mm-879 === Subject: Re: record intermediate steps The trap method is pretty straightforward and elegant, at least when one isn't trying to use it on all functions at once or limit the number of function calls recorded: The first idea is to take a function name (which is a symbol) and then assign a very specific DownValue to it, causing that DownValue to jump the queue and be executed before the symbol's internal DownValues. The second idea is that the right hand side of this specific DownValue then sets the condition to be False, Prints or otherwise records the function call, and then executes the built in DownValues by performing the same function call again. The condition must be set to false in order to avoid infinite tail recursion. -- http://chris.chiasson.name/ === Subject: Re: reverse polish notation 7 // Sqrt // N[#,30] & will be N[Sqrt[7],30] and 3 // Plus[#,5] & will be Plus[3,5] .. Jens === Subject: Re: Questions about Discrete Fourier Transform it is not clear, what a Series Fourier Transform may be but *sampling* the x value may help. Jens === Subject: Re: graphing with dates and values look what Graphics`Graphics`BarChart[] can do for you and look in the help files, there is an example that uses the month names to label the chart. Jens === Subject: Re: Showing defined functions Information[Global`*] or Definition /@ Names[Global`*] Jens === Subject: Re: NIntegrate - problems with HoldAll property(?) - not quite a A better description of the function I am trying to integrate is: f1[x_?NumericQ, anOtherObject_]:=Module[{res}, {res,Length[anOtherObject]} ] i.e. it is a function with 2 useful outputs in list form Now, when I try to integrate the first output using: I get a numerical answer, but it is wrong: 24.5 not 19! What I think is happening is: f1[4,{a,b,c}][[1]] gives 3 as expected BUT f1[i,{a,b,c}][[1]] gives i because Mathematica does not have a definition for this function with the i as input. It returns the first element of f1[i,{a,b,c}] , which is i. This i can then be resolved by the NIntegrate function to give me the answer I was not expecting - ouch! So I still have the original problem I think, in that NIntegrate is not resolving the i to a number at an early enough stage. You fixed my problem for functions that return a single variable, (although I'm not sure really why this works), but I still have the problem when my function returns a list. Can anyone have another go? === Subject: Re: NIntegrate - problems with HoldAll property(?) - still not a This does fix the problem for functions that return a number (not sure why though), but oddly not for functions that return a list of results. any other thoughts? rgds D === Subject: Re: Exporting expressions in Latex MapThread[Export[#1,#2,TeX] &,{yourFilenameList,yourExpressionList}] ?? Jens === Subject: String to number Hi all: The ToString command generates a string from an expression. Is there a similar command which generates numbers from strings? What I mean by this is: is there a command (let's call it ToNumber) such that ToNumber[12] generates the number 12? Jose Carlos Santos === Subject: Re: NIntegrate - problems with HoldAll property(?) While this fixes the problem, it's a weird fix! Why does this make NIntegrate resolve the i to a number before it calls f1[]? For instance, this still does not work even with the NumericQ: f1[x_?NumericQ] := Module[{res,y}, {res,{1,2,3}} ] Now when we integrate: NIntegrate[f1[i][[1]], {i, 0,7}] we still get problems! It gives the wrong answer (24.5), because NIntegrate does not resolve the i to a number before the call, so NIntegrate cannot see my definition of f1[]. So f1[i][[1]] gets resolved to i! So it ends up doing: NIntegrate[i, {i, 0,7}] wow! So I am back to my original question, how do I make NIntegrate reliably resolve the i to a number before it calls the f1[] function, for complex functions, Looking at the debugger, when f1[x_] returns a number, the trick works and i is resolved to a number before the call. But if it returns a list, it does not work, and it does not even get into the function Can u help? rgds D === Subject: Point inside polygon I have been reading mathgroup items for determining if a point is inside or outside a general polygon. David Park gave a method which he acknowledged still has some flaws. With the help of an internet search (Kreylos and point inside a polygon) I found an improvement on his method which works better than I expected. The basic method is to draw a line from the test point to infinity and count the number of edge crossings. If the number of edge crossings is odd then the test point is inside the polygon. This basic method needs extending to cover the cases where the test line goes through a vertex, where a vertex is tangent to the test line and where an edge lies on the test line. An additional problem, which I take separately, is when the test point lines on the boundary. The method can be simplified, from that given by David Park, by always drawing a horizontal test line from the test point to infinity in the positive x direction. Edges are only counted when they cross the test line. A crossing occurs if one edge end-point is above or on the test line while the other edge end-point is below the test line. If an edge crosses, the crossing point must be to the right of the test point. The careful definition eliminates edges that lie on the test line because they have both end-points on the test line. Tangent vertices cause no difficulty because those that touch the test line from below are counted twice while those that touch from above are not counted at all. Both cases add no odd counts to the total count. The passage of the test line through a vertex correctly gives just one count. The method can be coded in only a few lines. The code, PointInPolygon, is given below together with some test cases. I have introduced a scale factor so that the test may be repeated with big or small numbers. They all seem to work. Am I lucky or does Mathematica's inequality testing save me? Try changing the scale factors to 10^100 or 10^-100 to try and break the code. For the case of test points on the boundary I do an initial check and exit with False if the point lies on the boundary. I determine if a point is on the boundary by working out the area of the triangle formed by the test point and the two points defining a boundary edge. For these calculations I have converted to Integers using Rationalize. The method now works unless very big or small numbers (ie outside 10^14 to 10^-14) are used which I guess is down to Rationalize. The codes which include a boundary check are PointInsidePolygon and PointOnLine. I give examples below. Are there examples which break this method? Can this be improved? How can it be made faster? Hugh Goyder Cranfield University Tel: +44 (0) 1793 785122 Mob: +44 (0) 7804 252770 ClearAll[PointInPolygon]; PointInPolygon::usage == PointInPolygon[p0,poly] gives True if the point p0 is inside the polygon poly. The polygon is given as a list of lists where each sublist corresponds to a list of external or internal vertices. If p0 is on the boundary the behaviour is unpredictable.; PointInPolygon[{x0_, y0_}, poly_] :== Module[{edges, incount}, edges == Flatten[(Partition[Join[#1, {First[#1]}], 2, 1] & ) /@ poly, 1]; incount == 0; Do[{{x1, y1}, {x2, y2}} == edges[[n]]; {n, Length[edges]}]; OddQ[incount]]; size == 10; poly == N[{{{0, 0}, {1, -1}, {2, 0}, {2.5, -1.1}, {3, 0}, {4, 0}, {4, 1.5}, {3, 1.5}, {3, 1}, {2.5, 0}, {2, 1}, {2, 2}, {0.5, 2}, {0.5, 1}}, {{0.75, 1}, {1.75, 1}, {1.75, 1.75}, {0.75, 1.75}}}*size]; inpoints == N[{{0.62, 1.5}, {1.88, 1.5}, {0.62, 1}, {1.88, 1}, {1, 0}, {2.25, 0}, {2.75, 0}, {3, 0.5}}*size]; outpoints == N[{{1, 1.5}, {-0.5, 0}, {4.5, 0}, {0, 1}, {2.5, 1}}*size]; midpoints == N[((1/2)*(RotateLeft[#1] + #1) & )[poly[[1]], 1]]; {Green, PointSize[0.02], (Point[#1] & ) /@ inpoints}, {Red, PointSize[0.02], (Point[#1] & ) /@ outpoints}, {Blue, PointSize[0.02], (Point[#1] & ) /@ midpoints}}, (PointInPolygon[#1, poly] & ) /@ inpoints (PointInPolygon[#1, poly] & ) /@ outpoints Comment[The method fails if the vertices are tested]; (PointInPolygon[#1, poly] & ) /@ Partition[Flatten[poly], 2] Comment[The method fails if points on the boundary are tested]; (PointInPolygon[#1, poly] & ) /@ midpoints ClearAll[PointOnLine]; PointOnLine::usage == PointOnLine[p0,{p1,p2}] determines if the point p0 is on the line between points p1 and p2. The method works by determining if the area of the triangle formed by the three points is zero and if the point p0 lies between p1 and p2 when projected onto the x-axis (or y-axis if the line is vertical). The values are converted to integers.; PointOnLine[p0_, {p1_, p2_}] :== Module[{x0, y0, x1, y1, x2, y2}, {x0, y0} == Rationalize[p0, 0]; {x1, y1} == Rationalize[p1, 0]; {x2, y2} == Rationalize[p2, 0]; If[x1 !== x2, 0 <== (x0 - x1)/(x2 - x1) <== 1, 0 <== (y0 - y1)/(y2 - y1) <== 1]]; ClearAll[PointInsidePolygon]; PointInsidePolygon::usage == PointInPolygon[p0,poly] gives True if the point p0 is inside the polygon poly. The polygon is given as a list of lists where each sublist corresponds to a list of external or internal vertices.; PointInsidePolygon[{x0_, y0_}, poly_] :== Module[{edges, incount, x1, y1, x2, y2}, edges == Flatten[(Partition[Join[#1, {First[#1]}], 2, 1] & ) /@ poly, 1] ; incount == 0; Catch[Do[{{x1, y1}, {x2, y2}} == edges[[n]]; If[PointOnLine[{x0, y0},{{x1, y1}, {x2, y2}}], Throw[False]]; ++incount]], {n, Length[edges]}]; OddQ[incount]]]; (PointInsidePolygon[#1, poly] & ) /@ inpoints (PointInsidePolygon[#1, poly] & ) /@ outpoints Comment[The method works if the vertices are tested]; (PointInsidePolygon[#1, poly] & ) /@ Partition[Flatten[poly], 2] Comment[The method works if points on the boundary are tested]; (PointInsidePolygon[#1, poly] & ) /@ midpoints === Subject: Re: Problem with new Mathematica Installation on Linux I tried the primitive driver with Xorg 7.1 and Mathematica works fine with the display. But I can't use this driver because it only supports very low resolution. Are you using an ATI driver? If so, I believe this is a problem with display drivers. On 2=E6=9C=884=E6=97=A5, =E4=B8=8B=E5=8D=8811=E6=97=B652=E5=88=86, Ferdinan= mail t and === Subject: Re: Problem with new Mathematica Installation on Linux I must use the native ATI drivers, because it's the only way to use a second screen, to perform video projection etc. These drivers are required to handle the VGA output cable available on the laptop. Also, standard Xorg drivers don't implement hardware acceleration (OpenGL). The problem that was reported seems to be related to the alpha channel of the display, that means transparency, that is badly taken into account with Mathematica 5.2. Any help would be welcome. -- Fran.8dois LE COAT Author of Eureka 2.12 (2D Graph Describer, 3D Modeller) http://eureka.atari.org/ === Subject: Re: Re: Problem with new Mathematica Installation Try exporting XLIB_SKIP_ARGB_VISUALS=1 before running Mathematica. Sounds like it's a compositing problem. Hopefully, the next versions of the program will use more modern interfaces. Hope that helps! Curtis O. -- Curtis Osterhoudt gardyloo@mail.remove_this.wsu.and_this.edu PGP Key ID: 0x088E6D7A Please avoid sending me Word or PowerPoint attachments See http://www.gnu.org/philosophy/no-word-attachments.html === Subject: BarChart and Ticks problem. I have a problem with BarChart and Ticks. Needs[Statistics`DataManipulation`]; Needs[Graphics`Graphics`]; sid = N[Table[Sin[Pi Random[]], {1000}]]; freqtst = BinCounts[sid, {0, 1, 0.02}]; midp = Table[i, {i, 0.02, 1, 0.02}]; BarChart[Transpose[{freqtst, midp}]] (* The ticks on X axis is correct except crowded*) (*here, I have the wrong X axis ticks. The range of the ticks is from 0 to 50 which doesn't make any sense because Sin[x] is always less or equal than 1. *) (* this gives me the right answer*) Any suggestions? === Subject: Re: Remote Kernel does nothing I see the problem. I had you using -LinkHost incorrectly. Change the MLOpen line to: -LinkMode Listen -LinkProtocol TCPIP -LinkOptions MLDontInteract With the MLOpen arguments, -LinkHost tells MathLink to create a link on the listed interface. 192.168.187.99 is not an interface on your Windows system. If you want to use -LinkHost with the MLOpen argument, you have to be sure to use an actual ip number (or domain name) for an interface on your system (in this case 192.168.187.232). When you use the -LinkHost option with the Shell command, you are telling the remote process to connect to a link at the listed ip number (or domain name). So in effect the first time you ran this set up you were telling the remote Kernel to try and connect to a link at its own IP number. In general -LinkHost should not be used unless you have a good reason. It overrides the default ip number or domain name that MathLink generates when it automatically creates linknames. LinkHost is useful when you have multiple interfaces on a machine and want MathLink to bind to a particular interface without affecting any of the other interfaces. LinkHost can also be useful if you have firewalls, routers, or other kinds of network devices or setups that cause a bit of trickiness with ip numbers between two machines. If you don't have any of those conditions on your network, it is better to leave -LinkHost unused. One further note. You can also specify the interface to use by giving the interface in the -LinkName option for the MLOpen arguments. Your original example could have been: MLOpen: -LinkMode Listen -LinkProtocol TCPIP -LinkName 3500@192.168.187.232 Shell Command: ssh tsariysk@192.168.187.99 math -mathlink -LinkMode Connect - LinkProtocol TCPIP -LinkName `linkname` I should have seen this at first. My apologies for taking so long. Steve === Subject: Re: Remote Kernel does nothing Lets try a couple of more options. First, change the Advance Options to: -LinkMode Listen -LinkProtocol TCPIP -LinkHost 192.168.187.99 This change will allow the OS to determine the port number used for the link. In addition, MathLink will display a dialog box that tells you the name of the link that it created. Write that name down. Change the shell command to: ssh tsariysk@192.168.187.99 math -mathlink -LinkMode Connect - LinkProtocol TCPIP -LinkName `linkname` Now when you start the Kernel, log in to 192.168.187.99 in another ps axwww | grep MathKernel ( the arguments to ps may be different depending on your flavor or Unix.) Verify that the -LinkName command line argument to MathKernel is actually the same value as the value you gathered from the dialog box. Send me what you find out. Steve === Subject: Re: Remote Kernel I still get the same Low-level MathLink error: Mathematica could not establish a connection to the kernel. Kernel: craft99. Low-level MathLink error: The linkname was missing or not in the proper form. Here are the Kernel Configuration Options: Advanced Options: -LinkMode Listen -LinkProtocol TCPIP -LinkOptions MLDontInteract -LinkName 3500 -LinkHost 192.168.187.99 Shell command to launch kernel: ssh tsariysk@192.168.187.99 ' math -mathlink -LinkMode Connect -LinkProtocol TCPIP -LinkName 3500 -LinkHost 192.168.187.99' I did make sure that SSH_AUTH_SOCK environmental variable is visible for both windows and cygwin: I ssh tsariysk@192.168.187.99 without password from Windows Command Prompt as well as from Cygwin shell. I expect that Mathematica also acknowledges of SSH_AUTH_SOCK but I do not know how to verify it. Is there a debug mode for MathLink or other tools that make troubleshooting more transparent? === Subject: Integrating SphericalHarmonicY I would like Integrate[ Conjugate[SphericalHarmonicY[l,m,theta,phi]] SphericalHarmonicY[l,m,theta,phi] Sin[theta], {theta, 0, Pi}, {phi, 0, 2 Pi}] to evaluate to 1 (without having to force it through a rule every time). I have tried $Assumptions = {Element[Alternatives[theta,phi], Reals] && Element[Alternatives[l,m], Integers] && === Subject: dot minus operator Hi All, How can I define in the the infix style the (integer) operation In std texts it is usually noted by a minus with a dot over it. It would be fine to use the same notation. . === Subject: RE: NIntegrate - problems with HoldAll property(?) please see my reply to the post by Bob Hanlon (when it passes moderation...) I can see that this does fix the problem I presented for functions that return a single number, although I'm not sure why this forces NIntegrate to resolve the i to a number before calling f1[i] (?) For my real problem, my function f1[] returns a list of useful results, and I am trying to integrate over the first element of the list, akin to NIntegrate[f1[i][[1]], {i, 0,7}]. When I try your solution on this problem, I still get the same problems - in fact if u look at my new post, I actually get a numerical & unexpectedly wrong result, because NIntegrate cannot enter into my function now. any thoughts? i.e. this still does not work: f1[x_?NumericQ, ANOtherInput_] := Module[{res,y}, {res,Length[ANOtherInput]} ] NIntegrate[f1[i][[1]], {i, 0,7}] It actually gives the integral of f1[x,m]=x i.e. 24.5 any thoughts? rgds David -----Original Message----- Cc: mathgroup@smc.vnet.net === Subject: Re: NIntegrate - problems with HoldAll property(?) To prevent f1[x] from ever being called when x is not numerical, use the definition: instead. Then, your integral will still produce error messages, but will return a valid result: In[11]:= f1[x_?NumericQ] := First[Position[{1, 3, 5, 7, 9, Infinity}, y_ /; y ú x, Infinity, 1]][[1]] NIntegrate[f1[i], {i, 0, 7}] (* error messages suppressed *) Out[12]= 19.0012 Another possibility for this particular example is to use Interpolation and Integrate instead. For example: In[13]:= Out[14]= 19 Carl Woll Wolfram Research Please access the attached hyperlink for an important electronic communications disclaimer: http://www.credit-suisse.com/legal/en/disclaimer_email_ib.html === Subject: RE: NIntegrate - problems with HoldAll property(?) but I still have problems - please see my next posting... rgds dAvid -----Original Message----- === Subject: Re: NIntegrate - problems with HoldAll property(?) In[1]:= f1[(x_)?NumericQ] := First[Position[{1, 3, 5, 7, 9, Infinity}, NIntegrate[f1[i], {i, 0, 7}] See the FAQ (Frequently Asked Questions), How do I write a function which evaluates only when the argument is a number? at http://support.wolfram.com/mathematica/kernel/features/evalwhennumber.html Jean-Marc Please access the attached hyperlink for an important electronic communications disclaimer: http://www.credit-suisse.com/legal/en/disclaimer_email_ib.html === Subject: problem with fonts in linux Hi everyone, I have a problem with fonts under linux (*___________________Beginning of my notebook____________________*) (* This plot looks OK in my machine*) Plot[Sin[x],{x,0,10},Frame[Rule]True,FrameLabel[Rule]{x,y}] (* In this one I get a blank instead of the 0, and the vertical axis is broken*) Plot[Sin[x],{x,0,10},Frame[Rule]True,FrameLabel[Rule]{x,y}, RotateLabel[Rule]False] $TextStyle={FontFamily[Rule]Arial,FontSize[Rule]10}; (* In this plot the horizontal axis disappears*) Plot[Sin[x],{x,0,10},Frame[Rule]True,FrameLabel[Rule]{x,y}] (*___________________End of my notebook____________________*) As I suspect I might have a bad installation of fonts I copied the directories in /usr/local/Wolfram/Mathematica/5.2/SystemFiles/Fonts to a new directory called /usr/share/fonts/X11/Mathfonts/ and then I have reedited xorg.conf so that the files section looks like Section Files FontPath /usr/share/fonts/X11/misc FontPath /usr/share/fonts/X11/cyrillic FontPath /usr/share/fonts/X11/100dpi/:unscaled FontPath /usr/share/fonts/X11/75dpi/:unscaled FontPath /usr/share/fonts/truetype FontPath /usr/share/fonts/X11/Type1 FontPath /usr/share/fonts/X11/Mathfonts/Type1 FontPath /usr/share/fonts/X11/Mathfonts/AFM FontPath /usr/share/fonts/X11/Mathfonts/BDF FontPath /usr/share/fonts/X11/75dpi FontPath /usr/share/fonts/X11/100dpi FontPath /usr/share/fonts/X11/misc # path to defoma fonts FontPath /var/lib/defoma/x-ttcidfont-conf.d/dirs/TrueType EndSection and at the end of this file I also have Section Extensions Option Composite disable EndSection Below this lines, you can see what I get if I do xlsfonts | grep -wri- Hope someone can help me. ________________________________________________________ -wri-helvetica-medium-r-normal--0-0-75-75-p-0-iso8859-1 -wri-helvetica-medium-r-normal--9-90-75-75-p-40-iso8859-1 -wri-mathematica1-bold-r-normal--0-0-0-0-p-0-adobe-fontspecific -wri-mathematica1-bold-r-normal--0-0-75-75-p-0-adobe-fontspecific -wri-mathematica1-bold-r-normal--10-100-75-75-p-60-adobe-fontspecific -wri-mathematica1-bold-r-normal--11-110-75-75-p-60-adobe-fontspecific -wri-mathematica1-bold-r-normal--12-120-75-75-p-70-adobe-fontspecific -wri-mathematica1-bold-r-normal--13-130-75-75-p-80-adobe-fontspecific -wri-mathematica1-bold-r-normal--14-140-75-75-p-80-adobe-fontspecific -wri-mathematica1-bold-r-normal--15-150-75-75-p-90-adobe-fontspecific -wri-mathematica1-bold-r-normal--16-160-75-75-p-90-adobe-fontspecific -wri-mathematica1-bold-r-normal--17-170-75-75-p-100-adobe-fontspecific -wri-mathematica1-bold-r-normal--18-180-75-75-p-110-adobe-fontspecific -wri-mathematica1-bold-r-normal--20-200-75-75-p-120-adobe-fontspecific -wri-mathematica1-bold-r-normal--22-220-75-75-p-130-adobe-fontspecific -wri-mathematica1-bold-r-normal--24-240-75-75-p-140-adobe-fontspecific -wri-mathematica1-bold-r-normal--26-260-75-75-p-160-adobe-fontspecific -wri-mathematica1-bold-r-normal--28-280-75-75-p-170-adobe-fontspecific -wri-mathematica1-bold-r-normal--30-300-75-75-p-180-adobe-fontspecific -wri-mathematica1-bold-r-normal--32-320-75-75-p-190-adobe-fontspecific -wri-mathematica1-bold-r-normal--34-340-75-75-p-210-adobe-fontspecific -wri-mathematica1-bold-r-normal--36-360-75-75-p-220-adobe-fontspecific -wri-mathematica1-bold-r-normal--5-50-75-75-p-30-adobe-fontspecific -wri-mathematica1-bold-r-normal--6-60-75-75-p-30-adobe-fontspecific -wri-mathematica1-bold-r-normal--7-70-75-75-p-40-adobe-fontspecific -wri-mathematica1-bold-r-normal--8-80-75-75-p-40-adobe-fontspecific -wri-mathematica1-bold-r-normal--9-90-75-75-p-50-adobe-fontspecific -wri-mathematica1-medium-r-normal--0-0-0-0-p-0-adobe-fontspecific -wri-mathematica1-medium-r-normal--0-0-75-75-p-0-adobe-fontspecific -wri-mathematica1-medium-r-normal--10-100-75-75-p-50-adobe-fontspecific -wri-mathematica1-medium-r-normal--11-110-75-75-p-60-adobe-fontspecific -wri-mathematica1-medium-r-normal--12-120-75-75-p-70-adobe-fontspecific -wri-mathematica1-medium-r-normal--13-130-75-75-p-70-adobe-fontspecific -wri-mathematica1-medium-r-normal--14-140-75-75-p-80-adobe-fontspecific -wri-mathematica1-medium-r-normal--15-150-75-75-p-80-adobe-fontspecific -wri-mathematica1-medium-r-normal--16-160-75-75-p-90-adobe-fontspecific -wri-mathematica1-medium-r-normal--17-170-75-75-p-100-adobe-fontspecific -wri-mathematica1-medium-r-normal--18-180-75-75-p-100-adobe-fontspecific -wri-mathematica1-medium-r-normal--20-200-75-75-p-110-adobe-fontspecific 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-wri-mathematica7mono-medium-r-normal--5-50-75-75-m-10-adobe-fontspecific -wri-mathematica7mono-medium-r-normal--6-60-75-75-m-20-adobe-fontspecific -wri-mathematica7mono-medium-r-normal--7-70-75-75-m-20-adobe-fontspecific -wri-mathematica7mono-medium-r-normal--8-80-75-75-m-20-adobe-fontspecific -wri-mathematica7mono-medium-r-normal--9-90-75-75-m-20-adobe-fontspecific === Subject: Re: exporting graph eps and ?ImageSize ImageSize is an option for Export, Display and other graphics functions, as well as for Cell, which specifies the absolute size of an image to render. ?ImageResolution ImageResolution is an option for Export and Display which specifies at what resolution bitmap images should be rendered. can't help you ?? Jens === Subject: Re: Nice Integrate setting and it become more surprising ! you can also Integrate[f[x,y,z],z,y,x] that's called multiple integration. Jens