.}The option Diameter makes sence only when Shape->Circle, andThe options DiameterShort/Long make sense only when Shape->EllipsisIs there a quick way to tell Mathematica to warn if these conditions arenot satisfied? I could write a series of boolean tests, but I was wonderingif there is a more elegant way.Best,Kyriakos_____+**+____+**+___+**+__+**+_Kyriakos ChourdakisLecturer in Financial EconomicsURL: http://www.qmw.ac.uk/~te9001tel: (++44) (+20) 7882 5086Dept of EconomicsUniversity of London, QMLondon E1 4NSU.K. ==== i have a problem by creating a package. I need routines from another> packageI think that your second form of the package loading is correct: > BeginPackage[Seismo`Hazard`PSHA`,{Statistics` ContinuousDistributions`}]but you should use the full context with symbols inside your own package which are from Statistics`ContinuousDistributions`, e.g. writeStatistics`ContinuousDistributions` NormalDistributioninstead ofNormalDistribution> Random::randt: Type specification> Seismo`Hazard`PSHA`Private`NormalDistribution[<<19>> , 0.16] in Random[<< 1 >]> should be Real, Integer, or Complex.-- Antti Penttil.8a Antti.I.Penttila@invalid.helsinki.fi ==== One of the new features of Mathematica 4.2 are theXML tools and I have written an example of their usebased on SVG (an XML application for vector graphics).Tom Wickham-Jones CreatedBy='Mathematica 4.2' Mathematica-Compatible NotebookThis notebook can be used with any Mathematica-compatibleapplication, such as Mathematica, MathReader or Publicon. The datafor the notebook starts with the line containing stars above.To get the notebook into a Mathematica-compatible application, doone of the following:* Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application;* Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application.Data for notebooks contains only printable 7-bit ASCII and can beCR, LF or CRLF (Unix, Macintosh or MS-DOS style).NOTE: If you modify the data for this notebook not in a Mathematica-compatible application, you must delete the line below containingtry to use invalid cache data.For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com phone: +1-217-398-0700 (U.S.)Notebook reader applications are available free of charge from Wolfram Research.**************************************************** ***************)(* NotebookFileLineBreakTestNotebookFileLineBreakTest*)(* NotebookOptionsPosition[ 52820, 1633]*)(*NotebookOutlinePosition[ 53608, 1662]*)(* CellTagsIndexPosition[ 53538, 1656]*)(*WindowFrame->Normal*)Notebook[{Cell[TextData[{ Generating SVG with , StyleBox[Mathematica, FontSlant->Italic]}], Title],Cell[An example of the use of SymbolicXML, Subtitle],Cell[, Subsubtitle],Cell[CellGroupData[{Cell[What is SVG?, Section],Cell[TextData[{ SVG is an XML language for describing two-dimensional graphics. Since it is based on XML any XML aware application can work with SVG. , StyleBox[Mathematica, FontSlant->Italic], has some good tools for working with XML and some specific functions that support SVG, thus it is a good environment for some interesting SVG applications. SVG contains some interesting features including a variety of dynamic features such as animations.}], Text],Cell[TextData[{ SVG can be rendered with a browser plug-in from Adobe, , ButtonBox[http://www.adobe.com/svg, ButtonData:>{ URL[ http://www.adobe.com/svg], None}, ButtonStyle->Hyperlink], . which provides strong support including the animation functions. More information about SVG can be found at the W3C site: , ButtonBox[http://www.w3.org/Graphics/SVG/, ButtonData:>{ URL[ http://www.w3.org/Graphics/SVG/], None}, ButtonStyle->Hyperlink], .}], Text]}, Open ]],Cell[CellGroupData[{Cell[TextData[{ StyleBox[Mathematica, FontSlant->Italic], Commands for Generating SVG}], Section],Cell[TextData[{ StyleBox[Mathematica, FontSlant->Italic], has a rich graphics language for representing graphics as , StyleBox[Mathematica, FontSlant->Italic], expressions.}], Text],Cell[CellGroupData[{Cell[BoxData[ (p = Graphics[Line[ {{0, 0}, {1, 1}}]])], Input],Cell[BoxData[ TagBox[([SkeletonIndicator] Graphics [SkeletonIndicator]), False, Editable->False]], Output]}, Open ]],Cell[TextData[{ These print as expressions, if you want to see a graphical expression you use a command such as , StyleBox[Show, InlineInput], .}], Text],Cell[CellGroupData[{Cell[BoxData[ (Show[p])], Input],Cell[GraphicsData[PostScript, <%!%%Creator: Mathematica%%AspectRatio: .61803 MathPictureStart/Mabs {Mgmatrix idtransformMtmatrix dtransform} bind def/Mabsadd { Mabs3 -1 roll add3 1 roll addexch } bind def%% Graphics%%IncludeResource: font Courier%%IncludeFont: Courier/Courier findfont 10 scalefont setfont% Scaling calculations0.0238095 0.952381 0.0147151 0.588604 [[ 0 0 0 0 ][ 1 .61803 0 0 ]] MathScale% Start of Graphics1 setlinecap1 setlinejoinnewpath0 0 m1 0 L1 .61803 L0 .61803 Lclosepathclipnewpath0 g.5 Mabswid[ ] 0 setdash.02381 .01472 m.97619 .60332 Ls% End of GraphicsMathPictureEnd>], Graphics, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}},CF5dJ6E]HGAYHf4PAg9QL6QYHgmoo`00Yoo`00=Woo00< 007ooOol0igoo000gOol2003WOol003Uoo`800>Eoo`00>goo00< 007ooOol0hWoo000lOol2003ROol003ioo`03001oogoo0=moo`00?goo 0P00ggoo0011Ool2003MOol004=oo`03001oogoo0=Yoo` 00A7oo0P00fWoo0016Ool00`00Oomoo`3GOol004Moo`800=Moo` 00BGoo0P00eGoo001;Ool00`00Oomoo`3BOol004aoo`800=9oo` 00CWoo0P00d7oo001@Ool00`00Oomoo`3=Ool0055oo`800Ool0091oo`8008ioo` 00TWoo0P00S7oo002DOol00`00Oomoo`29Ool009Eoo`8008Uoo`00Ugoo00< 007ooOol0QWoo002HOol20026Ool009Yoo`8008Aoo`00W7oo00< 007ooOol0PGoo002MOol20021Ool009moo`8007moo`00XGoo00< 007ooOol0O7oo002ROol2001lOol00:Aoo`03001oogoo07Uoo`00YGoo0P00 NGoo002WOol2001gOol00:Uoo`03001oogoo07Aoo`00ZWoo0P00M7oo002/ Ool00`00Oomoo`1aOol00:eoo`80075oo`00[goo0P00Kgoo002aOol00` 00Oomoo`1/Ool00;9oo`8006aoo`00]7oo0P00JWoo002fOol00`00Oomoo` 1WOol00;Moo`8006Moo`00^Goo00<007ooOol0I7oo002jOol2001TOol00; aoo`80069oo`00_Woo00<007ooOol0Ggoo002oOol2001OOol00<5oo` 8005eoo`00`goo00<007ooOol0FWoo0034Ool2001JOol00Ool00`00Oomoo`1?Ool00=oo`8003]oo`00iGoo00< 007ooOol0>7oo003VOol2000hOol00>Qoo`03001oogoo03Eoo` 00jGoo0P00=Goo003[Ool2000cOol00>eoo`03001oogoo031oo` 00kWoo0P00<7oo003`Ool00`00Oomoo`0]Ool00?5oo`8002eoo` 00lgoo0P00:goo003eOol00`00Oomoo`0XOol00?Ioo`8002Qoo` 00n7oo0P009Woo003jOol00`00Oomoo`0SOol00?]oo`8002=oo`00oGoo00< 007ooOol087oo003nOol2000POol00?moo`5oo`8001ioo`00ogoo0goo00< 007ooOol06goo003oOol4Ool2000KOol00?moo`Ioo`8001Uoo` 00ogoo27oo00<007ooOol05Woo003oOol9Ool2000FOol00?moo`]oo`03 001oogoo01=oo`00ogoo37oo0P004goo003oOol>Ool2000AOol00?mooa1oo `03001oogoo00ioo`00ogoo4Goo0P003Woo003oOolCOol00`00Oomoo`0; Ool00?mooaAoo`8000]oo`00ogoo5Woo0P002Goo003oOolHOol00` 00Oomoo`06Ool00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00 >],0.00366761, 0.00593432}}],Cell[BoxData[ TagBox[([SkeletonIndicator] Graphics [SkeletonIndicator]), False, Editable->False]], Output]}, Open ]],Cell[TextData[{ StyleBox[Mathematica, FontSlant->Italic], can write an XML representation of a , StyleBox[Mathematica, FontSlant->Italic], graphics expression into a string with , StyleBox[ExportString, InlineInput], and into a file with , StyleBox[Export, InlineInput], .}], Text],Cell[CellGroupData[{Cell[BoxData[ (str = ExportString[p, ])], Input],Cell[BoxData[ (n nn n n n)], Output]}, Open ]],Cell[TextData[{ A string of XML can be read back into , StyleBox[Mathematica, FontSlant->Italic], with the command , StyleBox[ImportString, InlineInput], with a format of , StyleBox[XML, InlineInput], . This returns a symbolic XML expression that is an isomorphic representation of the original XML. The symbolic XML version of the XML can be worked with by standard , StyleBox[Mathematica, FontSlant->Italic], programming techniques. This is demonstrated in the , ButtonBox[next section, ButtonData:>t:1, ButtonStyle->Hyperlink], .}], Text],Cell[CellGroupData[{Cell[BoxData[ (ImportString[str, ])], Input],Cell[BoxData[ ((XMLObject[ Encoding [Rule] UTF-8], (XMLObject[Doctype])[svg, Public [Rule] -//W3C//DTD SVG 1.0//EN, System [Rule] http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd]}, XMLElement[ svg, {{http://www.w3.org/2000/xmlns/, xmlns} [Rule] http://www.w3.org/2000/svg, width [Rule] 288.0pt, height [Rule] 177.994pt, viewBox [Rule] -0.025 -0.0154508 1.05 0.648936, preserveAspectRatio [Rule] xMidYMid meet}, {XMLElement[ g, {transform [Rule] scale(1, -1) translate(0,-0.618034), style [Rule] fill:black; font-family:'Courier New', Courier, Symbol, monospace; font-size:0.021875pt; stroke:black; stroke-width:0.000911458pt}, {XMLElement[line, {fill [Rule] none, x1 [Rule] 0.0, y1 [Rule] 0.0, x2 [Rule] 1.0, y2 [Rule] 0.618034}, {}]}]}], {}, Valid [Rule] True])], Output]}, Open ]],Cell[TextData[{ The command , StyleBox[XML`SVG`GraphicsToSymbolicSVG, InlineInput], goes directly from a , StyleBox[Mathematica, FontSlant->Italic], graphics expression directly to the symbolic XML representation of the SVG.}], Text],Cell[CellGroupData[{Cell[BoxData[ (XML`SVG`GraphicsToSymbolicSVG[p])], Input],Cell[BoxData[ ((XMLObject[ Encoding [Rule] UTF-8], (XMLObject[Doctype])[svg, Public [Rule] -//W3C//DTD SVG 1.0//EN, System [Rule] http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd]}, XMLElement[ svg, {xmlns [Rule] http://www.w3.org/2000/svg, width [Rule] 288.0pt, height [Rule] 177.994pt, viewBox [Rule] -0.025 -0.0154508 1.05 0.648936, preserveAspectRatio [Rule] xMidYMid meet}, {XMLElement[ g, {transform [Rule] scale(1, -1) translate(0,-0.618034), style [Rule] fill:black; font-family:'Courier New', Courier, Symbol, monospace; font-size:0.021875pt; stroke:black; stroke-width:0.000911458pt}, {XMLElement[line, {fill [Rule] none, x1 [Rule] 0.0, y1 [Rule] 0.0, x2 [Rule] 1.0, y2 [Rule] 0.618034}, {}]}]}], {}])], Output]}, Open ]]}, Open ]],Cell[CellGroupData[{Cell[Generating an SVG Animation, Section, CellTags->t:1],Cell[TextData[{ StyleBox[Mathematica, FontSlant->Italic], can solve a differential equation:}], Text],Cell[CellGroupData[{Cell[BoxData[ (sol = NDSolve[{ (x'')[t] + 0.15 (x')[t] - x[t] + x[t]^3 [Equal] 5 Cos[t], [IndentingNewLine]x[0] [Equal] 1, (x')[0] [Equal] 2}, x, {t, 0, 20}])], Input],Cell[BoxData[ RowBox[{{, RowBox[{{, RowBox[{x, [Rule], TagBox[(InterpolatingFunction[{{0.`, 20.`}}, <>]), False, Editable->False]}], }}], }}]], Output]}, Open ]],Cell[and then the solution can be plotted., Text],Cell[CellGroupData[{Cell[BoxData[ ((p = ParametricPlot[ Evaluate[{x[t], (x')[t]} /. sol], {t, 0, 20}];))], Input],Cell[GraphicsData[PostScript, <%!%%Creator: Mathematica%%AspectRatio: .61803 MathPictureStart/Mabs {Mgmatrix idtransformMtmatrix dtransform} bind def/Mabsadd { Mabs3 -1 roll add3 1 roll addexch } bind def%% Graphics%%IncludeResource: font Courier%%IncludeFont: Courier/Courier findfont 10 scalefont setfont% Scaling calculations0.477803 0.15697 0.306151 0.0573087 [[.00689 .29365 -6 -9 ][.00689 .29365 6 0 ][.16386 .29365 -6 -9 ][.16386 .29365 6 0 ][.32083 .29365 -6 -9 ][.32083 .29365 6 0 ][.63477 .29365 -3 -9 ][.63477 .29365 3 0 ][.79174 .29365 -3 -9 ][.79174 .29365 3 0 ][.94871 .29365 -3 -9 ][.94871 .29365 3 0 ][.4653 .07692 -12 -4.5 ][.4653 .07692 0 4.5 ][.4653 .19153 -12 -4.5 ][.4653 .19153 0 4.5 ][.4653 .42077 -6 -4.5 ][.4653 .42077 0 4.5 ][.4653 .53539 -6 -4.5 ][.4653 .53539 0 4.5 ][ 0 0 0 0 ][ 1 .61803 0 0 ]] MathScale% Start of Graphics1 setlinecap1 setlinejoinnewpath0 g.25 Mabswid[ ] 0 setdash.00689 .30615 m.00689 .3124 Ls[(-3)] .00689 .29365 0 1 Mshowa.16386 .30615 m.16386 .3124 Ls[(-2)] .16386 .29365 0 1 Mshowa.32083 .30615 m.32083 .3124 Ls[(-1)] .32083 .29365 0 1 Mshowa.63477 .30615 m.63477 .3124 Ls[(1)] .63477 .29365 0 1 Mshowa.79174 .30615 m.79174 .3124 Ls[(2)] .79174 .29365 0 1 Mshowa.94871 .30615 m.94871 .3124 Ls[(3)] .94871 .29365 0 1 Mshowa.125 Mabswid.03829 .30615 m.03829 .3099 Ls.06968 .30615 m.06968 .3099 Ls.10108 .30615 m.10108 .3099 Ls.13247 .30615 m.13247 .3099 Ls.19526 .30615 m.19526 .3099 Ls.22665 .30615 m.22665 .3099 Ls.25805 .30615 m.25805 .3099 Ls.28944 .30615 m.28944 .3099 Ls.35223 .30615 m.35223 .3099 Ls.38362 .30615 m.38362 .3099 Ls.41501 .30615 m.41501 .3099 Ls.44641 .30615 m.44641 .3099 Ls.5092 .30615 m.5092 .3099 Ls.54059 .30615 m.54059 .3099 Ls.57198 .30615 m.57198 .3099 Ls.60338 .30615 m.60338 .3099 Ls.66617 .30615 m.66617 .3099 Ls.69756 .30615 m.69756 .3099 Ls.72895 .30615 m.72895 .3099 Ls.76035 .30615 m.76035 .3099 Ls.82314 .30615 m.82314 .3099 Ls.85453 .30615 m.85453 .3099 Ls.88592 .30615 m.88592 .3099 Ls.91732 .30615 m.91732 .3099 Ls.98011 .30615 m.98011 .3099 Ls.25 Mabswid0 .30615 m1 .30615 Ls.4778 .07692 m.48405 .07692 Ls[(-4)] .4653 .07692 1 0 Mshowa.4778 .19153 m.48405 .19153 Ls[(-2)] .4653 .19153 1 0 Mshowa.4778 .42077 m.48405 .42077 Ls[(2)] .4653 .42077 1 0 Mshowa.4778 .53539 m.48405 .53539 Ls[(4)] .4653 .53539 1 0 Mshowa.125 Mabswid.4778 .10557 m.48155 .10557 Ls.4778 .13423 m.48155 .13423 Ls.4778 .16288 m.48155 .16288 Ls.4778 .22019 m.48155 .22019 Ls.4778 .24884 m.48155 .24884 Ls.4778 .2775 m.48155 .2775 Ls.4778 .33481 m.48155 .33481 Ls.4778 .36346 m.48155 .36346 Ls.4778 .39211 m.48155 .39211 Ls.4778 .44942 m.48155 .44942 Ls.4778 .47808 m.48155 .47808 Ls.4778 .50673 m.48155 .50673 Ls.4778 .04826 m.48155 .04826 Ls.4778 .01961 m.48155 .01961 Ls.4778 .56404 m.48155 .56404 Ls.4778 .59269 m.48155 .59269 Ls.25 Mabswid.4778 0 m.4778 .61803 Ls0 0 m1 0 L1 .61803 L0 .61803 Lclosepathclipnewpath.5 Mabswid.63477 .42077 m.65038 .43313 L.66878 .44539 L.68599 .45489 L.70585 .46366 L.7185 .46803 L.73045 .47128 L.74207 .4736 L.75453 .47509 L.76573 .4755 L.77622 .47503 L.78766 .47348 L.79981 .47051 L.81209 .46593 L.82312 .46025 L.83472 .45238 L.84633 .44206 L.85653 .43038 L.86525 .41779 L.87232 .40508 L.87883 .39045 L.88384 .37607 L.88824 .35938 L.89118 .34355 L.89299 .32834 L.89392 .31008 L.89363 .29332 L.89194 .27411 L.88902 .25628 L.88482 .23893 L.87977 .22338 L.87306 .2073 L.86455 .19131 L.85491 .17697 L.8436 .16361 L.833 .15354 L.82092 .14431 L.80895 .13702 L.79765 .13152 L.78596 .12703 L.77468 .12368 L.76129 .12076 L.74879 .11894 L.73496 .11779 L.72796 .11751 L.72025 .11741 L.71264 .1175 L.70435 .1178 L.69654 .11826 L.68931 .11881 LMistroke.67573 .12013 L.66139 .12186 L.60063 .13087 L.57204 .13483 L.55824 .13642 L.54567 .13763 L.53426 .1385 L.52229 .13916 L.5103 .13954 L.50351 .13962 L.49719 .13961 L.48504 .13935 L.47891 .13909 L.47213 .13872 L.46011 .13783 L.44878 .13673 L.42293 .13332 L.39442 .12841 L.34361 .11798 L.31465 .11204 L.28696 .10706 L.27369 .10509 L.26106 .10354 L.2464 .10224 L.23303 .10159 L.21814 .10159 L.20446 .10237 L.18953 .1042 L.18207 .10556 L.17394 .10741 L.16083 .11131 L.14913 .11587 L.13601 .12241 L.12404 .12994 L.10417 .14661 L.0939 .15793 L.08509 .16961 L.07634 .18363 L.06819 .19973 L.0621 .21464 L.05663 .23146 L.052 .25043 L.04892 .26864 L.04763 .27996 L.04684 .29071 L.04645 .31085 L.0473 .32841 L.0494 .34662 L.05213 .36166 L.05611 .37753 LMistroke.06146 .39359 L.06837 .40956 L.08357 .43449 L.09417 .44687 L.10481 .45651 L.11722 .46505 L.12381 .46862 L.13109 .47186 L.13818 .4744 L.14478 .47626 L.15115 .47762 L.15793 .47864 L.16975 .47944 L.18273 .479 L.19546 .47735 L.20691 .47492 L.2199 .47112 L.23188 .46668 L.25229 .45715 L.27292 .44495 L.30794 .4177 L.33361 .39052 L.34441 .37598 L.35359 .36093 L.35751 .35318 L.36113 .34485 L.36364 .33796 L.3658 .33062 L.36676 .32664 L.36749 .32301 L.36804 .31964 L.36852 .31599 L.36899 .30975 L.36901 .30331 L.36882 .29972 L.36851 .29649 L.368 .29282 L.36736 .2894 L.36589 .28346 L.36378 .27721 L.35875 .26655 L.35176 .2561 L.34373 .24715 L.33538 .23988 L.32603 .23342 L.31487 .22747 L.30893 .22496 L.30238 .22266 L.29659 .22101 L.29019 .21961 LMistroke.28371 .21863 L.27768 .21811 L.2719 .21798 L.26577 .21824 L.26032 .21884 L.25526 .21973 L.24977 .22108 L.24398 .22297 L.23747 .22574 L.23165 .22888 L.22505 .23333 L.21943 .23804 L.21012 .24842 L.2057 .255 L.20205 .26173 L.19918 .26828 L.19666 .27559 L.19495 .28213 L.19354 .28958 L.19262 .29787 L.19237 .30261 L.19232 .307 L.1927 .31563 L.19365 .32391 L.19507 .33169 L.19717 .34008 L.20246 .35511 L.2064 .36364 L.21122 .37243 L.22152 .38753 L.23448 .40233 L.24842 .4151 L.28604 .44064 L.32474 .45991 L.36425 .47637 L.46796 .51632 L.5932 .56481 L.62766 .57685 L.66638 .58859 L.68927 .59431 L.71056 .59859 L.73223 .60171 L.75298 .60332 L.77522 .60327 L.78762 .60232 L.7988 .60083 L.82038 .59603 L.84028 .58898 L.85136 .58377 L.86282 .57728 LMistroke.88256 .56298 L.90246 .54359 L.92228 .51748 L.93718 .49136 L.94894 .46464 L.95463 .44876 L.96012 .43071 L.96814 .39609 L.97324 .36207 L.97602 .32492 L.97619 .29292 L.97404 .25795 L.96945 .22373 L.96307 .19333 L.95386 .16205 L.94166 .1316 L.92645 .10325 L.91016 .08025 L.89416 .06278 L.87562 .04723 L.85863 .03643 L.83926 .02733 L.81845 .02068 L.79864 .01681 L.77994 .01502 L.7628 .01472 L.74305 .01573 L.72442 .01782 L.70472 .02104 L.68325 .02551 L.64093 .03651 L.56944 .05825 L.49726 .0793 L.46033 .08833 L.42715 .09512 L.37011 .10405 L.31008 .11165 L.28463 .11534 L.26107 .11964 L.23467 .1261 L.21159 .1339 L.18738 .14523 L.16377 .16082 L.14573 .17727 L.1286 .19873 L.12043 .21218 L.11394 .22528 L.10769 .24118 L.10304 .2569 L.09991 .27172 LMistroke.098 .28562 L.09734 .29364 L.09702 .30088 L.09697 .30918 L.09725 .31692 L.0984 .3298 L.10057 .34313 L.10348 .35513 L.10683 .3655 L.11154 .37685 L.11755 .38811 L.13055 .40538 L.13786 .41235 L.14645 .41876 L.15589 .42403 L.16035 .42596 L.1651 .42768 L.1739 .43 L.18207 .43124 L.19093 .43169 L.19595 .43155 L.20061 .43118 L.20889 .42997 L.21774 .42792 L.22594 .42533 L.23332 .42243 L.24676 .41574 L.26002 .40719 L.28372 .38584 L.29455 .37216 L.3028 .3587 L.30633 .35154 L.30951 .34381 L.31178 .33706 L.31373 .32971 L.31467 .32518 L.31535 .32101 L.31585 .31701 L.31621 .3128 L.31642 .30548 L.31631 .30134 L.31606 .29749 L.31514 .28992 L.31376 .28282 L.31209 .27649 L.30984 .2697 L.30313 .25483 L.29495 .24169 L.27645 .22073 L.26374 .21033 LMistroke.2506 .2019 L.24308 .19798 L.23569 .19472 L.2288 .19219 L.22129 .18997 L.21304 .18819 L.20527 .18714 L.20049 .18681 L.19598 .18672 L.18755 .18717 L.17966 .18835 L.1713 .19048 L.16358 .19334 L.15673 .19669 L.149 .20152 L.14103 .20791 L.12799 .22247 L.12235 .23104 L.11687 .24147 L.11206 .25334 L.10846 .26526 L.10595 .27693 L.10439 .288 L.10353 .30046 L.1036 .31376 L.1045 .32546 L.10598 .33602 L.10849 .34803 L.11161 .3591 L.11894 .37784 L.12401 .38775 L.12926 .3964 L.14192 .41287 L.15811 .42812 L.16701 .43462 L.17707 .44077 L.1963 .44972 L.20747 .4536 L.21782 .4565 L.22999 .4592 L.24162 .46118 L.25255 .46259 L.26267 .46357 L.27384 .46437 L.28568 .46496 L.29771 .46534 L.30446 .46549 L.31062 .4656 L.33394 .4659 L.347 .46608 LMistroke.35439 .46623 L.36123 .4664 L.3738 .46683 L.38016 .46711 L.38718 .46749 L.39899 .46827 L.41148 .46933 L.43405 .47192 L.45882 .47578 L.48665 .48137 L.59226 .5106 L.6228 .51958 L.65734 .5288 L.67366 .53257 L.6912 .53606 L.70637 .5385 L.72321 .54046 L.73965 .5415 L.7547 .54156 L.77204 .54041 L.78836 .53794 L.8032 .53433 L.81671 .52973 L.83117 .52319 L.84602 .51441 L.86254 .50162 L.8767 .48741 L.89091 .46912 L.90412 .4469 L.91398 .42525 L.92163 .40342 L.92818 .37794 L.93098 .36312 L.93295 .34938 L.93518 .32343 L.93553 .29934 L.93405 .27316 L.93257 .2602 L.93038 .24621 L.92544 .22364 L.91844 .20085 L.91033 .18105 L.90174 .16456 L.89063 .1477 L.87909 .13395 L.86783 .12329 L.85527 .11392 L.84091 .10585 L.82724 .10033 L.81219 .09631 LMistroke.80354 .09485 L.79542 .094 L.78094 .0936 L.76724 .09443 L.75501 .09607 L.74185 .0987 L.72776 .10243 L.71311 .10725 L.68776 .11762 L.63666 .14562 L.59649 .17388 L.56147 .20358 L.53286 .23297 L.51587 .25449 L.50375 .27425 L.49937 .28373 L.49666 .29146 L.49574 .2949 L.49536 .29662 L.49501 .2984 L.49457 .30149 L.49435 .30417 L.4943 .30665 L.49439 .30876 L.49465 .31103 L.49504 .31302 L.49551 .31471 L.49604 .31615 L.4967 .31759 L.4975 .31897 L.49848 .3203 L.49963 .32152 L.50081 .32246 L.50194 .32315 L.503 .32364 L.50419 .32401 L.50546 .32422 L.50664 .32425 L.50796 .32411 L.50862 .32396 L.50933 .32375 L.51058 .32322 L.5117 .32257 L.51296 .32159 L.51404 .32051 L.51512 .31911 L.51613 .3174 L.51685 .31582 L.51749 .31396 L.51796 .31204 LMistroke.51827 .31015 L.51848 .30777 L.51851 .30634 L.51849 .30498 L.51832 .30234 L.51793 .29938 L.51739 .29658 L.51673 .2939 L.51462 .28744 L.51186 .28093 L.50845 .27429 L.49777 .25784 L.48078 .23743 L.43207 .19295 L.3479 .13631 L.29286 .10916 L.27643 .10271 L.25857 .09667 L.24274 .09226 L.23391 .09021 L.22549 .08855 L.20891 .08617 L.19372 .08515 L.17944 .0853 L.16401 .08684 L.15597 .08826 L.1472 .09035 L.13813 .09316 L.12977 .09637 L.11518 .10364 L.10014 .11369 L.08586 .12626 L.07383 .13977 L.0612 .15785 L.05072 .17718 L.04237 .19695 L.03596 .2165 L.03041 .23923 L.02634 .26432 L.02416 .29041 L.02381 .30518 L.02403 .31865 L.02595 .34457 L.02953 .36847 L.03229 .38154 L.03579 .39501 L.04347 .41794 L.0536 .4405 L.06681 .46249 L.07879 .47781 LMistroke.09252 .49158 L.105 .50143 L.11933 .51025 L.13544 .51759 L.14468 .52076 L.15318 .52309 L.1612 .52482 L.16995 .52624 L.18593 .52767 L.20087 .52783 L.21726 .52686 L.22548 .52598 L.23426 .52478 L.24999 .52201 L.27979 .51496 L.30606 .50728 L.40373 .47409 L.45045 .46018 L.47204 .45509 L.49129 .45146 L.50207 .44985 L.51375 .44843 L.52539 .44738 L.53171 .44696 L.53758 .44665 L.54802 .44632 L.55751 .44624 L.56276 .44628 L.56846 .44639 L.57884 .44674 L.58854 .44724 L.59928 .44794 L.62118 .4497 L.64181 .45152 L.66121 .45308 L.67138 .45374 L.68227 .45426 L.68851 .45446 L.69439 .45456 L.70539 .45449 L.71591 .45408 L.72556 .45334 L.73607 .45207 L.74707 .45016 L.75614 .44805 L.76569 .44525 L.78238 .43859 L.79211 .43346 L.80096 .42781 L.81634 .41513 LMistroke.83093 .3983 L.83732 .38867 L.84353 .37726 L.84805 .367 L.85213 .35545 L.85518 .34419 L.85728 .33365 L.85888 .32111 L.85952 .30943 L.85951 .30276 L.85928 .29676 L.85874 .28991 L.85796 .28355 L.85696 .27749 L.85565 .27121 L.85267 .26042 L.8486 .24957 L.84316 .23868 L.83783 .23039 L.83237 .22354 L.8253 .21649 L.81843 .21116 L.81154 .20702 L.80481 .20394 L.79751 .20156 L.79334 .20059 L.78948 .19993 L.78264 .19931 L.77625 .1993 L.76926 .19989 L.76184 .20119 L.75417 .20322 L.74708 .20574 L.73433 .2118 L.72123 .22027 L.7088 .23082 L.69954 .24076 L.69089 .25242 L.68354 .26542 L.68031 .27286 L.67792 .27969 L.67626 .28571 L.67494 .29225 L.67446 .29553 L.6741 .29901 L.67379 .30522 L.67389 .3103 L.67437 .31579 L.67526 .32139 L.67644 .3265 LMistroke.67786 .33115 L.6794 .33527 L.68371 .34407 L.68952 .35266 L.6971 .36088 L.70531 .36736 L.70924 .3698 L.71365 .3721 L.71785 .3739 L.72179 .37527 L.72563 .37631 L.72972 .3771 L.73427 .37761 L.73852 .37774 L.74317 .37747 L.74812 .3767 L.75285 .37547 L.75786 .37359 L.76245 .37128 L.76652 .36869 L.77373 .3626 L.77707 .35895 L.78047 .35449 LMfstroke% End of GraphicsMathPictureEnd>], Graphics, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}},CF5dJ6E]HGAYHf4PAg9QL6QYHgOol< 000POol00`00Oomoo`0EOol002Qoo`80025oo`@002Yoo`H000aoo` 03001oogoo04Yoo`@000aoo`@001eoo`03001oogoo01Aoo` 009Woo0P0067oo1`0027oo0P0087oo20004Woo00<007ooOol0AWoo1000 57oo0`006Woo00<007ooOol057oo000TOol2000AOol90007Ool= 000DOol9000JOol20013Ool4000KOol2000IOol00`00Oomoo`0COol002= oo`03001oogoo00ioo`<001aoo`H000Moo`P002=oo`03001oogoo03ioo`@ 0025oo`8001Moo`03001oogoo01=oo`008Goo0P003Goo10008goo2@00: goo00<007ooOol0?7oo0P009goo0P005Woo00<007ooOol04Woo000POol00 `00Oomoo`0;Ool2000QOol700000goo00000004Ool4000XOol00`00Oomoo `0jOol2000[Ool2000DOol00`00Oomoo`0BOol001moo`03001oogoo00Yoo `8001ioo`D000Yoo`8000Ioo`D002=oo`03001oogoo03Qooa<001ioo`8001 =oo`03001oogoo015oo` 007Goo0P002goo0P0077oo10004Goo0P002Goo10007goo00<007ooOol0; goo2@004goo100077oo00<007ooOol047oo00<007ooOol04Goo000LOol00 `00Oomoo`09Ool2000KOol3000GOol2000;Ool5000JOol00`00Oomoo` 0YOol60005Ool2000IOol4000IOol00`00Oomoo`0@Ool00`00Oomoo`0@ Ool001]oo`03001oogoo00Uoo`03001oogoo01Moo`@001aoo`8000ioo` H001Aoo`03001oogoo02=oo`H000Uoo`8001moo`<001Moo` 03001oogoo00moo`03001oogoo011oo`006Woo00<007ooOol02Goo00< 007ooOol05Woo0P008Woo0P004Woo200037oo00<007ooOol077oo1` 003Woo00<007ooOol08Woo0`005Goo00<007ooOol03goo00< 007ooOol03goo000IOol00`00Oomoo`09Ool00`00Oomoo`0E Ool2000VOol2000HOol60006Ool2000DOol9000COol2000XOol2000DOol00 `00Oomoo`0>Ool00`00Oomoo`0?Ool001Qoo`03001oogoo00Qoo`8001Moo `03001oogoo02Qoo`8001aooa`001Yoo`8002aoo`8001=oo` 03001oogoo00ioo`03001oogoo00ioo`005goo00<007ooOol027oo00< 007ooOol05Goo0P00;Goo00<007ooOol07goo00<007ooOol0:goo0P00< 7oo0P004Woo00<007ooOol03Goo00<007ooOol03Woo000GOol00`00Oomoo `07Ool00`00Oomoo`0EOol00`00Oomoo`0^Ool2000OOol00`00Oomoo` 0ZOol00`00Oomoo`0bOol00`00Oomoo`0@Ool00`00Oomoo`0Ool001Ioo`03001oogoo00Moo`03001oogoo01Aoo`8003=oo` 03001oogoo01aoo`03001oogoo02Qoo`8003Ioo`03001oogoo011oo` 03001oogoo00aoo`03001oogoo00eoo`005Woo00<007ooOol01Woo00< 007ooOol04goo0P00=Woo0P0077oo00<007ooOol09goo00<007ooOol0= goo00<007ooOol03goo00<007ooOol037oo00<007ooOol03Goo000EOol00 `00Oomoo`06Ool00`00Oomoo`0BOol2000jOol00`00Oomoo`0IOol00` 00Oomoo`0UOol2000kOol00`00Oomoo`0?Ool00`00Oomoo`0Ool00`00Oomoo`04Ool00`00Oomoo` 0EOol2000gOol00`00Ool00002Ool00`00Oomoo`03Ool00`00Oomoo` 0EOol00`00Oomoo`0gOol8000DOol00`00Oomoo`0;Ool00`00Oomoo`0: Ool00`00Oomoo`09Ool000moo`03001oogoo00Aoo`03001oogoo00ioo` 03001oogoo00=oo`8001Yoo`8003Ioo`04001oo`000006Ool00`00Oomoo` 0DOol00`00Oomoo`0dOol40008Ool3000BOol00`00Oomoo`0:Ool00` 00Oomoo`0;Ool00`00Oomoo`08Ool000moo`03001oogoo00Aoo`03001o ogoo00ioo`04001oogooOol2000NOol2000eOol00`00Oomoo`06Ool00` 00Oomoo`0COol00`00Oomoo`0cOol2000?Ool2000AOol00`00Oomoo`0: Ool00`00Oomoo`0:Ool00`00Oomoo`08Ool000moo`03001oogoo00=oo` 03001oogoo00ioo`05001oogooOol0000ROol2000dOol00`00Oomoo` 05Ool00`00Oomoo`0BOol00`00Oomoo`0bOol2000COol2000?Ool00` 00Oomoo`0:Ool00`00Oomoo`0:Ool00`00Oomoo`08Ool000ioo` 03001oogoo00Aoo`03001oogoo00ioo`05001oogooOol0000TOol00` 00Oomoo`0bOol00`00Oomoo`04Ool00`00Oomoo`0AOol00`00Oomoo` 0aOol2000GOol00`00Oomoo`0 Woo00<007ooOol05Goo00<007ooOol04Woo00<007ooOol01goo00< 007ooOol02Goo00<007ooOol02Goo00<007ooOol01Woo000Ool2000JOol00`00Oomoo`0BOol00`00 Oomoo`0Ool00` 00Oomoo`04Ool00`00Oomoo`0>Ool2000KOol00`00Oomoo`0=Ool00` 00Oomoo`0Ool00` 00Ool0000LOol00`00Oomoo`06Ool00`00Oomoo`0=Ool00`00Oomoo` 0YOol00`00Oomoo`1POol00`00Oomoo`09Ool00`00Oomoo`0;Ool00` 00Oomoo`0:Ool00`00Oomoo`08Ool000moo`03001oogoo00Aoo`03001o ogoo00moo`03001oo`0001aoo`03001oogoo00Aoo`03001oogoo00eoo` 03001oogoo02Yoo`03001oogoo05moo`03001oogoo00Yoo`03001oogoo00 ]oo`03001oogoo00Yoo`03001oogoo00Qoo`003goo00<007ooOol01Goo00 <007ooOol03goo0`0077oo00<007ooOol00Woo00<007ooOol03Woo00< 007ooOol0:Woo00<007ooOol0Ggoo00<007ooOol02Goo00< 007ooOol037oo00<007ooOol02Goo00<007ooOol02Goo000?Ool00` 00Oomoo`05Ool00`00Oomoo`0AOol2000LOol01000Ool0000047oo00< 007ooOol0:goo00<007ooOol0GWoo00<007ooOol02Woo00< 007ooOol02goo00<007ooOol02Woo00<007ooOol02Goo000@Ool00` 00Oomoo`05Ool00`00Oomoo`0AOol2000KOol2000AOol00`00Oomoo` 0SOol40005Ool00`00Oomoo`1MOol00`00Oomoo`0:Ool00`00Oomoo`0< Ool00`00Oomoo`0:Ool00`00Oomoo`09Ool0011oo`03001oogoo00Eoo` 03001oogoo019oo`8001Qoo`80009oo`8000ioo`03001oogoo02Aoo` 03001oogoo00Ioo`03001oogoo05aoo`03001oogoo00]oo` 03001oogoo00aoo`03001oogoo00Yoo`03001oogoo00Uoo`0047oo00< 007ooOol01Woo00<007ooOol04Woo0P005Goo0P001Woo00<0 07ooOol02Goo0P00:7oo00<007ooOol01Goo0`00:Goo00<007ooOol0; Woo0P003Goo00<007ooOol037oo00<007ooOol02Woo00< 007ooOol02Woo000AOol00`00Oomoo`05Ool00`00Oomoo`0COol3000A Ool20009Ool00`00Oomoo`07Ool00`00Oomoo`0YOol00`00Oomoo`04Ool00 `00Oomoo`0ZOol2000]Ool00`00Oomoo`0=Ool00`00Oomoo`0Ool00`00Oomoo`0goo0` 006Goo0`003Goo00<007ooOol047oo1000Egoo00<007ooOol047oo00< 007ooOol04Goo000ROol00`00Oomoo`0gOol3000OOol2000;Ool00` 00Oomoo`0DOol4001BOol00`00Oomoo`0@Ool00`00Oomoo`0BOol002=oo` 8003Aoo`<002Aoo`8000Uoo`8001Uoo`@004aoo`8001=oo`03001o ogoo019oo`009Goo0P00;Woo1000:Goo0`001Woo00<007ooOol077oo0` 00Agoo0P0057oo00<007ooOol04goo000WOol2000XOol4000` Ool20004Ool00`00Oomoo`0OOol30013Ool00`00Oomoo`0DOol00` 00Oomoo`0COol002Uoo`80029oo`@003Ioo`<00003Ool007oo02=oo`< 003moo`03001oogoo01Aoo`03001oogoo01Aoo`00:goo0`006goo1000? Goo0`009Woo1000>Goo0P005Woo00<007ooOol05Goo000^Ool8000= Ool60012Ool01000Ool00000:7oo1@007oo10008Goo0`00< Woo002;Ool00`00Oomoo`0lOol6000HOol3000eOol008]oo` 03001oogoo049ooaP003Qoo`00Rgoo00<007ooOol0TWoo002;Ool00` 00Oomoo`2BOol008]oo`03001oogoo099oo`00Rgoo00< 007ooOol0TWoo003oOolQOol00001>],0.0225154, 0.0616701}}]}, Open ]],Cell[, Text],Cell[BoxData[ ((( )(xml = XML`SVG`GraphicsToSymbolicSVG[p];)))], InputOnly],Cell[TextData[{ The SVG is larger than the , StyleBox[Mathematica, FontSlant->Italic], graphics language representation, }], Text],Cell[CellGroupData[{Cell[BoxData[ (ByteCount /@ {ExportString[xml, ], ToString[p, InputForm], ExportString[p, ]})], Input],Cell[BoxData[ ({20832, 27104, 13936})], Output]}, Open ]],Cell[TextData[{ Find the XML fragment that holds the line for the solution, it will be the first instance of , StyleBox[ , InlineInput], .}], Text],Cell[BoxData[ ((( )(pts = <> n First[ Cases[ xml, n XMLElement[, { -> _, -> x_}, _] -> x, Infinity]];)))], InputOnly],Cell[TextData[{ Generate a new fragment of symbolic XML that holds an SVG animation, this has the form n, StyleBox[ , InlineInput], .}], Text],Cell[BoxData[ ((( )(newElem = XMLElement[, n { -> <0>, -> <0>, -> <.1>, -> , [IndentingNewLine]tt -> , -> <0.01>}, n {XMLElement[ , [IndentingNewLine] { -> <6s>, -> , [IndentingNewLine] -> , -> pts}, {}]}];)))], InputOnly],Cell[Now we add this new fragment back into the original SVG, Text],Cell[BoxData[ ((newXML = xml /. x : XMLElement[, ___] -> Sequence[x, newElem] ;))], InputOnly],Cell[Export the SymbolicXML out to a file, Text],Cell[CellGroupData[{Cell[BoxData[ (((Export[, newXML, ])( )))], Input],Cell[BoxData[ (file.svg)], Output]}, Open ]],Cell[, Text]}, Open ]]},ScreenRectangle->{{0, 1280}, {0, 934}},WindowSize->{839, 690},WindowMargins->{{Automatic, 146}, {Automatic, 23}},StyleDefinitions -> DemoText.nb](********************************************** *********************the top of the file. The cache data will then be recreated whenyou save this file from within Mathematica.************************************************* ******************)(*CellTagsOutlineCellTagsIndex->{ t:1->{ Cell[12796, 351, 65, 1, 54, Section, CellTags->t:1]} }*)(*CellTagsIndexCellTagsIndex->{ {t:1, 53445, 1649} }*)(*NotebookFileOutlineNotebook[{Cell[1754, 51, 105, 4, 70, Title],Cell[1862, 57, 56, 0, 41, Subtitle],Cell[1921, 59, 82, 3, 76, Subsubtitle],Cell[CellGroupData[{Cell[2028, 66, 31, 0, 54, Section],Cell[2062, 68, 487, 9, 67, Text],Cell[2552, 79, 513, 13, 48, Text]}, Open ]],Cell[CellGroupData[{Cell[3102, 97, 115, 4, 54, Section],Cell[3220, 103, 214, 7, 29, Text],Cell[CellGroupData[{Cell[3459, 114, 71, 1, 40, Input],Cell[3533, 117, 130, 3, 49, Output]}, Open ]],Cell[3678, 123, 172, 5, 30, Text],Cell[CellGroupData[{Cell[3875, 132, 40, 1, 40, Input],Cell[3918, 135, 4217, 90, 194, 661, 42, GraphicsData, PostScript, Graphics],Cell[8138, 227, 130, 3, 49, Output]}, Open ]],Cell[8283, 233, 335, 11, 50, Text],Cell[CellGroupData[{Cell[8643, 248, 65, 1, 40, Input],Cell[8711, 251, 690, 10, 372, Output]}, Open ]],Cell[9416, 264, 623, 18, 68, Text],Cell[CellGroupData[{Cell[10064, 286, 63, 1, 40, Input],Cell[10130, 289, 1159, 20, 201, Output]}, Open ]],Cell[11304, 312, 268, 8, 49, Text],Cell[CellGroupData[{Cell[11597, 324, 65, 1, 40, Input],Cell[11665, 327, 1082, 18, 182, Output]}, Open ]]}, Open ]],Cell[CellGroupData[{Cell[12796, 351, 65, 1, 54, Section, CellTags->t:1],Cell[12864, 354, 119, 4, 29, Text],Cell[CellGroupData[{Cell[13008, 362, 221, 4, 60, Input],Cell[13232, 368, 225, 6, 49, Output]}, Open ]],Cell[13472, 377, 53, 0, 29, Text],Cell[CellGroupData[{Cell[13550, 381, 124, 3, 40, Input],Cell[13677, 386, 36505, 1162, 194, 13123, 869, GraphicsData, PostScript, Graphics]}, Open ]],Cell[50197, 1551, 123, 3, 29, Text],Cell[50323, 1556, 103, 2, 48, InputOnly],Cell[50429, 1560, 152, 5, 29, Text],Cell[CellGroupData[{Cell[50606, 1569, 139, 2, 40, Input],Cell[50748, 1573, 55, 1, 49, Output]}, Open ]],Cell[50818, 1577, 198, 5, 30, Text],Cell[51019, 1584, 325, 5, 88, InputOnly],Cell[51347, 1591, 206, 5, 61, Text],Cell[51556, 1598, 697, 10, 148, InputOnly],Cell[52256, 1610, 71, 0, 29, Text],Cell[52330, 1612, 145, 3, 48, InputOnly],Cell[52478, 1617, 52, 0, 29, Text],Cell[CellGroupData[{Cell[52555, 1621, 88, 1, 40, Input],Cell[52646, 1624, 44, 1, 49, Output]}, Open ]],Cell[52705, 1628, 99, 2, 29, Text]}, Open ]]}]*)(****************************************************** *************End of Mathematica Notebook file.********************************************************* **********)Reply-To: kuska@informatik.uni-leipzig.de ==== Hi,and preventing the evaluation of ComplicatedF[] for symbolicarguments withComplicatedF[x_?NumericQ] := Re[NIntegrate[E^(-(I x + y + I)^2), {y, 0,1}]];NIntegrate[ComplicatedF[x], {x, 0, 2}, Method -> MonteCarlo] Jens I have a rather complicated function that Mathematica can't seem to handle> with> NIntegrate, Method->MonteCarlo. This is not my function, but it shows the essence of the problem.> Suppose we have ComplicatedF[x_] := Re [NIntegrate [E^(- (I x+y+I)^2), {y,0,1}] ] Then, if you try: NIntegrate[ComplicatedF[x], {x,0,2}, Method->MonteCarlo] Mathematica will complain that the integrand is not numerical.> But of course it is numerical and removing the Method->MonteCarlo option> will generate an answer. Now my actual function is quite complicated which is why> I want to try the MonteCarlo method. Any suggestions? ==== Alan,complaining about its input. For some reason, the MonteCarlo NIntegrate isexamining the quantity ComplicatedF[x] where x is not numerical. TryThe way to avoid this situation is to change the function by restricting itsinput to only numeric quantities:Clear[ComplicatedF]ComplicatedF[x_?NumericQ] := Re [NIntegrate [E^(- (I x+y+I)^2), {y,0,1}] ]Now try your Monte Carlo integration and you will see no errors.Carl WollPhysics DeptU of Washington> I have a rather complicated function that Mathematica can't seem to handle> with> NIntegrate, Method->MonteCarlo.>> This is not my function, but it shows the essence of the problem.> Suppose we have>> ComplicatedF[x_] := Re [NIntegrate [E^(- (I x+y+I)^2), {y,0,1}] ]>> Then, if you try:>> NIntegrate[ComplicatedF[x], {x,0,2}, Method->MonteCarlo]>> Mathematica will complain that the integrand is not numerical.> But of course it is numerical and removing the Method->MonteCarlo option> will generate an answer.>> Now my actual function is quite complicated which is why> I want to try the MonteCarlo method. Any suggestions?>> ==== > I have a program which uses a random number in several places - the> same> number in a given run of the program. When I implement the program> however> the number changes in every new call to it. I've tried to overcome> this> using Which, Hold, Verbatim, and others, all to no avail. Any> help> greatly appreciated.> This is what SeedRandom is for, e.g.> SeedRandom[5];Table[Random[Integer,{1,10}],{3}]> {2,3,2}>> Now evaluating again:> SeedRandom[5];Table[Random[Integer,{1,10}],{3}]> {2,3,2}> Andrzej Kozlowski> Yokohama, Japan> http://www.mimuw.edu.pl/~akoz/> http://platon.c.u-tokyo.ac.jp/andrzej/>> suggested. There is some difficulty. If I try>> F[n_]= SeedRandom;Table[Random[Real,{-1,1}],{n}]> Don Darling.>>You need to use a seed with SeedRandom and you need to enclose the composite statement in parentheses:F[n_] := (SeedRandom[5]; Table[Random[Real, {-1, 1}], {n}])Now look:In[6]:=F[3]Out[6]={0.573197,0.696679,0.225655}In[7]:=F[5 ]Out[7]={0.573197,0.696679,0.225655,-0.203925,-0.523976}Each random sequence will be an extension of shorter ones.Andrzej KozlowskiYokohama, Japanhttp://www.mimuw.edu.pl/~akoz/http:// platon.c.u-tokyo.ac.jp/andrzej/Reply-To: kuska@informatik.uni-leipzig.de ==== Hi,http:// library.wolfram.com/database/MathSource/560/ Jens If I activate < want real values, how can I get rid of it so I can do a different> calculation involving complex values. In other words, how do I close the> RealOnly function. Is there another way of doing a calculation that will ==== Ray,The suggestion that I previously posted should have used Get (as Bob Hanlondid) instead ofNeeds.With Needs, On[RealOnly] does not load the package Miscellaneous`RealOnly`when use a second time, and in particular after using Off[RealOnly] ---thisis because Miscellaneous`RealOnly` will be in the list $Packages.Here is the corrected version,RealOnly /: On[RealOnly] := Get[ Miscellaneous`RealOnly`];RealOnly /: Off[RealOnly] := (Unprotect[Power, Solve, Roots]; Clear[Power, Solve, Roots]; Protect[Power, Solve, Roots]; Remove[Miscellaneous`RealOnly`Nonreal]; $Post =. )>> If I activate < want real values, how can I get rid of it so I can do a different> calculation involving complex values. In other words, how do I close the> RealOnly function. Is there another way of doing a calculation that will> Ray,> Here is a modification of a posting by Bob Hanlon in Sept 2000.> RealOnly /: On[RealOnly] :=> Needs[ Miscellaneous`RealOnly`];>> RealOnly /: Off[RealOnly] :=> (Unprotect[Power, Solve, Roots]; Clear[Power, Solve,> Roots]; Protect[Power, Solve, Roots];> Remove[Miscellaneous`RealOnly`Nonreal]; $Post =. )>> Check>> (-1.)^(1/3)>> 0.5 + 0.8660254037844387*I>> On[RealOnly]> (-1.)^(1/3)>> -1.>> Off[RealOnly]> (-1.)^(1/3)>> 0.5 + 0.8660254037844387*I> -->> ---------------------> Hayes> Mathematica Training and Consulting> Leicester UK> hay@haystack.demon.co.uk> Voice: +44 (0)116 271 4198>> ==== Hiit seems I have a simple problem, but I cannot find a (simple)solution:if I type 2^^1000111 mathematica calculates the correct dec. numberbut if I type: base=2; number=1000111; base^^number all I get is a errorSo a function Convert[number_,base_] for base convertions cannot work ...Any ideasThxWerner--********************************************* ******************************Prof. Mag. Werner CYRMONHTBLuVA Wr. Neustadt Abt. EDVOhttp://edvowww.htlwrn.ac.at/cyx************************** *************************************************If you can imagine it, you can do it! Walt Disney******************************************************* ********************Want to learn math with fun or calculating some stuff online:Look at http://Onlinemath.htlwrn.ac.atReply-To: kuska@informatik.uni-leipzig.de ==== Hi,Mathematica can't draw transparent surfaces but MathGL3d canGet[MathGL3d`OpenGLViewer`]MVShow3D[z2r, MVNewScene -> True, MVAlpha -> 0.5];MVShow3D[z2i, MVAlpha -> 0.5];you can get MathGL3d fromhttp://phong.informatik.uni-leipzig.de/~kuska/mathgl3dv3/ id3.htm Jens Is it possible to have a semi transparent view of surfaces so that one> may verify slopes by ParametricPlot3D for Cauchy-Riemann relations?> The following is program for 3 functions Z^2, Z^3, Sin[Z].It was> expected to check slopes at the line of intersection of Re and Im parts. R1=x^2-y^2 ; I1= 2 x y ;> z2r=Plot3D[R1 , {x,-Pi,Pi},{y,-Pi,Pi} ];> z2i=Plot3D[I1 , {x,-Pi,Pi},{y,-Pi,Pi} ];> Show[z2r,z2i] ; ÔTop view > Re,Im Intxn';> Plot[{x ArcTan[-Sqrt[2]+1],x ArcTan[Sqrt[2]+1]}, {x,-Pi,Pi} ]; R3=x^3 - 3 x y^2 ; I3= 3 x^2 y - y ^3 ;> z3r=Plot3D[R3 , {x,-Pi,Pi},{y,-Pi,Pi} ];> z3i=Plot3D[I3 , {x,-Pi,Pi},{y,-Pi,Pi} ];> Show[z3r,z3i] ; ÔTop view > Re,Im Intxn';> Plot[{x,x (-Sqrt[3]+2) , x (-Sqrt[3]-2) }, {x,-Pi,Pi} ]; R2=Cosh[y] Sin[x] ; I2=Sinh[y] Cos[x] ;> scr=Plot3D[R2,{x,-Pi/2,Pi/2},{y,-Pi/2,Pi/2}];> sci=Plot3D[I2,{x,-Pi/2,Pi/2},{y,-Pi/2,Pi/2}];> Show[scr,sci]; ÔTop view > Re,Im Intxn';> Plot[{ArcTanh[Tan[x]]},{x,-Pi/2,Pi/2 }];> --> To contact in private, remove ==== Show::gtype: CartesianMap is not a type of graphics.Is it version realated? mine is V 2.2 -- Narasimham> My friend Rip Pelletier pointed me to a better method to> illustrate the> Cauchy-Riemann relations for analytic functions. He> pointed me to Tristan> Needham's book ÔVisual Complex Analysis'. In Chapter 5, Section I -> Cauchy-Riemann Revealed, the CR conditions are related to the complex> mapping.>> If a small patch of squares are mapped by an analytic> function, then they go> into another small patch in which all the squares have> been amplified and> rotated in exactly the same way.>> Fortunately, we have the ComplexMap package in Mathematica> and can easily> illustrate this for your functions. For example, for the> Sin function...>> Needs[ÔGraphics`ComplexMap`']>> With[> {x = 2,> y = 2,> del = 0.01,> f = Sin},> Show[GraphicsArray[{CartesianMap[> Identity, {x - del, x + del, del/5}, {y - del,> y + del, del/5},> Axes -> False,> DisplayFunction -> Identity],>> CartesianMap[> f, {x - del, x + del, del/5}, {y - del, y + del, del/5},> Axes -> False,> DisplayFunction -> Identity]}],> ImageSize -> 500]];>> A square patch maps into a rotated square patch. Just> change f and/or the> mapping points for other cases. Use a pure function for z^2.>> For a case that is not analytic, and so the CR relations> do not hold, use> f = # + 2Abs[#] &. The squares go to parallelograms.>> David Park> djmp@earthlink.net> http://home.earthlink.net/~djmp/> Is it possible to have a semi transparent view of surfaces> so that one> may verify slopes by ParametricPlot3D for Cauchy-Riemann relations?> The following is program for 3 functions Z^2, Z^3, Sin[Z].It was> expected to check slopes at the line of intersection of Re> and Im parts.>> R1=x^2-y^2 ; I1= 2 x y ;> z2r=Plot3D[R1 , {x,-Pi,Pi},{y,-Pi,Pi} ];> z2i=Plot3D[I1 , {x,-Pi,Pi},{y,-Pi,Pi} ];> Show[z2r,z2i] ; ÔTop view > Re,Im Intxn';> Plot[{x ArcTan[-Sqrt[2]+1],x ArcTan[Sqrt[2]+1]}, {x,-Pi,Pi} ];>> R3=x^3 - 3 x y^2 ; I3= 3 x^2 y - y ^3 ;> z3r=Plot3D[R3 , {x,-Pi,Pi},{y,-Pi,Pi} ];> z3i=Plot3D[I3 , {x,-Pi,Pi},{y,-Pi,Pi} ];> Show[z3r,z3i] ; ÔTop view > Re,Im Intxn';> Plot[{x,x (-Sqrt[3]+2) , x (-Sqrt[3]-2) }, {x,-Pi,Pi} ];>> R2=Cosh[y] Sin[x] ; I2=Sinh[y] Cos[x] ;> scr=Plot3D[R2,{x,-Pi/2,Pi/2},{y,-Pi/2,Pi/2}];> sci=Plot3D[I2,{x,-Pi/2,Pi/2},{y,-Pi/2,Pi/2}];> Show[scr,sci]; ÔTop view > Re,Im Intxn';> Plot[{ArcTanh[Tan[x]]},{x,-Pi/2,Pi/2 }];-- To contact in private, remove Reply-To: kuska@informatik.uni-leipzig.de ==== Hi,what is withFindPrimes[n_Integer] := Select[Table[i, {i, n^2, (n + 1)^2}], PrimeQ] Jens Folks, I am trying to come up with a snazzy way to hunt for a prime between n^2 and> (n+1)^2.> ==== =================================================> God made the integers, all else is the work of man.> L. Kronecker, Jahresber. DMV 2, S. 19. ==== Hi, How can I (vertically) align several Plots (graphs) in theGraphicsArray to have y axis in the same x position?Somehing like plots = Table[Plot[Sin[i x], {x, 1, [Pi]}], {i, 1, 3}];Show[GraphicsArray[Partition[plots, 1], GraphicsSpacing -> {1, -0.1}]]And how can I impose the AspectRatio of the individual graphs to havex axis spanning the whole x resolution and y axis only one third of yresolution?Cyril FischerReply-To: kuska@informatik.uni-leipzig.de ==== Hi,andresult = Solve[{a == 1/(1/r2 + 1/50), 50 == 1/(1/(a + r1) + 1/r2)}, r1,a]Plot[Evaluate[r1 /. result], {r2, -25, 25}]works fine. Jens I'd sure like to find out how to clean up a process I do a lot. Namely, get> a solution to some set of equations and then plot the result. For example,> I recently did result = Solve[{a == 1/(1/r2 + 1/50), 50 == 1/(1/(a + r1) + 1/r2)}, r1, a] This gives {{r1 -> (a function of r2) }} Then, I plot it by> Plot[ (this function of r2), {r2, startvalue, stopvalue}] where I carefully type in this function. I feel sure you Mathematica pros> don't have to do that so I have made several feeble attempts to automate> this over the years. They fail because I still don't have a clue how Mathematica works. Here's my last attempt:> Plot[ result /. %]> a thing to me. Surely there is a way to get this plot without having to type the Solve[] result> into Plot[]. Any hints would be appreciated, as usual. Rob ==== I have a complex-valued function f(z).If z = x + I y, suppose f(z) has a finite number of simple zerosin the rectangle a < x < b, c < y < d. (and no poles).I can start FindRoot somewhere and it will likely find a root.But, my question is:is there a (best?) systematic way to use Mathematica to findall the roots in the region? ==== Dear MathGroup,I am working on an application where I define a number of graphical objects,which can then be used like graphical primitives. I also want to definegraphical primitives that will control the color, position and size of someof these objects. The use of color is slightly complicated because the colorthat is set may be used for lines, or in SurfaceColor or in EdgeForm and itmay be lightened or darkened.My basic approach is to store the value of the directives in internalvariables and then the graphical primitives use these values.But it is difficult to make it all behave just like regular Mathematicagraphical directives.1) The list of primitives must be HoldFirst. Premature evaluation will causethe last instance of a programmed directive to be used for all cases.2) The default values of any primitives must be set before the primitivesare evaluated else whatever is left over from the last plot will be used.I can pretty much handle those problems. The last problem is more difficultand is the core of my question.3) Regular graphics directives are nested in the sense that if one is setinside brackets, {directive,... }, then, after exiting the brackets, thedirective reverts to the value existing before the brackets were entered.Is it possible to program that behavior?Here is an example. It could be done with regular Mathematica directives,but it was picked to be a simple example. In my actual cases I have to useprogramming. The extra graphical primitive is a ColoredLine. The color to beLineColor. The value is stored in currentcolor.Needs[Graphics`Colors`]currentcolor = Black;ColoredLine[start_, end_] := {currentcolor, Line[{start, end}]}LineColor[color_] := (currentcolor = color; Sequence[]) Show[Graphics[ {LineColor[Black], Sequence @@ primitives}], opts]In the following use everything works. {ColoredLine[{0, 0}, {1, 0}], LineColor[Red], ColoredLine[{0, 1}, {1, 1}], LineColor[Blue], Coloredline[{0, 2}, {1, 2}]}, Background -> Linen, ImageSize -> 400];But if I use nesting it, of course, doesn't work like regular Mathematicadirectives. The color does not revert to Black. {ColoredLine[{0, 0}, {1, 0}], {LineColor[Red], ColoredLine[{0, 1}, {1, 1}]}, Coloredline[{0, 2}, {1, 2}]}, Background -> Linen, ImageSize -> 400];It appears that I need to somehow implement a recursive evaluation of theprimitives list. Any ideas on how I could do that.David Parkdjmp@earthlink.nethttp://home.earthlink.net/~djmp/ Reply-To: kuska@informatik.uni-leipzig.de ==== Hi,try FullForm to see all digits of a ßoating point numberthat is truncated by the Print/Output functions. Jens I tried some of my Mathematica3.01 programs on a computer with> Mathematica4.1,> there where some differences that I could not explain. Regarding N[]: consider for example:> with version 4.1 I got: N[Sqrt[2.],16]->1.4142> and> N[Sqrt[2.],17]->1.4142135623730950 and in version 3.01: N[Sqrt[2.],16]->1.414213562373095> and> N[Sqrt[2.],17]->1.4142135623730950 Using SetPrecision[Sqrt[2.],16] I could make Mathematica4.1 give me 16> digits precision.> Ideas? Peter WReply-To: kuska@informatik.uni-leipzig.de ==== Hi,a interpolation gives for the data x[i], y[i] at everypoint x[i] the original y[i], a fit must not do that. Jens > Another in a series of potentially simple questions: What is the difference between using Fit and Interpolation?> f[x_]=Fit[data, {1,x},x]> -or-> f[x_]=Interpolation[data][x] I do know that Fit can take arguments for the independant variables> form like:> f[x_]=Fit[data, {1,x},x]> f[x_]=Fit[data, {1,x,x^2},x]> but that's a bit of guesswork if you have a limited set of points, no? Also, is there a function in Mathematica that allows me to swap> dependent and independent variables? e.g. x=2.5y --> y=x/2.5 > David Seruyange> Student ==== >What is the difference between using Fit and Interpolation?>f[x_]=Fit[data, {1,x},x] -or- f[x_]=Interpolation[data][x]There are several differences between the expressions aboveFirst, Interpolation[data][x] isn't correct syntax. It should be Interpolation[data]. Interpolation returns a pure function of data. By default that is a 3rd order polynominal that passes through each of the points specified by the variable data.In contrast, Fit[data,{1,x},x] returns a best fit *line* for the points specified by data. The result is not a pure function but an expression. The result is a least squares fit to the data and will not pass through the points specified unless they lie exactly on a line.The two functions, Interpolation and Fit, are intended for different purposes.Suppose you had a list of data points that were known to be accurate to the precesion specified and wanted to estimate the value of the unknown function at an intermediate point. For this you would use interpolation since you want the result to pass through each of the data points you started with.Now suppose you had a list of data points where each data point you have is really the sum of a true value and a random error. The best result would ideally subtract out the error and yeild the true values. So, you would definitely not want the result to pass through the points with error. For this problem you would use Fit. ==== Hi group:When loading Combinatorica with < Calculus, Graphics, Statistics, and Personal (this with some private utilities).Emilio Martin-Serrano___________________________________Reply-To: kuska@informatik.uni-leipzig.de ==== Hi,can you explain how you simple example was obtained ? Jens I want to make a matrix of derivations, so I will be able to multiply> it by a matrix of functions and get the result matrix> simple example: |d/dx 0 | |xy x| |y 1|> | |.| |=| |> |d/dy d/dx| |x+y 3| |x+1 0| thank you ==== When your first matrix is a matrix of functions, then the dot productresults in a matrix of sums of products of arguments and functions. A simplesubstitution then will give you the result you are looking for.In[1]:=mat1 = {{D[#1, x] & , 0 & }, {D[#1, y] & , D[#1, x] & }}Out[1]={{D[#1, x] & , 0 & }, {D[#1, y] & , D[#1, x] & }}In[2]:=mat2 = {{x*y, x}, {x + y, 3}}Out[2]={{x*y, x}, {x + y, 3}}In[3]:=mat1 . mat2 /. a_.*b_Function -> b[a]Out[3]={{y, 1}, {1 + x, 0}}Fred SimonsEindhoven University of Technology> -----Original Message-----> Sent: maandag 3 februari 2003 7:08> To: mathgroup@smc.vnet.net > I want to make a matrix of derivations, so I will be able to multiply> it by a matrix of functions and get the result matrix> simple example: |d/dx 0 | |xy x| |y 1|> | |.| |=| |> |d/dy d/dx| |x+y 3| |x+1 0| thank you> ==== > I want to make a matrix of derivations, so I will be able to multiply> it by a matrix of functions and get the result matrix> simple example:>> |d/dx 0 | |xy x| |y 1|> | |.| |=| |> |d/dy d/dx| |x+y 3| |x+1 0|>> thank you>Inner[#1[#2]&, {{D[#, x]&, #*0&},{D[#, y]&, D[#, x]&}}, {{x*y, x}, {x + y, 3}}, Plus]{{y, 1}, {1 + x, 0}}orInner[D[#2,#1]&, {{x, Unique[]},{y, x}}, {{x*y, x},{x + y, 3}}, Plus]{{y, 1}, {1 + x, 0}}Bob Hanlon ==== Dear all,Suppose I create a function f[x_,opts___]with optionsShape in {Circle, Ellipsis} and Diameter in R+, DiameterLong in R+,DiameterShort in R+Say that the defaults areOptions[x]={Shape->Circle, Diameter->1.}The option Diameter makes sence only when Shape->Circle, andThe options DiameterShort/Long make sense only when Shape->EllipsisIs there a quick way to tell Mathematica to warn if these conditions arenot satisfied? I could write a series of boolean tests, but I was wonderingif there is a more elegant way.Best,Kyriakos_____+**+____+**+___+**+__+**+_Kyriakos ChourdakisLecturer in Financial EconomicsURL: http://www.qmw.ac.uk/~te9001tel: (++44) (+20) 7882 5086Dept of EconomicsUniversity of London, QMLondon E1 4NSU.K. ==== i have a problem by creating a package. I need routines from another> packageI think that your second form of the package loading is correct: > BeginPackage[Seismo`Hazard`PSHA`,{Statistics` ContinuousDistributions`}]but you should use the full context with symbols inside your own package which are from Statistics`ContinuousDistributions`, e.g. writeStatistics`ContinuousDistributions` NormalDistributioninstead ofNormalDistribution> Random::randt: Type specification> Seismo`Hazard`PSHA`Private`NormalDistribution[<<19>> , 0.16] in Random[<< 1 >]> should be Real, Integer, or Complex.-- Antti Penttil.8a Antti.I.Penttila@invalid.helsinki.fi ==== One of the new features of Mathematica 4.2 are theXML tools and I have written an example of their usebased on SVG (an XML application for vector graphics).Tom Wickham-Jones CreatedBy='Mathematica 4.2' Mathematica-Compatible NotebookThis notebook can be used with any Mathematica-compatibleapplication, such as Mathematica, MathReader or Publicon. The datafor the notebook starts with the line containing stars above.To get the notebook into a Mathematica-compatible application, doone of the following:* Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application;* Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application.Data for notebooks contains only printable 7-bit ASCII and can beCR, LF or CRLF (Unix, Macintosh or MS-DOS style).NOTE: If you modify the data for this notebook not in a Mathematica-compatible application, you must delete the line below containingtry to use invalid cache data.For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com phone: +1-217-398-0700 (U.S.)Notebook reader applications are available free of charge from Wolfram Research.**************************************************** ***************)(* NotebookFileLineBreakTestNotebookFileLineBreakTest*)(* NotebookOptionsPosition[ 52820, 1633]*)(*NotebookOutlinePosition[ 53608, 1662]*)(* CellTagsIndexPosition[ 53538, 1656]*)(*WindowFrame->Normal*)Notebook[{Cell[TextData[{ Generating SVG with , StyleBox[Mathematica, FontSlant->Italic]}], Title],Cell[An example of the use of SymbolicXML, Subtitle],Cell[, Subsubtitle],Cell[CellGroupData[{Cell[What is SVG?, Section],Cell[TextData[{ SVG is an XML language for describing two-dimensional graphics. Since it is based on XML any XML aware application can work with SVG. , StyleBox[Mathematica, FontSlant->Italic], has some good tools for working with XML and some specific functions that support SVG, thus it is a good environment for some interesting SVG applications. SVG contains some interesting features including a variety of dynamic features such as animations.}], Text],Cell[TextData[{ SVG can be rendered with a browser plug-in from Adobe, , ButtonBox[http://www.adobe.com/svg, ButtonData:>{ URL[ http://www.adobe.com/svg], None}, ButtonStyle->Hyperlink], . which provides strong support including the animation functions. More information about SVG can be found at the W3C site: , ButtonBox[http://www.w3.org/Graphics/SVG/, ButtonData:>{ URL[ http://www.w3.org/Graphics/SVG/], None}, ButtonStyle->Hyperlink], .}], Text]}, Open ]],Cell[CellGroupData[{Cell[TextData[{ StyleBox[Mathematica, FontSlant->Italic], Commands for Generating SVG}], Section],Cell[TextData[{ StyleBox[Mathematica, FontSlant->Italic], has a rich graphics language for representing graphics as , StyleBox[Mathematica, FontSlant->Italic], expressions.}], Text],Cell[CellGroupData[{Cell[BoxData[ (p = Graphics[Line[ {{0, 0}, {1, 1}}]])], Input],Cell[BoxData[ TagBox[([SkeletonIndicator] Graphics [SkeletonIndicator]), False, Editable->False]], Output]}, Open ]],Cell[TextData[{ These print as expressions, if you want to see a graphical expression you use a command such as , StyleBox[Show, InlineInput], .}], Text],Cell[CellGroupData[{Cell[BoxData[ (Show[p])], Input],Cell[GraphicsData[PostScript, <%!%%Creator: Mathematica%%AspectRatio: .61803 MathPictureStart/Mabs {Mgmatrix idtransformMtmatrix dtransform} bind def/Mabsadd { Mabs3 -1 roll add3 1 roll addexch } bind def%% Graphics%%IncludeResource: font Courier%%IncludeFont: Courier/Courier findfont 10 scalefont setfont% Scaling calculations0.0238095 0.952381 0.0147151 0.588604 [[ 0 0 0 0 ][ 1 .61803 0 0 ]] MathScale% Start of Graphics1 setlinecap1 setlinejoinnewpath0 0 m1 0 L1 .61803 L0 .61803 Lclosepathclipnewpath0 g.5 Mabswid[ ] 0 setdash.02381 .01472 m.97619 .60332 Ls% End of GraphicsMathPictureEnd>], Graphics, ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}},CF5dJ6E]HGAYHf4PAg9QL6QYHgmoo`00Yoo`00=Woo00< 007ooOol0igoo000gOol2003WOol003Uoo`800>Eoo`00>goo00< 007ooOol0hWoo000lOol2003ROol003ioo`03001oogoo0=moo`00?goo 0P00ggoo0011Ool2003MOol004=oo`03001oogoo0=Yoo` 00A7oo0P00fWoo0016Ool00`00Oomoo`3GOol004Moo`800=Moo` 00BGoo0P00eGoo001;Ool00`00Oomoo`3BOol004aoo`800=9oo` 00CWoo0P00d7oo001@Ool00`00Oomoo`3=Ool0055oo`800Ool0091oo`8008ioo` 00TWoo0P00S7oo002DOol00`00Oomoo`29Ool009Eoo`8008Uoo`00Ugoo00< 007ooOol0QWoo002HOol20026Ool009Yoo`8008Aoo`00W7oo00< 007ooOol0PGoo002MOol20021Ool009moo`8007moo`00XGoo00< 007ooOol0O7oo002ROol2001lOol00:Aoo`03001oogoo07Uoo`00YGoo0P00 NGoo002WOol2001gOol00:Uoo`03001oogoo07Aoo`00ZWoo0P00M7oo002/ Ool00`00Oomoo`1aOol00:eoo`80075oo`00[goo0P00Kgoo002aOol00` 00Oomoo`1/Ool00;9oo`8006aoo`00]7oo0P00JWoo002fOol00`00Oomoo` 1WOol00;Moo`8006Moo`00^Goo00<007ooOol0I7oo002jOol2001TOol00; aoo`80069oo`00_Woo00<007ooOol0Ggoo002oOol2001OOol00<5oo` 8005eoo`00`goo00<007ooOol0FWoo0034Ool2001JOol00Ool00`00Oomoo`1?Ool00=oo`8003]oo`00iGoo00< 007ooOol0>7oo003VOol2000hOol00>Qoo`03001oogoo03Eoo` 00jGoo0P00=Goo003[Ool2000cOol00>eoo`03001oogoo031oo` 00kWoo0P00<7oo003`Ool00`00Oomoo`0]Ool00?5oo`8002eoo` 00lgoo0P00:goo003eOol00`00Oomoo`0XOol00?Ioo`8002Qoo` 00n7oo0P009Woo003jOol00`00Oomoo`0SOol00?]oo`8002=oo`00oGoo00< 007ooOol087oo003nOol2000POol00?moo`5oo`8001ioo`00ogoo0goo00< 007ooOol06goo003oOol4Ool2000KOol00?moo`Ioo`8001Uoo` 00ogoo27oo00<007ooOol05Woo003oOol9Ool2000FOol00?moo`]oo`03 001oogoo01=oo`00ogoo37oo0P004goo003oOol>Ool2000AOol00?mooa1oo `03001oogoo00ioo`00ogoo4Goo0P003Woo003oOolCOol00`00Oomoo`0; Ool00?mooaAoo`8000]oo`00ogoo5Woo0P002Goo003oOolHOol00` 00Oomoo`06Ool00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00 >],0.00366761, 0.00593432}}],Cell[BoxData[ TagBox[([SkeletonIndicator] Graphics [SkeletonIndicator]), False, Editable->False]], Output]}, Open ]],Cell[TextData[{ StyleBox[Mathematica, FontSlant->Italic], can write an XML representation of a , StyleBox[Mathematica, FontSlant->Italic], graphics expression into a string with , StyleBox[ExportString, InlineInput], and into a file with , StyleBox[Export, InlineInput], .}], Text],Cell[CellGroupData[{Cell[BoxData[ (str = ExportString[p, ])], Input],Cell[BoxData[ (n nn n n n)], Output]}, Open ]],Cell[TextData[{ A string of XML can be read back into , StyleBox[Mathematica, FontSlant->Italic], with the command , StyleBox[ImportString, InlineInput], with a format of , StyleBox[XML, InlineInput], . This returns a symbolic XML expression that is an isomorphic representation of the original XML. The symbolic XML version of the XML can be worked with by standard , StyleBox[Mathematica, FontSlant->Italic], programming techniques. This is demonstrated in the , ButtonBox[next section, ButtonData:>t:1, ButtonStyle->Hyperlink], .}], Text],Cell[CellGroupData[{Cell[BoxData[ (ImportString[str, ])], Input],Cell[BoxData[ ((XMLObject[ Encoding [Rule] UTF-8], (XMLObject[Doctype])[svg, Public [Rule] -//W3C//DTD SVG 1.0//EN, System [Rule] http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd]}, XMLElement[ svg, {{http://www.w3.org/2000/xmlns/, xmlns} [Rule] http://www.w3.org/2000/svg, width [Rule] 288.0pt, height [Rule] 177.994pt, viewBox [Rule] -0.025 -0.0154508 1.05 0.648936, preserveAspectRatio [Rule] xMidYMid meet}, {XMLElement[ g, {transform [Rule] scale(1, -1) translate(0,-0.618034), style [Rule] fill:black; font-family:'Courier New', Courier, Symbol, monospace; font-size:0.021875pt; stroke:black; stroke-width:0.000911458pt}, {XMLElement[line, {fill [Rule] none, x1 [Rule] 0.0, y1 [Rule] 0.0, x2 [Rule] 1.0, y2 [Rule] 0.618034}, {}]}]}], {}, Valid [Rule] True])], Output]}, Open ]],Cell[TextData[{ The command , StyleBox[XML`SVG`GraphicsToSymbolicSVG, InlineInput], goes directly from a , StyleBox[Mathematica, FontSlant->Italic], graphics expression directly to the symbolic XML representation of the SVG.}], Text],Cell[CellGroupData[{Cell[BoxData[ (XML`SVG`GraphicsToSymbolicSVG[p])], Input],Cell[BoxData[ ((XMLObject[ Encoding [Rule] UTF-8], (XMLObject[Doctype])[svg, Public [Rule] -//W3C//DTD SVG 1.0//EN, System [Rule] http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd]}, XMLElement[ svg, {xmlns [Rule] http://www.w3.org/2000/svg, width [Rule] 288.0pt, height [Rule] 177.994pt, viewBox [Rule] -0.025 -0.0154508 1.05 0.648936, preserveAspectRatio [Rule] xMidYMid meet}, {XMLElement[ g, {transform [Rule] scale(1, -1) translate(0,-0.618034), style [Rule] fill:black; font-family:'Courier New', Courier, Symbol, monospace; font-size:0.021875pt; stroke:black; stroke-width:0.000911458pt}, {XMLElement[line, {fill [Rule] none, x1 [Rule] 0.0, y1 [Rule] 0.0, x2 [Rule] 1.0, y2 [Rule] 0.618034}, {}]}]}], {}])], Output]}, Open ]]}, Open ]],Cell[CellGroupData[{Cell[Generating an SVG Animation, Section, CellTags->t:1],Cell[TextData[{ StyleBox[Mathematica, FontSlant->Italic], can solve a differential equation:}], Text],Cell[CellGroupData[{Cell[BoxData[ (sol = NDSolve[{ (x'')[t] + 0.15 (x')[t] - x[t] + x[t]^3 [Equal] 5 Cos[t], [IndentingNewLine]x[0] [Equal] 1, (x')[0] [Equal] 2}, x, {t, 0, 20}])], Input],Cell[BoxData[ RowBox[{{, RowBox[{{, RowBox[{x, [Rule], TagBox[(InterpolatingFunction[{{0.`, 20.`}}, <>]), False, Editable->False]}], }}], }}]], Output]}, Open ]],Cell[and then the solution can be plotted., Text],Cell[CellGroupData[{Cell[BoxData[ ((p = ParametricPlot[ Evaluate[{x[t], (x')[t]} /. sol], {t, 0, 20}];))], Input],Cell[GraphicsData[PostScript, <%!%%Creator: Mathematica%%AspectRatio: .61803 MathPictureStart/Mabs {Mgmatrix idtransformMtmatrix dtransform} bind def/Mabsadd { Mabs3 -1 roll add3 1 roll addexch } bind def%% Graphics%%IncludeResource: font Courier%%IncludeFont: Courier/Courier findfont 10 scalefont setfont% Scaling calculations0.477803 0.15697 0.306151 0.0573087 [[.00689 .29365 -6 -9 ][.00689 .29365 6 0 ][.16386 .29365 -6 -9 ][.16386 .29365 6 0 ][.32083 .29365 -6 -9 ][.32083 .29365 6 0 ][.63477 .29365 -3 -9 ][.63477 .29365 3 0 ][.79174 .29365 -3 -9 ][.79174 .29365 3 0 ][.94871 .29365 -3 -9 ][.94871 .29365 3 0 ][.4653 .07692 -12 -4.5 ][.4653 .07692 0 4.5 ][.4653 .19153 -12 -4.5 ][.4653 .19153 0 4.5 ][.4653 .42077 -6 -4.5 ][.4653 .42077 0 4.5 ][.4653 .53539 -6 -4.5 ][.4653 .53539 0 4.5 ][ 0 0 0 0 ][ 1 .61803 0 0 ]] MathScale% Start of Graphics1 setlinecap1 setlinejoinnewpath0 g.25 Mabswid[ ] 0 setdash.00689 .30615 m.00689 .3124 Ls[(-3)] .00689 .29365 0 1 Mshowa.16386 .30615 m.16386 .3124 Ls[(-2)] .16386 .29365 0 1 Mshowa.32083 .30615 m.32083 .3124 Ls[(-1)] .32083 .29365 0 1 Mshowa.63477 .30615 m.63477 .3124 Ls[(1)] .63477 .29365 0 1 Mshowa.79174 .30615 m.79174 .3124 Ls[(2)] .79174 .29365 0 1 Mshowa.94871 .30615 m.94871 .3124 Ls[(3)] .94871 .29365 0 1 Mshowa.125 Mabswid.03829 .30615 m.03829 .3099 Ls.06968 .30615 m.06968 .3099 Ls.10108 .30615 m.10108 .3099 Ls.13247 .30615 m.13247 .3099 Ls.19526 .30615 m.19526 .3099 Ls.22665 .30615 m.22665 .3099 Ls.25805 .30615 m.25805 .3099 Ls.28944 .30615 m.28944 .3099 Ls.35223 .30615 m.35223 .3099 Ls.38362 .30615 m.38362 .3099 Ls.41501 .30615 m.41501 .3099 Ls.44641 .30615 m.44641 .3099 Ls.5092 .30615 m.5092 .3099 Ls.54059 .30615 m.54059 .3099 Ls.57198 .30615 m.57198 .3099 Ls.60338 .30615 m.60338 .3099 Ls.66617 .30615 m.66617 .3099 Ls.69756 .30615 m.69756 .3099 Ls.72895 .30615 m.72895 .3099 Ls.76035 .30615 m.76035 .3099 Ls.82314 .30615 m.82314 .3099 Ls.85453 .30615 m.85453 .3099 Ls.88592 .30615 m.88592 .3099 Ls.91732 .30615 m.91732 .3099 Ls.98011 .30615 m.98011 .3099 Ls.25 Mabswid0 .30615 m1 .30615 Ls.4778 .07692 m.48405 .07692 Ls[(-4)] .4653 .07692 1 0 Mshowa.4778 .19153 m.48405 .19153 Ls[(-2)] .4653 .19153 1 0 Mshowa.4778 .42077 m.48405 .42077 Ls[(2)] .4653 .42077 1 0 Mshowa.4778 .53539 m.48405 .53539 Ls[(4)] .4653 .53539 1 0 Mshowa.125 Mabswid.4778 .10557 m.48155 .10557 Ls.4778 .13423 m.48155 .13423 Ls.4778 .16288 m.48155 .16288 Ls.4778 .22019 m.48155 .22019 Ls.4778 .24884 m.48155 .24884 Ls.4778 .2775 m.48155 .2775 Ls.4778 .33481 m.48155 .33481 Ls.4778 .36346 m.48155 .36346 Ls.4778 .39211 m.48155 .39211 Ls.4778 .44942 m.48155 .44942 Ls.4778 .47808 m.48155 .47808 Ls.4778 .50673 m.48155 .50673 Ls.4778 .04826 m.48155 .04826 Ls.4778 .01961 m.48155 .01961 Ls.4778 .56404 m.48155 .56404 Ls.4778 .59269 m.48155 .59269 Ls.25 Mabswid.4778 0 m.4778 .61803 Ls0 0 m1 0 L1 .61803 L0 .61803 Lclosepathclipnewpath.5 Mabswid.63477 .42077 m.65038 .43313 L.66878 .44539 L.68599 .45489 L.70585 .46366 L.7185 .46803 L.73045 .47128 L.74207 .4736 L.75453 .47509 L.76573 .4755 L.77622 .47503 L.78766 .47348 L.79981 .47051 L.81209 .46593 L.82312 .46025 L.83472 .45238 L.84633 .44206 L.85653 .43038 L.86525 .41779 L.87232 .40508 L.87883 .39045 L.88384 .37607 L.88824 .35938 L.89118 .34355 L.89299 .32834 L.89392 .31008 L.89363 .29332 L.89194 .27411 L.88902 .25628 L.88482 .23893 L.87977 .22338 L.87306 .2073 L.86455 .19131 L.85491 .17697 L.8436 .16361 L.833 .15354 L.82092 .14431 L.80895 .13702 L.79765 .13152 L.78596 .12703 L.77468 .12368 L.76129 .12076 L.74879 .11894 L.73496 .11779 L.72796 .11751 L.72025 .11741 L.71264 .1175 L.70435 .1178 L.69654 .11826 L.68931 .11881 LMistroke.67573 .12013 L.66139 .12186 L.60063 .13087 L.57204 .13483 L.55824 .13642 L.54567 .13763 L.53426 .1385 L.52229 .13916 L.5103 .13954 L.50351 .13962 L.49719 .13961 L.48504 .13935 L.47891 .13909 L.47213 .13872 L.46011 .13783 L.44878 .13673 L.42293 .13332 L.39442 .12841 L.34361 .11798 L.31465 .11204 L.28696 .10706 L.27369 .10509 L.26106 .10354 L.2464 .10224 L.23303 .10159 L.21814 .10159 L.20446 .10237 L.18953 .1042 L.18207 .10556 L.17394 .10741 L.16083 .11131 L.14913 .11587 L.13601 .12241 L.12404 .12994 L.10417 .14661 L.0939 .15793 L.08509 .16961 L.07634 .18363 L.06819 .19973 L.0621 .21464 L.05663 .23146 L.052 .25043 L.04892 .26864 L.04763 .27996 L.04684 .29071 L.04645 .31085 L.0473 .32841 L.0494 .34662 L.05213 .36166 L.05611 .37753 LMistroke.06146 .39359 L.06837 .40956 L.08357 .43449 L.09417 .44687 L.10481 .45651 L.11722 .46505 L.12381 .46862 L.13109 .47186 L.13818 .4744 L.14478 .47626 L.15115 .47762 L.15793 .47864 L.16975 .47944 L.18273 .479 L.19546 .47735 L.20691 .47492 L.2199 .47112 L.23188 .46668 L.25229 .45715 L.27292 .44495 L.30794 .4177 L.33361 .39052 L.34441 .37598 L.35359 .36093 L.35751 .35318 L.36113 .34485 L.36364 .33796 L.3658 .33062 L.36676 .32664 L.36749 .32301 L.36804 .31964 L.36852 .31599 L.36899 .30975 L.36901 .30331 L.36882 .29972 L.36851 .29649 L.368 .29282 L.36736 .2894 L.36589 .28346 L.36378 .27721 L.35875 .26655 L.35176 .2561 L.34373 .24715 L.33538 .23988 L.32603 .23342 L.31487 .22747 L.30893 .22496 L.30238 .22266 L.29659 .22101 L.29019 .21961 LMistroke.28371 .21863 L.27768 .21811 L.2719 .21798 L.26577 .21824 L.26032 .21884 L.25526 .21973 L.24977 .22108 L.24398 .22297 L.23747 .22574 L.23165 .22888 L.22505 .23333 L.21943 .23804 L.21012 .24842 L.2057 .255 L.20205 .26173 L.19918 .26828 L.19666 .27559 L.19495 .28213 L.19354 .28958 L.19262 .29787 L.19237 .30261 L.19232 .307 L.1927 .31563 L.19365 .32391 L.19507 .33169 L.19717 .34008 L.20246 .35511 L.2064 .36364 L.21122 .37243 L.22152 .38753 L.23448 .40233 L.24842 .4151 L.28604 .44064 L.32474 .45991 L.36425 .47637 L.46796 .51632 L.5932 .56481 L.62766 .57685 L.66638 .58859 L.68927 .59431 L.71056 .59859 L.73223 .60171 L.75298 .60332 L.77522 .60327 L.78762 .60232 L.7988 .60083 L.82038 .59603 L.84028 .58898 L.85136 .58377 L.86282 .57728 LMistroke.88256 .56298 L.90246 .54359 L.92228 .51748 L.93718 .49136 L.94894 .46464 L.95463 .44876 L.96012 .43071 L.96814 .39609 L.97324 .36207 L.97602 .32492 L.97619 .29292 L.97404 .25795 L.96945 .22373 L.96307 .19333 L.95386 .16205 L.94166 .1316 L.92645 .10325 L.91016 .08025 L.89416 .06278 L.87562 .04723 L.85863 .03643 L.83926 .02733 L.81845 .02068 L.79864 .01681 L.77994 .01502 L.7628 .01472 L.74305 .01573 L.72442 .01782 L.70472 .02104 L.68325 .02551 L.64093 .03651 L.56944 .05825 L.49726 .0793 L.46033 .08833 L.42715 .09512 L.37011 .10405 L.31008 .11165 L.28463 .11534 L.26107 .11964 L.23467 .1261 L.21159 .1339 L.18738 .14523 L.16377 .16082 L.14573 .17727 L.1286 .19873 L.12043 .21218 L.11394 .22528 L.10769 .24118 L.10304 .2569 L.09991 .27172 LMistroke.098 .28562 L.09734 .29364 L.09702 .30088 L.09697 .30918 L.09725 .31692 L.0984 .3298 L.10057 .34313 L.10348 .35513 L.10683 .3655 L.11154 .37685 L.11755 .38811 L.13055 .40538 L.13786 .41235 L.14645 .41876 L.15589 .42403 L.16035 .42596 L.1651 .42768 L.1739 .43 L.18207 .43124 L.19093 .43169 L.19595 .43155 L.20061 .43118 L.20889 .42997 L.21774 .42792 L.22594 .42533 L.23332 .42243 L.24676 .41574 L.26002 .40719 L.28372 .38584 L.29455 .37216 L.3028 .3587 L.30633 .35154 L.30951 .34381 L.31178 .33706 L.31373 .32971 L.31467 .32518 L.31535 .32101 L.31585 .31701 L.31621 .3128 L.31642 .30548 L.31631 .30134 L.31606 .29749 L.31514 .28992 L.31376 .28282 L.31209 .27649 L.30984 .2697 L.30313 .25483 L.29495 .24169 L.27645 .22073 L.26374 .21033 LMistroke.2506 .2019 L.24308 .19798 L.23569 .19472 L.2288 .19219 L.22129 .18997 L.21304 .18819 L.20527 .18714 L.20049 .18681 L.19598 .18672 L.18755 .18717 L.17966 .18835 L.1713 .19048 L.16358 .19334 L.15673 .19669 L.149 .20152 L.14103 .20791 L.12799 .22247 L.12235 .23104 L.11687 .24147 L.11206 .25334 L.10846 .26526 L.10595 .27693 L.10439 .288 L.10353 .30046 L.1036 .31376 L.1045 .32546 L.10598 .33602 L.10849 .34803 L.11161 .3591 L.11894 .37784 L.12401 .38775 L.12926 .3964 L.14192 .41287 L.15811 .42812 L.16701 .43462 L.17707 .44077 L.1963 .44972 L.20747 .4536 L.21782 .4565 L.22999 .4592 L.24162 .46118 L.25255 .46259 L.26267 .46357 L.27384 .46437 L.28568 .46496 L.29771 .46534 L.30446 .46549 L.31062 .4656 L.33394 .4659 L.347 .46608 LMistroke.35439 .46623 L.36123 .4664 L.3738 .46683 L.38016 .46711 L.38718 .46749 L.39899 .46827 L.41148 .46933 L.43405 .47192 L.45882 .47578 L.48665 .48137 L.59226 .5106 L.6228 .51958 L.65734 .5288 L.67366 .53257 L.6912 .53606 L.70637 .5385 L.72321 .54046 L.73965 .5415 L.7547 .54156 L.77204 .54041 L.78836 .53794 L.8032 .53433 L.81671 .52973 L.83117 .52319 L.84602 .51441 L.86254 .50162 L.8767 .48741 L.89091 .46912 L.90412 .4469 L.91398 .42525 L.92163 .40342 L.92818 .37794 L.93098 .36312 L.93295 .34938 L.93518 .32343 L.93553 .29934 L.93405 .27316 L.93257 .2602 L.93038 .24621 L.92544 .22364 L.91844 .20085 L.91033 .18105 L.90174 .16456 L.89063 .1477 L.87909 .13395 L.86783 .12329 L.85527 .11392 L.84091 .10585 L.82724 .10033 L.81219 .09631 LMistroke.80354 .09485 L.79542 .094 L.78094 .0936 L.76724 .09443 L.75501 .09607 L.74185 .0987 L.72776 .10243 L.71311 .10725 L.68776 .11762 L.63666 .14562 L.59649 .17388 L.56147 .20358 L.53286 .23297 L.51587 .25449 L.50375 .27425 L.49937 .28373 L.49666 .29146 L.49574 .2949 L.49536 .29662 L.49501 .2984 L.49457 .30149 L.49435 .30417 L.4943 .30665 L.49439 .30876 L.49465 .31103 L.49504 .31302 L.49551 .31471 L.49604 .31615 L.4967 .31759 L.4975 .31897 L.49848 .3203 L.49963 .32152 L.50081 .32246 L.50194 .32315 L.503 .32364 L.50419 .32401 L.50546 .32422 L.50664 .32425 L.50796 .32411 L.50862 .32396 L.50933 .32375 L.51058 .32322 L.5117 .32257 L.51296 .32159 L.51404 .32051 L.51512 .31911 L.51613 .3174 L.51685 .31582 L.51749 .31396 L.51796 .31204 LMistroke.51827 .31015 L.51848 .30777 L.51851 .30634 L.51849 .30498 L.51832 .30234 L.51793 .29938 L.51739 .29658 L.51673 .2939 L.51462 .28744 L.51186 .28093 L.50845 .27429 L.49777 .25784 L.48078 .23743 L.43207 .19295 L.3479 .13631 L.29286 .10916 L.27643 .10271 L.25857 .09667 L.24274 .09226 L.23391 .09021 L.22549 .08855 L.20891 .08617 L.19372 .08515 L.17944 .0853 L.16401 .08684 L.15597 .08826 L.1472 .09035 L.13813 .09316 L.12977 .09637 L.11518 .10364 L.10014 .11369 L.08586 .12626 L.07383 .13977 L.0612 .15785 L.05072 .17718 L.04237 .19695 L.03596 .2165 L.03041 .23923 L.02634 .26432 L.02416 .29041 L.02381 .30518 L.02403 .31865 L.02595 .34457 L.02953 .36847 L.03229 .38154 L.03579 .39501 L.04347 .41794 L.0536 .4405 L.06681 .46249 L.07879 .47781 LMistroke.09252 .49158 L.105 .50143 L.11933 .51025 L.13544 .51759 L.14468 .52076 L.15318 .52309 L.1612 .52482 L.16995 .52624 L.18593 .52767 L.20087 .52783 L.21726 .52686 L.22548 .52598 L.23426 .52478 L.24999 .52201 L.27979 .51496 L.30606 .50728 L.40373 .47409 L.45045 .46018 L.47204 .45509 L.49129 .45146 L.50207 .44985 L.51375 .44843 L.52539 .44738 L.53171 .44696 L.53758 .44665 L.54802 .44632 L.55751 .44624 L.56276 .44628 L.56846 .44639 L.57884 .44674 L.58854 .44724 L.59928 .44794 L.62118 .4497 L.64181 .45152 L.66121 .45308 L.67138 .45374 L.68227 .45426 L.68851 .45446 L.69439 .45456 L.70539 .45449 L.71591 .45408 L.72556 .45334 L.73607 .45207 L.74707 .45016 L.75614 .44805 L.76569 .44525 L.78238 .43859 L.79211 .43346 L.80096 .42781 L.81634 .41513 LMistroke.83093 .3983 L.83732 .38867 L.84353 .37726 L.84805 .367 L.85213 .35545 L.85518 .34419 L.85728 .33365 L.85888 .32111 L.85952 .30943 L.85951 .30276 L.85928 .29676 L.85874 .28991 L.85796 .28355 L.85696 .27749 L.85565 .27121 L.85267 .26042 L.8486 .24957 L.84316 .23868 L.83783 .23039 L.83237 .22354 L.8253 .21649 L.81843 .21116 L.81154 .20702 L.80481 .20394 L.79751 .20156 L.79334 .20059 L.78948 .19993 L.78264 .19931 L.77625 .1993 L.76926 .19989 L.76184 .20119 L.75417 .20322 L.74708 .20574 L.73433 .2118 L.72123 .22027 L.7088 .23082 L.69954 .24076 L.69089 .25242 L.68354 .26542 L.68031 .27286 L.67792 .27969 L.67626 .28571 L.67494 .29225 L.67446 .29553 L.6741 .29901 L.67379 .30522 L.67389 .3103 L.67437 .31579 L.67526 .32139 L.67644 .3265 LMistroke.67786 .33115 L.6794 .33527 L.68371 .34407 L.68952 .35266 L.6971 .36088 L.70531 .36736 L.70924 .3698 L.71365 .3721 L.71785 .3739 L.72179 .37527 L.72563 .37631 L.72972 .3771 L.73427 .37761 L.73852 .37774 L.74317 .37747 L.74812 .3767 L.75285 .37547 L.75786 .37359 L.76245 .37128 L.76652 .36869 L.77373 .3626 L ==== Is there a reason for this strange behavior of TrigExpand?All of these expressions simplify both the numerator and denominator.(Cos[t]^2 + Sin[t]^2 is replaced by 1.)expr = (1 + Cos[t]^2 + Sin[t]^2)/(2 + Cos[t]^2 + Sin[t]^2);TrigExpand[expr]2/3expr = (1 + f[t] + Cos[t]^2 + Sin[t]^2)/(2 + f[t] + Cos[t]^2 + Sin[t]^2);TrigExpand[expr](2 + f[t])/(3 + f[t])expr = (1 + Cos[t] + Cos[t]^2 + Sin[t]^2)/(2 + f[t] + Cos[t]^2 + Sin[t]^2);TrigExpand[expr](2 + Cos[t])/(3 + f[t])But the following leaves the denominator untouched.expr = (1 + Cos[t] + Cos[t]^2 + Sin[t]^2)/(2 + Cos[t] + Cos[t]^2 + Sin[t]^2);TrigExpand[expr](2 + Cos[t])/(2 + Cos[t] + Cos[t]^2 + Sin[t]^2)On the other hand, Simplify, which uses the trig identities works.expr = (1 + Cos[t] + Cos[t]^2 + Sin[t]^2)/(2 + Cos[t] + Cos[t]^2 + Sin[t]^2);Simplify[expr](2 + Cos[t])/(3 + Cos[t])David Parkdjmp@earthlink.nethttp://home.earthlink.net/~djmp/ ==== David,I don't know what the answer is but I notice the following: expr = (1 + Cos[t] + Cos[t]^2 + Sin[t]^2)/ (2 + Cos[t] + Cos[t]^2 + Sin[t]^2); TrigExpand[expr] (2 + Cos[t])/(2 + Cos[t] + Cos[t]^2 + Sin[t]^2) TrigExpand //@ expr (2 + Cos[t])/(3 + Cos[t])----------------------- HayesMathematica Training and ConsultingLeicester UKhay@haystack.demon.co.ukVoice: +44 (0)116 271 4198> Is there a reason for this strange behavior of TrigExpand? All of these expressions simplify both the numerator and denominator.> (Cos[t]^2 + Sin[t]^2 is replaced by 1.) expr = (1 + Cos[t]^2 + Sin[t]^2)/(2 + Cos[t]^2 + Sin[t]^2);> TrigExpand[expr]> 2/3 expr = (1 + f[t] + Cos[t]^2 + Sin[t]^2)/(2 + f[t] + Cos[t]^2 +> Sin[t]^2);> TrigExpand[expr]> (2 + f[t])/(3 + f[t]) expr = (1 + Cos[t] + Cos[t]^2 + Sin[t]^2)/(2 + f[t] + Cos[t]^2 +> Sin[t]^2);> TrigExpand[expr]> (2 + Cos[t])/(3 + f[t]) But the following leaves the denominator untouched. expr = (1 + Cos[t] + Cos[t]^2 + Sin[t]^2)/(2 + Cos[t] + Cos[t]^2 +> Sin[t]^2);> TrigExpand[expr]> (2 + Cos[t])/(2 + Cos[t] + Cos[t]^2 + Sin[t]^2) On the other hand, Simplify, which uses the trig identities works. expr = (1 + Cos[t] + Cos[t]^2 + Sin[t]^2)/(2 + Cos[t] + Cos[t]^2 +> Sin[t]^2);> Simplify[expr]> (2 + Cos[t])/(3 + Cos[t]) David Park> djmp@earthlink.net> http://home.earthlink.net/~djmp/ ==== I'm also using 4.2.0, and on my machine the Limit package gives 0 for both, like yours, but without the package loaded, it leaves both forms unevaluated (unlike your experience). Weirder and weirder.BobbyOn Sun, 26 Jan 2003 18:44:27 -0500 (EST), David W. Cantrell > I just noticed something strange, closely related to the original > question> in this thread, which I can't explain. Using version 4.2.0 for Windows: Limit[(Exp[-x]-Exp[-2x])/(Exp[-x]+Exp[-2x]), x-> Infinity] does not give an answer (although the built-in Limit function _should_> of course be able to do so) but, merely using an alternative notation, Limit[(E^(-x)-E^(-2x))/(E^(-x)+E^(-2x)), x-> Infinity] yields, incorrectly, 0 . [The correct answer is 1 .] The reason I think of these notations as alternatives is that both> Exp[x] and E^x have FullForm of Power[E, x]. So what's going on? Why does the first not give an answer, while the> second gives a wrong answer? BTW, using the Standard Add-on Package Calculus`Limit`, _both_ give the> incorrect answer 0 . PLEASE do not respond with workarounds. I know several already, the> easiest of which is to just do the problem in my head! David Cantrell-- majort@cox-internet.comBobby R. Treat ==== Selwyn,things aren't, what they appear to be:In[2]:= Through[{InputForm, Floor}[#]] & /@ {3.0000000000000000, 3.00000000000000000}Out[2]= {{3., 3}, {2.999999999999999999999999999991459`17.6021, 2}}You're right, of course, perhaps, except for wow.--Hartmut>-----Original Message----->Sent: Saturday, January 25, 2003 7:27 AM>To: mathgroup@smc.vnet.net>Wow. But apparently it has nothing to do with Log. Look:Floor[3.0000000000000000] 3Floor[3.00000000000000000] 2--->Selwyn Hollis> With Mathematica 4.1 on Windows98:> N[Log[8]/Log[2]]> 3.> Floor[N[Log[8]/Log[2]]]> 2> Beware!>>Reply-To: kuska@informatik.uni-leipzig.de ==== Esc pd Esc Ctrl_ xEsc is the Escape key, Ctrl the Ctrl-Key and Ctrl_ meanthe bot keys must be pressed at the same time. Jens How do you enter the partial derivative shown at: www.previze.com/ partialderivative.gif to make it available on a web site? (as a downloadable source file> only, sufficiently brief that file compression is not needed, nothing> live or intended for online execution, no need for Output cells or> graphics outputs in the online file, but intended to be dowbnloaded and> executed by users on multiple platforms, with header and text cells kept> distinct from Input cells) --> Power tends to corrupt. Absolute power corrupts absolutely.> Lord Acton (1834-1902)> Dependence on advertising tends to corrupt. Total dependence on> advertising corrupts totally. (today's equivalent)Reply-To: kuska@informatik.uni-leipzig.de ==== Solve[Exp[-(x - m1)/(2s1)]/Sqrt[s1] == Exp[-(x - m2)/(2s2)]/Sqrt[s2], x]?? Jens Can anyone please tell me how to find the intersection of two gaussians?> Is there any standard method to do that?> Vaidyanathan. --> Vaidyanathan Ramadurai> Graduate Student> http://www4.ncsu.edu/~vramadu ==== Or better:Solve[Exp[-(x - m1)^2/(2s1^2)]/s1 == Exp[-(x - m2)^2/(2s2^2)]/s2, x]MichalJens-Peer Kuska p.92Íe v diskusn.92m Solve[Exp[-(x - m1)/(2s1)]/Sqrt[s1] == Exp[-(x - m2)/(2s2)]/Sqrt[s2], x] ?? Jens Can anyone please tell me how to find the intersection of two gaussians?> Is there any standard method to do that?> Vaidyanathan. --> Vaidyanathan Ramadurai> Graduate Student> http://www4.ncsu.edu/~vramadu> ==== Selwyn, ,You might also (or instead of showing the MagnificationPopUp) like to set WindowSize width -> Fit height -> FitSo that the window size adjusts to fit the contents; otherwise if themagnification is made greater than 1 we need to add ResizeArea to theWindowFrameElements so as to be able to do this manually.--------------------- HayesMathematica Training and ConsultingLeicester UKhay@haystack.demon.co.ukVoice: +44 (0)116 271 4198> , A major improvement to the palette is to set these options: WindowElements->MagnificationPopUp> WindowFrameElements->{CloseBox, ZoomBox} You can do this with a text editor or with the Options Inspector. If> you do it with a text editor, delete the cache ID line (as instructed> in the comments at the top). To use the Options Inspector, it's easiest if you close all notebooks> and other palettes first. Open the Options Inspector, and then click on> the title bar of the palette. The title bar of the Options Inspector> should then read Options for BasicInput.nb. Now select Show Option> Values for notebook. Then under Notebook Options > File Options, set Editable -> True. Next,> under Notebook Options > Window Properties, choose the desired values> for WindowElements and WindowFrameElements. Finally, go back and to Notebook Options > File Options, and set> Editable -> False. Et voila! ----> Selwyn Hollis> Folks, I have used Mathematica for about two months, and it appears that the> BasicInput.nb palette had shrunk, in that the walls of the window have> come> in. I can't, therefore, access all of the icons that I want. Is there a way to fix this, other than re-installing the application?> --> ==== =================================================> God made the integers, all else is the work of man.> L. Kronecker, Jahresber. DMV 2, S. 19.Reply-To: kuska@informatik.uni-leipzig.de ==== what manyTable[f[i,4],{i,1,4}]produce ? Jens I have a function f[a_,b_] defined some way. i want to fix one argument,> and then generate an array of values where the other argument varies. How> can I do this? For example, I want: {f[1, 4], f[2, 4], f[3, 4], f[4, 4]} Is there an easy way to do this?> ==== >-----Original Message----->Sent: Sunday, January 26, 2003 11:23 AM>To: mathgroup@smc.vnet.net> I have a function f[a_,b_] defined some way. i want to fix one>argument,> and then generate an array of values where the other >argument varies.>How> can I do this?> For example, I want:> {f[1, 4], f[2, 4], f[3, 4], f[4, 4]}> Is there an easy way to do this?> Zachary,> Table[f[x,4],{x,1,4}]> {f[1, 4], f[2, 4], f[3, 4], f[4, 4]}> Or, for irregular values or a known list of values:> f[x,#]&/@{ 1, 2.3, 8,-3+I, Pi,a}> {f[x, 1], f[x, 2.3], f[x, 8], f[x, -3 + I], f[x, Pi],> f[x, a]}Good lord. I didn't expect this many responses :) Anyway, >the Table method>seems the simplest. Now I extend on this a little bit. Is >there any way I>can apply FullSimplify to the result before it gets inserted >into the array?>Zachary,to molest you further...In[5]:= Thread[f[{1, 2, 3.5, 4}, 4]]Out[5]= {f[1, 4], f[2, 4], f[3.5, 4], f[4, 4]}In[7]:= ArcTan[{1, 2, 3.5, 4}, 4]Out[7]= {ArcTan[4], ArcTan[2], 0.8519663271732721`, Pi/4}...as this didn't show up among the responses. The second, utmost simple,form applies to function having the Listable attribute.As to your last question, it's not quite clear to me, what do you meanbefore it gets inserted into the array. If you do that, you risk to missall simplifications with the arguments inserted. Compare:In[17]:= FullSimplify[Thread[Log[#1]/Log[#2] &[{1, 2, 3.5, 4}, 4]]]Out[17]= {0, 1/2, 0.9036774610288021`, 1}This simplifies the result: as a list is simple enough, all elements aresimplified.In[16]:= Thread[Evaluate[FullSimplify[Log[#1]/Log[#2]]] &[{1, 2, 3.5, 4},4]]Out[16]= {0, Log[2]/Log[4], 0.9036774610288021`, 1}This simplifies the function expression before it is applied, such not allsimplifications of interest can be done (in this case). However it might bethat this last step ist not needed nor desired, then this might be moreperformant, esp. if the list is quite long.--HartmutIn[11]:= Thread[FullSimplify[Log[#1]/Log[#2] &[{1, 2, 3.5, 4}, 4]]]Out[11]= {0, 1/2, 0.9036774610288021`, 1}Reply-To: kuska@informatik.uni-leipzig.de ==== With[{x=10}, First /@ FactorInteger[10]]may help you. Jens All, I know that I can generate the divisors of any integer with the Divisors> command. I would like to start with x = 10, for example, and generate the> divisors of x, and then determine the sum of the divisors. I would then> like to increment x, up to 100, for example. > --> ==== =================================================> God made the integers, all else is the work of man.> L. Kronecker, Jahresber. DMV 2, S. 19.Reply-To: kuska@informatik.uni-leipzig.de ==== AFIK there is no posibility to connect to a kernel thatis already listen to a parent link. The kernel can connectto a second frontend like program but a second frontend can notconnect to a kernel that is already running and know nothingabout the new link. The only way to tell the kernelthat i has to listen to a parent link is the command linebut if the kernel is already running ou can't send a newcommand line to it. Jens > How does one determine whether an instance of the Mathematica Kernal is> running via Mathlink , or even Visual Basic. I only want to keep one> connect to this instance not start up a new instance. All I can think of is> keep the MLINK variable as a global and check that it does not equal zero. that will connect to this. > --> Daniel HeneghanReply-To: kuska@informatik.uni-leipzig.de ==== Mathematica can't do Gouraud shading because it assign the colorsper polygon and not per vertex. You can try to make a huge number of PlotPoints to obtain so manypolygons that the difference is invisible or you can use MathGL3dhttp://phong.informatik.uni-leipzig.de/~kuska/ mathgl3dv3/id3.htm Jens i'm looking for a function to plot a cone with a interpolated gouraud> shading in Mathematica.> I tried with another system, but the> result is awful, because the circle of the cone is squared. thanks.Reply-To: kuska@informatik.uni-leipzig.de ==== without the t I want to plot 3D Data (Curves) and export it to vrml. IÇve found this nice> MathGL3D Tool, but canÇt manage to change the scales of the axes, as one can> do with BoxRatios for ordinary Mathematica Graphics3D. for example: Show[Graphics3D[{Line[{{0, 0, 0}, {1, 1, 0.1}}]}, BoxRatios -> {1, 1, 1}]] shows a scaled Plot, but MVShow3D[Graphics3D[{Line[{{0, 0, 0}, {1, 1, 0.1}}]}, BoxRatios -> {1, 1,> 1}]] doesnÇt.> Is there an easy way to create scaled Plots in MathGL3D?You will not happy with it, butMVShow3D[Graphics3D[{Line[{{0, 0, 0}, {1, 1, 0.1}}]}, BoxRatios -> {.1, .1, 1}]]should do it. How about exporting axes and text to vrml? It is not possible with MathGL3d. > Are there easier ways than> tool?Why not use LiveGraphics3D http://wwwvis.informatik.uni-stuttgart.de/~kraus/ LiveGraphics3D/index.htmlby Martin Kraus orJavaView http://www-sfb288.math.tu-berlin.de/vgp/javaview/on the www-page. It has the advantage that the visitor don't needa VRML browser. Jens ==== In version 4.2.1.1 for Mac OS X both return the same result: the original expression rewritten in two dimensional form> I just noticed something strange, closely related to the original > question> in this thread, which I can't explain. Using version 4.2.0 for Windows: Limit[(Exp[-x]-Exp[-2x])/(Exp[-x]+Exp[-2x]), x-> Infinity] does not give an answer (although the built-in Limit function _should_> of course be able to do so) but, merely using an alternative notation, Limit[(E^(-x)-E^(-2x))/(E^(-x)+E^(-2x)), x-> Infinity] yields, incorrectly, 0 . [The correct answer is 1 .] The reason I think of these notations as alternatives is that both> Exp[x] and E^x have FullForm of Power[E, x]. So what's going on? Why does the first not give an answer, while the> second gives a wrong answer? BTW, using the Standard Add-on Package Calculus`Limit`, _both_ give the> incorrect answer 0 . PLEASE do not respond with workarounds. I know several already, the> easiest of which is to just do the problem in my head! David CantrellGarry HelzerDepartment of MathematicsUniversity of Maryland1303 Math BldgCollege Park, MD 20742-4015 ==== Mathematica is NOT giving wrong answers in this case. It is assuming (non-zero) real parameters and giving the right> answer in that case. Whether Mathematica is or is not giving a wrong answer in the case> result = Integrate[ Abs[Sin[k x]]^2, {x,0,1}]; N[ result /. k->I+1 ]> depends upon whether it is or is not appropriate for Mathematica to> make a default assumption that k is a nonzero real. IMO, that could be> debated.It would be extremely silly to defend this as a default assumption,since in all other cases Mathematica goes through a lot of troubleto single out cases like Im[k] == 0 in its answers. > But surely, as I noted previously in this thread, Mathematica -- at> least version 4.2 for Windows -- does give a wrong answer for> result = Integrate[ Abs[Sin[k x]]^2, {x,0,1}, Assumptions- Element[k, Complexes]; N[ result /. k->I+1 ]. I do not see how the> incorrectness of this can be debated (other than to say that> Mathematica should be allowed to ignore an _explicitly stated_> assumption!)Coming to think of it, Mathematica could of course also ignore _any_explicitly stated fact in its input and give the default result 42to all questions! But version 4.2 is probably still lacking one orderof magnitude in wisdom to do this. :-)-- Jos < Jos.Bergervoet@philips .n_o_spa_m. com > ==== I realize that we're dealing with the vagaries of internal arithmetic, but it is highly disquieting that 3.000... (with any number of zeros) would ever be anything but the binary ßoating-point number .11 * 2^2 !Selwyn> Selwyn, things aren't, what they appear to be: In[2]:= Through[{InputForm, Floor}[#]] & /@> {3.0000000000000000, 3.00000000000000000}> Out[2]= {{3., 3},> {2.999999999999999999999999999991459`17.6021, 2}} You're right, of course, perhaps, except for wow. --> Hartmut> -----Original Message-----> Sent: Saturday, January 25, 2003 7:27 AM> To: mathgroup@smc.vnet.net> Wow. But apparently it has nothing to do with Log. Look:> Floor[3.0000000000000000]> 3> Floor[3.00000000000000000]> 2> ---> Selwyn Hollis>> With Mathematica 4.1 on Windows98:>> N[Log[8]/Log[2]]>> 3.>> Floor[N[Log[8]/Log[2]]]>> 2>> Beware!> ==== : Look up DivisorSigma. Table[DivisorSigma[1,x],{x,10,100}] willgive you what you want directly, I believe. Best, HarveyHarvey P. DaleUniversity Professor of Philanthropy and the LawDirector, National Center on Philanthropy and the LawNew York University School of LawRoom 206A110 West 3rd StreetNew York, N.Y. 10012-1074-----Original Message-------God made the integers, all else is the work of man.L. Kronecker, Jahresber. DMV 2, S. 19. ==== Im using Mathematica 4.2 on my MacOSX notebook but still have 4.0 on mydesktop. I have encountered a strange thing which is causing meproblems. I have defined the wavefunction in momentum space for a shoin 4.0 when i evaluate for the ground state I get the answer I wouldexpect. In 4.2 the answer is the same but I get an Integer 1 appearing whichmakes it very difficult to manipulate the result to the form I want.I have attached the Notebook content below. This is the 4.0 version butwith the 4.2 result copied across.Any comments/help?DonNotebook[{Cell[BoxData[ ([CurlyPhi]_[Gamma]_[ p_] := (([ImaginaryI]^(-[Gamma])) (((@[Pi]2^[Gamma] ([Gamma]!))/a)))^(-(1/2)) ([ExponentialE]^(((-p^2) a^2)/2)) HermiteH[[Gamma], a p])], Input],Cell[BoxData[ (In 4.0)], Input],Cell[CellGroupData[{Cell[BoxData[ ([CurlyPhi]_0[p])], Input],Cell[BoxData[ (TraditionalForm`[ExponentialE]^((-(1/2)) a^2 p^2)/(@(1/a) @[Pi]%4))], Output]}, Open ]],Cell[BoxData[ ([ExponentialE]^((-(1/2)) a^2 p^2)/(@(1/a) @[Pi]%4))], Text],Cell[BoxData[ (In 4.2)], Input],Cell[CellGroupData[{Cell[BoxData[ (TraditionalForm`[CurlyPhi]_0[p])], Input],Cell[BoxData[ (TraditionalForm`[ExponentialE]^((-(1/2)) a^2p^2)/@1[@[Pi]/a])], Output]}, Open ]]},ScreenRectangle->{{0, 1056}, {0, 772}},WindowSize->{520, 650},WindowMargins->{{28, Automatic}, {-30, Automatic}},MacintoshSystemPageSetup-><00<0001804P000000 ]P2:?oQon82n@960dL5:0?l0080001804P000000]P2:0010000I00000400` <300000Gd000400@ 0000000000000004P801T1T000000000000000000000000000000000000000 0000>] ==== If I enter Sum[p^i, {i, 0, Infinity}] Mathematica says, it is 1/(1-p), but doesn't say something about the domain for p: 1/(1-p) is only valid for-1=1 and p<=-1?PS: you can find a nice animation for the geometric series at http://www.matheprisma.de/Module/Craps/summe.htm-- Frank Bu¤, fb@frank-buss.dehttp://www.frank-buss.de, http://www.it4-systems.de ==== hi,maybe it's a foolish question, but i'm new to mathematica:i want to plot (using Plot3D of course) at least 2 3D-functions into thesame diagram. how to i have to handle this?thanx in regard.lhuv ==== Mathematica can automatically combine graphics. Here is an example:generate two different 3D graphics:g1=Plot3D[1/(1+Exp[-x-y]),{x,-5,5},{y,-5,5}];g2= Plot3D[1/(1+Exp[x-y]),{x,-5,5},{y,-5,5}];show the 3D graphics together:Show[g1,g2];--Steve LuttrellWest Malvern, UK hi,> maybe it's a foolish question, but i'm new to mathematica: i want to plot (using Plot3D of course) at least 2 3D-functions into the> same diagram. how to i have to handle this? thanx in regard. lhuv> ==== hi,> maybe it's a foolish question, but i'm new to mathematica: i want to plot (using Plot3D of course) at least 2 3D-functions into the> same diagram. how to i have to handle this? thanx in regard. lhuv>Use Show: gr1= Plot3D[3x+3y, {x,-2,2},{y,-2,2}] gr2 = Plot3D[x^2+y^2, {x,-2,2},{y,-2,2}] Show[gr1,gr2]----------------------- HayesMathematica Training and ConsultingLeicester UKhay@haystack.demon.co.ukVoice: +44 (0)116 271 4198Reply-To: kuska@informatik.uni-leipzig.de ==== Block[{$DisplayFunction = Identity}, g1 = Plot3D[Sin[x*y], {x, 0, Pi}, {y, 0, Pi}]; g2 = Plot3D[Cos[x*y], {x, 0, Pi}, {y, 0, Pi}]; ];Show[g1, g2]; Jens hi,> maybe it's a foolish question, but i'm new to mathematica: i want to plot (using Plot3D of course) at least 2 3D-functions into the> same diagram. how to i have to handle this? thanx in regard. lhuv ==== I'm relatively new using mathematica 4.2 .I have a set of integro-differential equations to solve.Does anyone have an idea how to proceed? ==== I'm student and using mathematica 4.0.At the moment I have to write a report for my university. I want to useLaTeX to write this document. Since I do a lot of calculations withmathematica I use the TexForm[...] (//HoldForm) command to get a latexoutput. I just have to copy/paste the output; it works quite well.But then I wanted to include some plots from mathematica in my latexdocument. If I apply it to Plot[...]: e.g.: TeXForm[Plot[Sin[x], {x, -Pi,Pi}]] I get a strange outputs.Is it possible to get a LaTeX package, which compiles these instructions? Oris this output just nonsense? Are there other possibilities than using copyas bitmap to get my plot into the latex document?Perhaps anyone had similar problems or knows a useful link.JochenReply-To: kuska@informatik.uni-leipzig.de ==== you have to save the graphics into a EPS file and includeit into the LaTeX file withincludegraphics[width=textwidth]{yourPostScriptFile} Jens > I'm student and using mathema