mm-478 Subject: Re: Maple bugs: the next freeze frame calculated by GEMM by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3F296v22382; > > Leader? Premium? Highest? OK, let's consider concrete examples. > I tried your examples on mma, opps, I mean MATHEMATICA, 5.0 > to compare. Here are the results. BB> You do realize you're pretty much advertising Mathematica BB> with your comparison, right? :-) Sorry for breaking in upon your dialogue, but do you really want a different direction? ;) If yes then please tell me, and 'on my word you will be amazed with the outcome of your request 8) By the way, for a long time I keep eye on your postings here and there as well as your homepage and testing remarks, and I like them, really. You have light nice style like Andy Shiekh. Especially, I am eager to enjoy at last your wonderful aunt's homepage... but visiting regularly this link I understand that great achievements should not come quickly 8-) BTW do you still use Derive/TI calculator occasionally? Just curious. http://www.cybertester.com/ http://maple.bug-list.org/ http://www.CAS-testing.org/ ........................................................... === Subject: Re: Maple bugs: the next freeze frame calculated by GEMM > Sorry for breaking in upon your dialogue, but do you really > want a different direction? ;) If yes then please tell me, > and 'on my word you will be amazed with the outcome of your > request 8) Do you mean your bug list for Mathematica (especially Integrate)? > By the way, for a long time I keep eye on your postings here > and there as well as your homepage and testing remarks, and I > like them, really. You have light nice style like Andy Shiekh. Perhaps that's not a coincidence. Andy and I are very good friends. > Especially, I am eager to enjoy at last your wonderful aunt's > homepage... but visiting regularly this link I understand that > great achievements should not come quickly 8-) LOL! She was never very much into computers or the Internet, so I gave up updating her webpage after a while... > BTW do you still use Derive/TI calculator occasionally? > Just curious. Oh, yes. Actually, they sometimes help me at work when testing Mathematica. The big advantages of the TI-68k are portability and that they use operating systems that are smaller and more stable than computer OS's. === Subject: Re: replace mathematics completely and totally by mma programming. can it be done? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3F294c22322; BB>> expresses my high appreciation and admiration for the BB>> wholistic oeuvre of Stephen Wolfram with its many facets: ANN> When you use show-off words, you should at least spell ANN> them properly. I was wondering have your ever read the whole paper? (Mathematica: A system for doing mathematics by computer?) I assure you that Prof Buchberger's English is rich and impressive and I can bet my bottom dollar on the fact that he certainly can spell this your 'holistic' correctly. So why 'wholistic' ? My interpretation: it might be a subconscious typo; in other words, BB might banter with SW (subconsciously, without ever noticing this!)... compare... His Britannic Maiesty Then this mock 'w' conveys a droplet of veiled sneer, a vestige of tongue-in-cheek candour. Personally, while reading this paper I cannot help feeling an intangible touch of kind of this... Maybe to see BB's point more clearly you may wish to read Best wishes, Vladimir Bondarenko http://www.cybertester.com/ http://maple.bug-list.org/ http://www.CAS-testing.org/ === Subject: Re: [mma] basic question. When an expression value is displayed? > the For[] function in Mathematica return Null, and the StandardForm[] > of Null is to supress the output. Ok, that is good to know. > The ; is the short cut for CompoundExpression[] and the > value of a CompoundExpression[] function call is the > result of the last evaluation in the compound expression. > If you enter > i=3; > this is CompoundExpression[Set[i,3],Null] and the output is supressed > because the last evaluated expression is Null. > In the Out[] values Mathematica display the result of the > last evaluated function call, Ok, let me make sure I understand the above with this example: In[3]:= For[i = 0, i < 3, i++, i; ] In[4]:= Out[3] Out[4]= 2 In the above, since a ; was added after the i, this causes a function call to be made, which is CompoundExpression[Set[i,2],Null] Now when For[] returns the Out[] will display the last evaluated expression which in this case will be that Compound expression. And the last evaluated expression in that expression is Null. So no output is displayed. So far so good? But when I typed Out[3] to 'see' what the output of In[2] (which was not displayed) was, I get back a '2', which is not the last expression in the last expression which was evaluated which was a Null. And the reason this happened, is becuase the Out[3] call itself evaluated the 'hidden' Out[3] expression (which was not displayed) and the evaluation of the Null in that was removed and left the '2' as the last evaluated expression, and this is why Out[4] returned 2 and not Null. > > I have been trying to uderstand this basic issue. > When does mma display the value of a variable/expression. > look at this simple example: > In[1]:= For[i = 0, i < 3, i++, i ] > In[2]:= > see, No output is printed. I was expecting to see something like > 0,1,2 printed, one on each line or something like that. For example, > when I do the above in maple, this is the output: > maple> for i from 1 to 3 do > i > end do; > 1 > 2 > 3 > Now back to mma. On the command line, now when I type > In[2]:= i > Out[2]= 3 > so it does display the 'i' value. > So my question is why it does not display the value of 'i' when it is > inside the For loop? > I know it has something to do with value of the expression itself, and > above it is the 'For' loop which is the expression and not values > inside it, or some mumpljumple like this. But it is annoying that I > have to do Print on every variable to see its value : > In[3]:= For[i = 0, i < 3, i++, Print[i] ] > 0 > 1 > 2 > I have first thought that when one uses ; it means to supress the > otuput, see > In[4]:= i; > In[5]:= > but I am NOT using a ; in the original For loop. > in maple, if I use : it will supress output. > any one can tell me what is going on here? === Subject: Re: [mma] basic question. When an expression value is displayed? Some options to play with in Ver 5. For[i = 0, i < 3, i++; Print[i]] 0 1 2 Reap[For[i = 0, i < 3, i++; Sow[i]]] {Null, {{0, 1, 2}}} Flatten[Reap[For[i = 0,i < 3, i++; Sow[i]]][[2]]] {0, 1, 2} = = = = = = = = = = = = = = = = = > the For[] function in Mathematica return Null, and the StandardForm[] > of Null is to supress the output. > Ok, that is good to know. > The ; is the short cut for CompoundExpression[] and the > value of a CompoundExpression[] function call is the > result of the last evaluation in the compound expression. > If you enter > i=3; > this is CompoundExpression[Set[i,3],Null] and the output is supressed > because the last evaluated expression is Null. > In the Out[] values Mathematica display the result of the > last evaluated function call, > Ok, let me make sure I understand the above with this example: > In[3]:= For[i = 0, i < 3, i++, i; ] > In[4]:= Out[3] > Out[4]= 2 > In the above, since a ; was added after the i, this causes a function > call to be made, which is CompoundExpression[Set[i,2],Null] > Now when For[] returns the Out[] will display the last evaluated expression > which in this case will be that Compound expression. And the last > evaluated expression in that expression is Null. So no output is displayed. > So far so good? > But when I typed Out[3] to 'see' what the output of In[2] > (which was not displayed) was, I get back a '2', which is > not the last expression in the last expression which was evaluated > which was a Null. And the reason this happened, is becuase the > Out[3] call itself evaluated the 'hidden' Out[3] expression > (which was not displayed) and the evaluation of the Null in that was > removed and left the '2' as the last evaluated expression, and > this is why Out[4] returned 2 and not Null. > >I have been trying to uderstand this basic issue. >When does mma display the value of a variable/expression. >look at this simple example: >In[1]:= For[i = 0, i < 3, i++, i ] >In[2]:= >see, No output is printed. I was expecting to see something like >0,1,2 printed, one on each line or something like that. For example, >when I do the above in maple, this is the output: >maple> for i from 1 to 3 do > i > end do; > 1 > 2 > 3 >Now back to mma. On the command line, now when I type >In[2]:= i >Out[2]= 3 >so it does display the 'i' value. >So my question is why it does not display the value of 'i' when it is >inside the For loop? >I know it has something to do with value of the expression itself, and >above it is the 'For' loop which is the expression and not values >inside it, or some mumpljumple like this. But it is annoying that I >have to do Print on every variable to see its value : >In[3]:= For[i = 0, i < 3, i++, Print[i] ] >0 >1 >2 >I have first thought that when one uses ; it means to supress the >otuput, see >In[4]:= i; >In[5]:= >but I am NOT using a ; in the original For loop. >in maple, if I use : it will supress output. >any one can tell me what is going on here? === Subject: Re: MuPad 3.0 and Scilab version. I must have misread the literature as I assumed that Scilab was > also available during the trail. I thought so, too. In any case, domtype(scilab) should return DOM_DOMAIN even if Scilab is disabled. Maybe Torsten Metzner can say more about this. +--+ +--+| |+-|+ Christopher Creutzig (ccr@mupad.de) +--+ Tel.: 05251-60-5525 === Subject: package management in CAS systems I am finding mma and maple package loading/mechanism to be very weak. This is about mma, but also just as well applies to maple. There does not seem to be any sort of a package manager with some easy to use GUI interface to manage all these .m files and packages and directories. Right now I download some files from the net, throw the files in one of the directories under AddOns suggested by documentation, and that is about it. No mechanism to track what packages are added, removed, when, etc... A system is needed, with a DB, to allow one better control on what packages are being added/removed to the system, where, when, content, etc... a real solid database package manager type of thing with an easy to use GUI interface as the main single control point to manage all of this. Matlab has at least a basic GUI interface to allow one to easily add/remove paths to where they put the files. Scattered commands to do some of these things is not the best way to go about this. Maple has a rudimentary package manager based on commands. But nothing more. This is an area that is completely ignored by all these CAS systems as far as I can see. === Subject: Re: package management in CAS systems > Scattered commands to do some of these things is not the best > way to go about this. Maple has a rudimentary package manager based > on commands. But nothing more. Maple 9 has a GUI for many of those tasks. Please see ?LibraryTools,Browse for more information. http://www.scientific.de === Subject: Re: package management in CAS systems > Scattered commands to do some of these things is not the best > way to go about this. Maple has a rudimentary package manager based > on commands. But nothing more. > Maple 9 has a GUI for many of those tasks. > Please see ?LibraryTools,Browse for more information. Do you really think so? I found this tool to be useless and very badly designed. I am amazed a company will release a product the woked like this does. Ok, lets examine this so called library manager: 1. First I notied that there is no button that one can click on to start the library tools GUI interface. One must issue command lines to do this (which is contrary to the whole idea of use GUI to manage things in the first place). 2. After bringing up the ëLibrary tools' interface, which took about 60 seconds to come up (it is Java, what can you say), I noticed that now I am unable to click on main maple window below it(where I type the actuall maple commands). The Library tool GUI is on the way, and must be closed to be able to access the main window (a Brilliant design idea), so I click exit to close it the library tools, so I can access the main window. Now I use File->new to open a new maple window, then I start the ëlibrary tools' GUI again by typing the command Browse(). Now, it will not come up. So I typed the with(LibraryTools): again, and then the Browse() command again. And now it came up (again, a simple button to click on would have helped here). 3. Now that the Library tools GUI is up, I can now access type on the first main maple window since it is not locked, only the second maple window is locked, 4. The first thing I did is click on the help button. And what I see is a description of a command line calling sequence! (A help about the GUI showing how to use a command line sequence?) Ok, I skip that, I read below it, and see the part about description of the library browser. Below it, it talks about ëDropDownBox' I look at the GUI and I do not see anything called ëDropDownBox'. May be this is the variable name the programmer used? I guess so. Below that it says ëLibrary: Contains all the active libraries listed in libname.' So I look at the GUI to see if I can view the what libname is, but do not see an option to do this. A library tool manger that does not have an option to tell the user what the current libname is. Really good design. 5. Now I wanted to use the ëlibrary' pull down to see what is actually listed there. I found I am unable to do this. The help window has locked the GUI window out, so I have to close the help window to use the GUI. Another brilliant design idea. Now I can't read help and use the tool at the same time. 6. So I close the help window to use the library GUI. And I notice there is no ëclose' button on it, and must use the X window corner to kill it. Bad design. 7. Now I use the pull down menu to see what is there. I see a number of file names listed. I see the first name with number 1 next to it, then 1.1, then 2 then 2.1, etcá I am not sure what 2.1 means in reference to 2. It probably means 2.1 is inside library 2? What is the meaning of this ordering? Any way, I select one by random. I select 2.1, which is called standard.lib. Now I wanted to see what functions are inside this library, simply to browse the library content. I click the ëopen' button. 8. Now I get another popup window with two dialogs. The first is already filled with text, which says ëOpen libraries and add them in the Active Library Path' Not sure what the active library path is. Is this libnane, not important now. Let me go on, The text area below it is blank, meaning the user is meant to type the library full path name there or something like that but I thought I have already selected a ëlibrary' to get to here? Ok, so I click the ëBrowse' button to see what will happen. 9. Now windows manager opens up to ëMy documents'. OK. I see the file type is set to ëlib' below. So I am supposed to navigate to where maple 9 is located and click on the file (which I thought I already selected in step 7 above, and hopefully I'll remember its name and can find it' 10. I remember that maple is installed under the C:Program files, so I navigate there. I am inside maple 9 folder now. I see a folder called Lib, I go inside there. I see a number of files called ë*.lib'. So I click on the file ëstandard.lib' and click open. Now I am back to the open dialogue of the library tools GUI, I click open again on that. 11. Now I wait. 12. Now I am still waiting. I do not see anything happening. Isn't something supposed to happen now? Did it actually open it? May be it did, I did not get any notification of a successful open. I have just spent 5 minutes to ëopen' a library. Now what do I do? All what I wanted is to see what functions are in it. 13. Ok, since nothing happened, I clicked on the ëedit' button to see what will happen. Now I get a dialog called ëContents'. It says that the number of members in it is 0. All other buttons are disabled. With an empty text area with no title next to it which is empty. So I guess this library is empty. Too bad. Let me try another one. 14. Now I click close on the window titled ëcontents'. 15. Now I am back to the ëlibrary tools' window, with the standard.lib name displayed in the pull down menu. 16. Now that did not go too well. Let me pick another file. 17. So I repeat steps 7 to 10 again. Now I am smarter. No need to use the pull down menu to select a different library since that did not do anything before. I had to still navigate to open the library any way. I just click on the ëopen' button. Then click on Bowse. Now I find that the tool did not remember the last folder I was in, which means I have to navigate all the way back to maple folder (bad design). 18. Now I select Student.lib, click open, open again, and now I am back to the Library tools GUI. 19. I noticed that the ëLibrary' name remains at ëmaple.lib' the library I selected earlier. Isn't that supposed to change? Never mind, I keep going. Now what do I do? I click edit again. 20. Now I think there is some progress, the hourglass is on for some time, may be this library has something in it I can actually see something finally. 21. humm, still waiting. The hourglass is still active. It has been 5 minutes now and nothing happened. 22. I click in windows task manager to see what happened. I see the CPU at 100%. 23. I waited more, and nothing happened. So kill the library tool GUI. Now maple is not responding any more. I kill it also, and I get the windows message that the program is not responding, I click ok to kill it. 24. Ok, this was fun. I have spent 20 minutes so far, and I still have no idea how to use the library tools ëmanager' to see at least the contents of a library. So now I decided to try the ëNew' option to see what will happen. So far what I got out from the library tools manager is a pull down menu showing the names of some files, which I can find by simply looking at the libname variable. 25. So I go back to step 1. I start maple 9, and type the commands to start the GUI. 26. Now I click ëNew' on the library tools GUI 27. I get a ëNew library' dialoug with the name c:/Program Files/Maple 9/LIB/DemoLibuser.lib already filled in the text area. I see a button, which says ëcreate' and one called ëclose' and one called ëbrowse'. Not sure why ëuser.lib' shows up there, since I have not selected it and it is not even the first one listed in the pull down library choices in the initial GUI. May be the programmer wanted a name to fill in that text area and they just picked this name as it seems like a good generic name?. Not knowing if this library actually already exist or not, and not wanting to overwrite something important and not knowing if the library tool will warn me if I create a library with the same name as an existing one, I changed the name to foo.lib just to see what will happen. Now I click ëcreate' 28. Now it tells me that ëDirectory does not exist, and if I want to create it'? If directory does not exist, then why did the program select that folder to start with? Ok, I click yes any way. Just do something. 29. Now the hour glass comes up 30. It is still up. 31. I noticed that when I move the mouse over the library tools GUI, the hourglass is busy, but not if I move the mouse over the ënew library' dialog it is not buys. So may be the ënew library' dialogue has actually finished its job? But if so, why did I not get a notification pop-up window saying the library was created? Has the library been created? Not knowing what is going on, I decided to click ëcreate again' 32. Now it tells me that the directory does not exist and if I want to create a new one. But I already told it YES before? So I click YES again. 33. Again, nothing happens. So I click ëclose' 34. Now I am back to the library tools GUI. 35. That was fun, 36. Now did foo.lib get created? Let me try the pull down menu to see if it shows up there. 37. Nope, nothing there, no foo.lib to be seen. May be I can use the library tools manager to add foo.lib to ëlibname' ? After all this is what a library tools manager is supposed to do. 38. I look and see no option to allow me to do this. 39. Ok, nothing more to do, I decided to try to compress button to see if that at least works. 40. I get a dialogue with name maple.lib shown. I click the ëcompress' button. 41. I get a pop-up windows saying the library was compressed ! that was fun. 42. Ok, I think I used all the options shown. New and Edit do not seem to do anything. No option to list content of libraries, no option to allow one to view/manage the which libraries are visible to a maple session, etc,etc,,á I would say this is a very useful library tools manager indeed (NOT) and was a complete waste of time. === Subject: A Useful Function While Working with the other stuff that I've posted recently, I Totally-Busted Incommens- urability. And it's Easy to see. Given a Circle, having =any= radius, construct a right-Triangle, 1. having the Circle's radius as it's hypotenuse, call it C, 2. one side as a semi-chord, with one end shar- ing a point with the circle-end of the hypotenuse, call it A, 3. and the other side drawn from the center of the Circle, to meet the semi-chord, forming a right-angle, and sharing a point with the 'dangl- ing'-end of the semi-chord, call it B. 4. The Pythagorean Theorem applies, and A^2 + B^2 - C^2 = 0, 5. and is =ALWAYS= Equals Zero. 6. As one varies the angle that the hypotenuse make with the X axis, A and B adjust their lengths continuously, and A^2 + B^2 - C^2 = 0, always, 7. even when A or B becomes Equal to Zero, 8. at which point, either the semi-chord, A, or the center-pinned line, B, becomes Equal to the hypotenuse, C. 9. This seems, to me, to be quite astounding, because Incommensurability is nowhere to be seen. 10. Since the radius can be of =any= length, this Circle operation scales from zero to Infinity, which covers =any= plane, and does so, Continuously, without a hint of Incom- mensurability. 11. It does this be-cause when A and B go- Irrational, they balence each other =Exactly=! 12. Which means that Irrational Numbers are no longer a Problem - just construce a Circle with the necessary radious, and, voil.88, there's your Conjugated-pair of Irrationals, ready to do anything that you want to do with them. 13. Of course, you cannot measure these Numbers, but you can address them, Exactly, through the Circle-Geometry, given above. You know, pick your favorite Greek symbol, and its, Bye-bye, 'Irrationals'. Q. E. D. === Subject: Filterquestion I am wondering if it is possible to design a filter with the impulseresponse h(t) such that the convolution of a signal p(t)=f(t)*cos(w*t)+g(t)*sin(w*t) with h(t) is equal to f(t)*sin(w*t)+g(t)*cos(w*t)??? In other words, I am looking for a filter H(s) in the s-domain that has the following property: InverseLaplace { H(s)*P(s) } = f(t)*sin(w*t)+g(t)*cos(w*t) where P(s)=Laplace{p(t)} Some more info: f(t) is a train of half-sine pulses with the period T g(t) is also a train of half-sine pulses with the period T, but g(t) is delayed 0.5T in relation to f(t) The pulsefrequency in rad/sec = 2*pi/T is much lower than the carrier-frequency w. === Subject: Re: Computer Algebra System by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3FI3tQ14877; There is a mistake in your message. It should be I'm trying to make.. Luv Papa >Hi! > I'm trying a make a small Computer Algebra System as a college >project. More importantly,I'm trying to design a data structure for a >CAS. So I would like to know what kind of data structures are used in >standard Computer Algebra Systems. I would be grateful for any pointer. >Parijat >(z2d05002@reg.iitb.ac.in) === Subject: Re: Computer Algebra System >Hi! > I'm trying a make a small Computer Algebra System as a college >project. More importantly,I'm trying to design a data structure for a >CAS. So I would like to know what kind of data structures are used in >standard Computer Algebra Systems. I would be grateful for any > pointer. Expression trees are certainly the most important structure. Whether you represent them as nested Lisp lists or as n-ary trees with pointers in C is of secondary importance. A pointer? Try http://www.mupad.de/doc30+M5b034e24790.htm, especially section 4.4.2, http://www.mupad.de/doc30+M53626fec927.html, and the page linked from there as next. +--+ +--+| |+-|+ Christopher Creutzig (ccr@mupad.de) +--+ Tel.: 05251-60-5525 === Subject: upgrade from macsyma 2.2 to 2.4 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3FI3qc14765; I have been using macsyma since it was under development in the 70's. The latest version that I own is 2.2 for windows. I would like to upgrade to 2.4, but the company is out of business. Does anyone out there have the installation disks for 2.4? If so, could I get copies? I would appreciate any help. Mike === Subject: Re: upgrade from macsyma 2.2 to 2.4 > I have been using macsyma since it was under development in the 70's. > The latest version that I own is 2.2 for windows. I would like to > upgrade to 2.4, but the company is out of business. Does anyone out > there have the installation disks for 2.4? If so, could I get copies? > I would appreciate any help. > Mike This might be your best bet: I don't know if they're still offering the disks, but if anyone can sell them it is probably Symbolics. CY === Subject: Re: upgrade from macsyma 2.2 to 2.4 > I have been using macsyma since it was under development in the 70's. > The latest version that I own is 2.2 for windows. I would like to > upgrade to 2.4, but the company is out of business. Does anyone out > there have the installation disks for 2.4? If so, could I get copies? > I would appreciate any help. > Mike Mike: Macsyma has been released to the public domain; now referred to as Maxima. Available on several platforms. See: http://sourceforge.net/projects/maxima/ Good luck! TomCee === Subject: Re: upgrade from macsyma 2.2 to 2.4 Macsyma 2.2 and 2.4 are commercial versions. The Maxima system is based on a version from 1982 or so. Although related, they are not the same. >I have been using macsyma since it was under development in the 70's. >The latest version that I own is 2.2 for windows. I would like to >upgrade to 2.4, but the company is out of business. Does anyone out >there have the installation disks for 2.4? If so, could I get copies? >I would appreciate any help. > Mike: > Macsyma has been released to the public domain; now referred to as Maxima. > Available on several platforms. > See: http://sourceforge.net/projects/maxima/ > Good luck! > TomCee === Subject: Re: Find a Function > This is a very simple problem which I haven't been able to solve. I > need to find a function q=f(x,y) with x>0 and y>0 such that (1) > partial derivatives f1<0, f2>0 and f12<0, (2)for p=x*f(x,y), partial > derivatives p1=0, p11<0 and p12<0 and .... > ^^^^^^^^^^^^^^^^^^^^^ > If p1 = 0 everywhere, then p11 and p12 are 0 as well, so > can't be negative. Is there a typo? > . >Yes - I think my message could have been clearer. I'm not requiring >p1=0 everywhere but just at some point (which will be the maximum for >the function). It is also required that p11<0 and p12<0 at this point >but also over a range of values. > Well, let's try a quadratic. Say you want your conditions at the point > (x,y) = (1,1). For convenience change variables to u=x-1 and v=y-1, and > write f(x,y)=F(u,v) = a_0 + a_1 u + a_2 v + a_{11} u^2 + a_{12} uv + > a_{22} v^2 > and p(x,y) = x f(x,y) = (u+1) F(u,v) > = a_0 + (a_0 + a_1) u + a_2 v + (a_1 + a_{11}} u^2 + (a_2 + a_{12}) uv + > a_{22} v^2 + ... > Your requirements seem to be > 1) f_1(1,1) = F_1(0,0) = a_1 < 0 > f_2(1,1) = F_2(0,0) = a_2 > 0 > f_{12}(1,1) = F_{12}(0,0) = a_{12} < 0 > 2) p_1(1,1) = a_0 + a_1 = 0 > p_{11}(1,1) = 2 (a_1 + a_{11}) < 0 > p_{12}(1,1) = a_2 + a_{12} < 0 > Well, that should be easy enough. Try, say, > a_0 = 1, a_1 = -1, a_2 = 1, a_{11} = -2, a_{12} = -2 > Robert Israel israel@math.ubc.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia > Vancouver, BC, Canada V6T 1Z2 but there is another requirement which I need which I only half covered in my (3). More accurately, define the original function q1=f(x,y) and another function q2=g(x,y) which is symmetric with q1. Then the requirement is that g(x,y)=0 intersects p1=0 at positive Roger === Subject: Re: Journals and my papers Professor Basti; I though you might be interested in knowing that new Maple 9.5 has the following new item in it: Exact Solutions .89´¢ New algorithms for solving Riccati type ODEs, second order linear ODEs of Mathieu type, polynomial solutions for nonlinear ODEs and systems of ODEs, linear and nonlinear PDEs and systems of PDEs Since your research work is on Riccati ODE's you might want to check this out. === Subject: Re: Journals and my papers Since steve_H doesn't provide a valid email address, it is impossible to send him a note without sending it to this newsgroup. Apologies to others. steve_H: you can send mail to Dr. Basti, or to Maplesoft, or to any individual, by using e-mail, not newsgroups. Some of your messages are of limited interest, and (increasingly often not correct), and perhaps should not be broadcast, stored on archives forever, making newsgroups less and less valuable. Think about it. > I though you might be interested in knowing that new Maple 9.5 has > the following new item in it: Exact Solutions > .89´¢ New algorithms for solving Riccati type ODEs, second > order linear ODEs of Mathieu type, polynomial solutions > for nonlinear ODEs and systems of ODEs, linear and > nonlinear PDEs and systems of PDEs > Since your research work is on Riccati ODE's you might want to > check this out. === Subject: Re: Journals and my papers > steve_H: you can send mail to Dr. Basti, or to Maplesoft, > or to any individual, by using e-mail, not newsgroups. I am posting something that could be of an interest to others as well. > Some of your messages are of limited interest, you should speak for yourself only and not for others. if you find my message of no interest to you, then you are free not to read it. this is a free country. >and (increasingly often not correct), if you think so, then do not answer it or read it. In addition this is not one of your classrooms. one is not being graded here. > and perhaps > should not be broadcast, stored on archives forever, that is your opinion. and I would not care less about it. but you are free to think anything you like. > making newsgroups less and less valuable. feel free to put me on your kill-list. I would appreaciate it if you do. > I though you might be interested in knowing that new Maple 9.5 has > the following new item in it: Exact Solutions > .89´¢ New algorithms for solving Riccati type ODEs, second > order linear ODEs of Mathieu type, polynomial solutions > for nonlinear ODEs and systems of ODEs, linear and > nonlinear PDEs and systems of PDEs > Since your research work is on Riccati ODE's you might want to > check this out. === Subject: Re: [mma,maple] piecewise integration problem. Not an expert, but mma is also trying to be Exact. Because the answer is zero, it is having a numerically hard time arriving at zero. removeall; f[x_] := x /; -1 < x < 0 f[x_] := x /; 0 < x < 1 NIntegrate[f[x], {x, -1, 1}] NIntegrate::inum : Integrand f[x] is not numerical at {x} = {0.`} Even the option Method -> Oscillatory won't work here as it tries to home in on the Zero value. Here we uses .99 (exactly) to get a close answer, but not exactly zero. As you increase the second number, you will get an answer closer to zero. NIntegrate[f[x], {x, -1,99/100}] -0.009950000000000011 You can break it up into parts. NIntegrate[f[x], {x, -1, 0}] -0.5 NIntegrate[f[x], {x, 0, 1}] 0.5 Together, the answer is an zero. It's interesting that if you change the function so that the area is 1, it still wont work unless the upper limit is close to 1. f[x_] := -x /; -1 < x < 0 f[x_] := x /; 0 < x < 1 NIntegrate[f[x], {x, -1., 1 - $MachineEpsilon}] 0.9999999999999998 I find the following interesting for study... f[x_] := x /; -1 < x < 0 f[x_] := x /; 0 < x < 3 NIntegrate[f[x], {x, -1, 2}] 1.5 Using Windows XP & Office XP = = = = = = = = = = = = = = = = = > ; > I asked my math professor on this. > Let me quickly recall the problem with a simple example: > given a piecwise function not defined on a single point in its > domain, I want to integrate it over a range that includes the point. > f[x_] := x /; -1 < x < 0 > f[x_] := x /; 0 < x < 1 > Integrate[f[x], {x, -1, 1}] > Here mma will not integrate it, but maple will: >f:=x->piecewise( -1 0 int(f(x),x=-1..1); > 0 > Accoding to the math teacher, mma is correct in the strict mathematical > sense. Since a function must be defined at EACH point on the domain of > the integration (normal sense of integration). > However, he also said that the function can have any value at the > point 0 above (where it is not defined) and the answer will still be > the same, which is 0 for the area under the curve in this example. > So, mma is correct to complain, but maple is also correct in its > answer. It seems maple must be using hueristics here to determine > this, and it must have seen that the function is not defined over countable > number of points and 'let is pass' through the integration. > Which do you think is the better approach? === Subject: Re: [mma,maple] piecewise integration problem. > Not an expert, but mma is also trying to be Exact. Because the answer > is zero, it is having a numerically hard time arriving at zero. The fact that it's zero has nothing to do with the fact that the numerical integration is returned unevaluated. > removeall; > f[x_] := x /; -1 < x < 0 > f[x_] := x /; 0 < x < 1 > NIntegrate[f[x], {x, -1, 1}] > NIntegrate::inum : Integrand f[x] is not numerical at {x} = {0.`} > Even the option Method -> Oscillatory won't work here as it tries to > home in on the Zero value. I think someone has already mentioned this in this thread, but I'll mention it again: In[1]:= f[x_] := x /; -1 < x < 0 In[2]:= f[x_] := x /; 0 < x < 1 In[3]:= NIntegrate[f[x], {x, -1, 0, 1}] ...Numerical integration stopping due to loss of precision... Out[3]= -5.55112*10^-17 which is pretty close to zero. > Here we uses .99 (exactly) to get a close answer, but not exactly zero. As you increase the second number, you will get an answer closer > to zero. > NIntegrate[f[x], {x, -1,99/100}] > -0.009950000000000011 The reason that this works, while what you tried initially did not, is due, I presume, to the fact that Mathematica never notices here that f is not numerical at x = 0. That's because here it never tries to evaluate f at x = 0. In what you tried initially however, x = 0 was precisely the midpoint of the limits of integration, and so it tried to evaluate f there. > You can break it up into parts. > NIntegrate[f[x], {x, -1, 0}] > -0.5 > NIntegrate[f[x], {x, 0, 1}] > 0.5 > Together, the answer is an zero. Sure. That's in essence the same as NIntegrate[f[x], {x, -1, 0, 1}]. > It's interesting that if you change the function so that the area is 1, > it still wont work unless the upper limit is close to 1. I believe you're implying that it still won't work if the upper limit is exactly 1. Well, that's right of course. Again, in that case x = 0 would be the midpoint of the limits of integration, so Mathematica tries to evaluate f there but finds that it is not numerical... > f[x_] := -x /; -1 < x < 0 > f[x_] := x /; 0 < x < 1 > NIntegrate[f[x], {x, -1., 1 - $MachineEpsilon}] > 0.9999999999999998 > I find the following interesting for study... > f[x_] := x /; -1 < x < 0 > f[x_] := x /; 0 < x < 3 > NIntegrate[f[x], {x, -1, 2}] > 1.5 I wonder why you think it's interesting for study. === Subject: Re: [mma,maple] piecewise integration problem. on a related topic, I found this mma package http://library.wolfram.com/infocenter/MathSource/514/ The package RLSCF.m contains a function named PlotFR similar to Plot. PlotFR locates and avoids the discontinuities of real functions as Tan[x], 1/(x-2), and others, download it, but can not load it for some reason.... the command < look at this VERY simple case > f[x_] := x /; -1 < x < 0 > f[x_] := x /; 0 < x < 1 > Integrate[f[x], {x, -1, 1}] > This, MATHEMATICA did not do. > even with numeric N[]: > NIntegrate::inum: Integrand f[x] is not numerical at {x} = {0.`} It works (giving a precision loss warning) if you test for singular points in the integration range: NIntegrate[f[x], {x, -1, 0, 1}] Paul > The math book i am studying from does integration of things as the > above every where. i.e. on functions which has 'break' in them, where > the function is not defined one a point where it breaks/jumps. > i.e. it uses < instead of <= in the definition. > A function is not defined over one point, but I thought the whole > idea of piecewise function is to be able to handle this? >; >It seems maple and mma have different semantics when it comes >to piecewise functions, at least when it comes to using them >with integrations. >I define a function f, which is 0 from -Pi to Pi/2 and 1 from Pi/2 >to Pi. simple function. >f[x_] := 0 /; -Pi < x < Pi/2 >f[x_] := 1 /; Pi/2 < x < Pi >Notice the function f is not defined on point point x=Pi/2. >Then I asked mma to integrate cos[x]*f[x] from 0 to Pi. This >means becuase f is zero over -Pi to Pi/2, I expected the above >integral should be the same as integrating cos[x] from Pi/2 to Pi, >right? This is how we do in by hand. >What do you think the answer should be? -1, right? >--------------- >In[1]:= f[x_] := 0 /; -Pi < x < Pi/2 >In[2]:= f[x_] := 1 /; Pi/2 < x < Pi >In[3]:= Integrate[Cos[x] f[x], {x, -Pi, Pi}] >Out[3]= Integrate[Cos[x] f[x], {x, -Pi, Pi}] >--------------- >see, it does not do it. >So I tell it to use numerical. >--------------- >In[4]:= N[%] >NIntegrate::inum: Integrand Cos[x] f[x] is not numerical at {x} = >{1.5708}. >NIntegrate::inum: Integrand Cos[x] f[x] is not numerical at {x} = >{1.5708}. >NIntegrate::inum: Integrand Cos[x] f[x] is not numerical at {x} = >{1.5708}. >General::stop: Further output of NIntegrate::inum > will be suppressed during this calculation. >NIntegrate::inum: Integrand Cos[x] f[x] is not numerical at {x} = >{1.5708}. >NIntegrate::inum: Integrand Cos[x] f[x] is not numerical at {x} = >{1.5708}. >NIntegrate::inum: Integrand Cos[x] f[x] is not numerical at {x} = >{1.5708}. >General::stop: Further output of NIntegrate::inum > will be suppressed during this calculation. >Out[4]= NIntegrate[Cos[x] f[x], {x, -Pi, Pi}] >---------------- >see, it does not like the integrand at Pi/2, which is a jump point >(or more accurately I should say a discontinuity point) for the function >f[x]. >If mma is correct, then how come maple does the same thing with >no problem? without even asking it to use numerical integration: >f:=x->piecewise( -Pi Pi/2int(cos(x)*f(x),x=-Pi..Pi); > -1 >evalf(int(cos(x)*f(x),x=-Pi..Pi)); > -1 >So, my question to the experts, who is correct in this? I am asking >this, becuase the book I am looking at does show the function f[x] >defined as I showed above. i.e. >f[x_] := 0 /; -Pi < x < Pi/2 >f[x_] := 1 /; Pi/2 < x < Pi >and NOT >f[x_] := 0 /; -Pi < x <= Pi/2 <--- notice the <= here. now mma is >happy >f[x_] := 1 /; Pi/2 < x < Pi >Also, when I use the above new defintion for f[x], mma still will NOT >give >a symbolic answer (I mean without using N[]), but I still must >use numerical integration, then it will give the answer -1. This >is very annoying. Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul@physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul === Subject: Re: [mma,maple] piecewise integration problem. >int[numeric](cos(x)*f(x),x=-Pi..Pi); > -1 I have a typo there, I meant to type >int[numerical] and not >int[numeric] funny thing is that maple did not complain at all about my typo that why I did not notice it! This should be a bug. === Subject: Re: [mma,maple] piecewise integration problem. >int[numeric](cos(x)*f(x),x=-Pi..Pi); > -1 > I have a typo there, I meant to type >int[numerical] > and not >int[numeric] > funny thing is that maple did not complain at all about my typo > that why I did not notice it! This should be a bug. Ok, ok, there is no such thing as int[numerical] either. But, but, I was reading maple on-line help, and it says, under ?int the following: For numerical integration, see int[numerical]. so I hope now I can be execused for this. Even though when now I clicked on the link, I do see it says to use evalf(Int()). but when I read this first time, I just assumed to use int[numerical] will cause numerical integration and I did not bother to click on the link to read more at the time. May be maple help should be better written so it is not confusing! this is maple 9 btw. === Subject: Re: [mma,maple] piecewise integration problem. > >int[numeric](cos(x)*f(x),x=-Pi..Pi); > -1 > > I have a typo there, I meant to type >int[numerical] > and not >int[numeric] > funny thing is that maple did not complain at all about my typo > that why I did not notice it! This should be a bug. >Ok, ok, there is no such thing as int[numerical] either. >But, but, I was reading maple on-line help, and it says, under ?int >the following: > For numerical integration, see int[numerical]. >so I hope now I can be execused for this. You misspelled 'executed'. :-) === Subject: Re: [mma,maple] piecewise integration problem. >int[numeric](cos(x)*f(x),x=-Pi..Pi); > -1 >I have a typo there, I meant to type >int[numerical] >and not >int[numeric] >funny thing is that maple did not complain at all about my typo >that why I did not notice it! This should be a bug. As you were told before, neither of these is the way to do numerical integration. evalf(Int(...)) is. In general, Maple does not check functions for subscripts. So pick your typical function f, enter f[foo](bar), and if f(bar) returns some result (rather than returning unevaluated), f[foo](bar) will probably return the same result. The main exceptions: 1) functions whose calling sequence can include a subscript. 2) results returned via a remember table: f[foo] and f will have separate remember tables. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: Re: Please repeat link to MINSE by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3GJSiJ25121; Could we please have an active link to MINSE as I have a lot of downloaded files containing text that should be rendered with MINSE and Will soon be in trouble if I can`t get it right.