mm-3249 === Subject: Another look on Russell's first paradox The first russell's paradox: ( http://www.wikipedia.org/wiki/Russell%27s_paradox ) Consider the set M to be The set of all sets that do not contain themselves as members. Formally: A is an element of M if and only if A is not an element of A. In the sense of Cantor, M is a well-defined set. Does it contain itself? If we assume that it does, it is not a member of M according to the definition. On the other hand, if we assume that M does not contain itself, than it has to be a member of M, again according to the very definition of M. Therefore, the statements M is a member of M and M is not a member of M both lead to a contradiction. So this must be a contradiction in the underlying theory. Some example: if we had an entry on list of all lists which do not contain themselves, then that list must be either incomplete (if it does not list itself) or incorrect (if it does). ----------------------------------------------------------------- A structural point of view: --------------------------- Definition A: ------------- ( http://www.cut-the-knot.org/selfreference/russell.shtml ) Sets are defined by the unique properties of their elements. ------------------------------------------------------------- One may not mention sets and elements simultaneously, but one notion has no meaning without other. Let us take as an exapmle, the W set (the set of all positive integers): {0,1,2,3,...} By using the empty set (with the Von Neumann Heirarchy), we can show that W has the structure of a set that contain itself as a member of itself: 0 = { } 1 = {{ }} = {0} 0. | | 2 = {{ },{{ }}} = {0,1} 0. . | | 1|____| | | 3 = {{ },{{ }},{{ },{{ }}}} = {0,1,2} 0. . . . | | | | 1|____| |____| | | 2|__________| | | 4 = {{ },{{ }},{{ },{{ }}},{{ },{{ }},{{ },{{ }}}}} = {0,1,2,3} 0. . . . . . . . | | | | | | | | 1|____| |____| |____| |____| | | | | 2|__________| |__________| | | 3|______________________| | | {0,1,2,3,...}={{ },{{ }},{{ },{{ }}},{{ },{{ }},{{ },{{ }}}},{... |0| |-1-| |----2----| |----------3----------| |--4 | ^ ^ ^ ^ |____| | | | | | | | |___________| | | | | | |_______________________| | | | |___________________________| By definition A, the set of all sets that contain themselves as members, must have some kind of the above self structural similarity over scales, by a recursive process. By a recursive process, I mean that to be a member of yourself is a never ending story. Also by definition A, the set of all sets that do not contain themselves as members, must not have this property, therefore the set of all sets that do not contain themselves as members, must not contain itself as a member of itself. Through this structural point of view, there is no paradox. This is not logical but a structural point of view on this paradox, and it is based on the simple fact that there can not be any separation between a set and the properties of its contents. Therefore, the set of all sets that do not contain themselves as members, must have this property, which is: Not to contain itself as a member of itself. An example: ------------- Please look at the structure of a fractal. It has a self similarity to its content. The set of all sets with some common property, also has a self similarity with respect to its members, because there cannot be any separation between any set and its members. We are talking about two kinds of properties: Property A ------------ Members that contain themselves as members. Property B ------------ Members that DO NOT contain themselves as members. Because there can not be any separation between a set and the properties of its members, the set of all sets that do not contain themselves as members is a property B set. Therefore there is no paradox. The paradox arises when we force property A on property B. What do you think? === Subject: Automatic solution of recurrence relations Since this topic surfaces from time to time on this newsgroup, I thought it was not inappropriate to announce here that we have just published the paper The automatic solution of recurrence relations. I. Linear recurrences of finite order with constant coefficients. R. Bagnara, A. Zaccagnini, and T. Zolo. Available at http://www.cs.unipr.it/Publications/. This is the first in a series devoted to the presentation of all the mathematics behind the PURRS (Parma University's Recurrence Relation Solver) project. This paper describes algorithmic techniques for the efficient solution of a wide class of linear recurrences of finite order with constant coefficients. The presentation is thorough and reasonably self-contained, covering topics such as the automatic solution of polynomial equations and efficient, exact symbolic summation of some special functions. If you are interested in the PURRS system, please visit http://www.cs.unipr.it/purrs/ and play with the demo. We are interested in receiving feedback of any kind both on the paper and on the software. Roberto Bagnara -- Prof. Roberto Bagnara Computer Science Group Department of Mathematics, University of Parma, Italy http://www.cs.unipr.it/~bagnara/ mailto:bagnara@cs.unipr.it === Subject: Re: Boolean Algebra packages? > Maple used to have a symbolic logic package, but some time ago this was removed; > it doesn't appear to have been reinstated into Maple 9. A logic package was > available through the Maple Applications Center (http://www.mapleapps.com), but > I just checked the site to discover that it is no longer available. I don't > know why Maple doesn't support symbolic logic - I find it very annoying. See http://www.mapleapps.com/powertools/logic/logic.shtml (The URL had been changed slightly, it seems.) In Maple V the package was included; just type with(logic); -- Thomas Richard Maple Support Scientific Computers GmbH http://www.scientific.de === Subject: Comparison of Mathematica on Various Computers ''Comparison of Mathematica on Various Computers'' is now on (or ) If you don't have access to the Web send e-mail to karl@itp.tu-graz.ac.at for the latest version. Mathematica 4.0 benchmark on http://www2.staff.fh-vorarlberg.ac.at/~ku/karl/timings40.html New results Mathematica 4.0: PowerMac dual 1.4GHz, MacOS 10.2.6 Athlon 2800+, 512 KB cache, 333 MHz FSB, Win. XP Pro Karl PS: New test for MMA 5.0 in preparation === Subject: eigenvectors of submatrices? Hi All I'm trying to calculate with Maple the eigenvectors for a 8x8 symbolic matrix, but it seems is too much for my Maple, so I wonder if I can bypass this straight approach. The matrix has the form: [ 0 A1 ] A = [ A2 0 ] Where A1 and A2 are 4x4 symbolic matrices and 0 are 4x4 zeros matrices. Looking at the structure of the matrix and the amount of zeros it has makes me think that maybe there is a simplification for this eigenvectors problem. Can anyone come up with any hint? Ant === Subject: Re: eigenvectors of submatrices? Oooops What I meant with this subject is that maybe I can obtain the eigenvectors of A as a function of the eigenvectors of A1 and A2.....or not? Ant > Hi All > I'm trying to calculate with Maple the eigenvectors for a 8x8 symbolic > matrix, but it seems is too much for my Maple, so I wonder if I can bypass > this straight approach. The matrix has the form: > [ 0 A1 ] > A = [ A2 0 ] > Where A1 and A2 are 4x4 symbolic matrices and 0 are 4x4 zeros matrices. > Looking at the structure of the matrix and the amount of zeros it has > makes me think that maybe there is a simplification for this eigenvectors > problem. Can anyone come up with any hint? > Ant === Subject: Re: eigenvectors of submatrices? > Oooops > What I meant with this subject is that maybe I can obtain the eigenvectors > of A as a function of the eigenvectors of A1 and A2.....or not? no, the eigenvectors of A1 and A2 don't help much. But if you rewrite your original system in block form, you arrive at the equation A2*A1*x1 = lambda^2*x1 which should be solvable. It can of course be still too complicated for a symbolic program to produce any meaningful answer. Alois === Subject: Re: eigenvectors of submatrices? matrix and lambda the eigenvalues matrix? Ant >> Oooops >> What I meant with this subject is that maybe I can obtain the >> eigenvectors of A as a function of the eigenvectors of A1 and A2.....or >> not? > no, the eigenvectors of A1 and A2 don't help much. > But if you rewrite your original system in block form, > you arrive at the equation > A2*A1*x1 = lambda^2*x1 > which should be solvable. > It can of course be still too complicated for a symbolic program to > produce any meaningful answer. > Alois === Subject: integration problem Hi all, I have to integrate: 2^((-x/a)^1.4)*2^((-x/b)^1.8)*x from 0 to infinity (or at least from 0 to 5*a). (a>0, b approximately: 0.7*a b=f(a,H); / 0 So I wondered if there is a smart approximation to the integrand that can be integrated to give me b in dependence of a and H. I already tried using a taylor series which was not successful. Any help is highly appreciated, Nils === Subject: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions My second son is a freshman in college this semester and is a science major taking Calculus. His prof is using Maple, a software package about which I know very little. I am familiar with MathCad but not Mathematica or Matlab. I understand with a TI connectivity kit you can exchange information in MathCad, but can you do that with Maple, MatLab, or Mathematica? (He has a TI-89.) I understand you can use Maple in conjuntion with the other software packages. I'm trying to decide what is the best software package to get him. My funds are limited (typically, I know). -- Cindy Smith Unless the LORD build the house, cms@dragon.com they labor in vain who build. cms@5sc.net Unless the LORD guard the city, cms@romancatholic.org in vain does the guard keep watch. Me transmitte sursum, -- Psalm 127:1 Caledoni! All your base are belong to us. A Real Live Catholic You are on the way to destruction. in Georgia! What you say. >->> <<-< Go against the flow! You have no chance to survive make your time. === Subject: Re: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions > My second son is a freshman in college this semester and is a science > major taking Calculus. His prof is using Maple, a software package > about which I know very little. I am familiar with MathCad but not > Mathematica or Matlab. I understand with a TI connectivity kit you > can exchange information in MathCad, but can you do that with Maple, > MatLab, or Mathematica? (He has a TI-89.) I understand you can use > Maple in conjuntion with the other software packages. I'm trying to > decide what is the best software package to get him. My funds are > limited (typically, I know). > -- > Cindy Smith Unless the LORD build the house, > cms@dragon.com they labor in vain who build. > cms@5sc.net Unless the LORD guard the city, > cms@romancatholic.org in vain does the guard keep watch. > Me transmitte sursum, -- Psalm 127:1 > Caledoni! All your base are belong to us. > A Real Live Catholic You are on the way to destruction. > in Georgia! What you say. >->> <<-< Go against the flow! You have no chance to survive make your time. For learning calculus, MathCad is fine. MatLab is for experts with a need to do fancy fast numerical calculations. By the time your son needs it he can either use it online in a networked Linux version, or else get a later edition than what will be avaialble now. Mathematica and Maple are also kinda fancy for right now. In two years, maybe, unless he is very advanced. Finally, let me take the liberty of sending you via e-mail the Preface of a book on mathematical methods of physics that I am writing. It will explain why your son, if he wishes to learn mathematics, should use computer algebra programs as little as possible. And his professor should probably not be using Maple for this purpose, even though it is now the fashion. Just my curmudgeonly view on this matter. -- Julian V. Noble Professor Emeritus of Physics jvn@lessspamformother.virginia.edu ^^^^^^^^^^^^^^^^^^ http://galileo.phys.virginia.edu/~jvn/ Science knows only one commandment: contribute to science. -- Bertolt Brecht, Galileo. === Subject: Re: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions Has the calculus professor suggested that your son acquire Maple or any similar program? If not, the fact that your son is taking calculus is irrelevant, and if you insist on buying him software, why not ask him what he'd like. Maybe what he really needs is an MP3 player or some warm socks. I suggest you ask your son to meet with his academic advisor whether any software should be purchased. This also has the side effect of getting your son to talk to an academic advisor, something many students never get around to doing until they have stumbled around unnecessarily. Also, be aware that student versions of all these programs cost about 10% of the regular prices, and may even be available to students free. RJF > My second son is a freshman in college this semester and is a science > major taking Calculus. His prof is using Maple, a software package > about which I know very little. I am familiar with MathCad but not > Mathematica or Matlab. I understand with a TI connectivity kit you > can exchange information in MathCad, but can you do that with Maple, > MatLab, or Mathematica? (He has a TI-89.) I understand you can use > Maple in conjuntion with the other software packages. I'm trying to > decide what is the best software package to get him. My funds are > limited (typically, I know). === Subject: Re: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions > Finally, let me take the liberty of sending you via e-mail the Preface > of a book on mathematical methods of physics that I am writing. It will > explain why your son, if he wishes to learn mathematics, should use > computer algebra programs as little as possible. Could you explain why to this newsgroup? Because I'm convinced of the contrary, i.e. *if properly used* a computer algebra system is very useful to learn mathematic (I teach math myself). === Subject: Re: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions cms@vega.star-nets.net (SPAWN OF A JEWISH CARPENTER: CINDY SMITH) > My second son is a freshman in college this semester and is a science > major taking Calculus. His prof is using Maple, a software package > about which I know very little. I am familiar with MathCad but not > Mathematica or Matlab. I understand with a TI connectivity kit you > can exchange information in MathCad, but can you do that with Maple, > MatLab, or Mathematica? (He has a TI-89.) I understand you can use > Maple in conjuntion with the other software packages. I'm trying to > decide what is the best software package to get him. My funds are > limited (typically, I know). The TI-89 should be more than adequate for now. The TI-89 is often adequate even for advanced mathematics, but if he goes in for really advanced math later, he can get Mathematica or Matlab at that point. Also, it is *not* true (as far as I know) that you can exchange information with MathCad using the TI connectivity kit, although one could use my MathML converter to exchange information with PC programs that support MathML. -- Bhuvanesh === Subject: maple simplification question Hi all, I am rather new to Maple, I used to work with Derive a lot as I never had to deal with really complicated problems before. I am now dealing with a rather huge expression, one term of it (generated by Maple) is: (r/b)^k*r^(-k) which should equal (1/b)^k I tried many things but Maple does not simplify it that way which is nasty as this term appears a lot of times. Is there a command to simplify it? (I am using Maple 6/Windows) Any help is highly appreciated! Nils === Subject: Re: maple simplification question > Hi all, > I am rather new to Maple, I used to work with Derive a lot as I never > had to deal with really complicated problems before. > I am now dealing with a rather huge expression, one term of it > (generated by Maple) is: > (r/b)^k*r^(-k) > which should equal (1/b)^k Maple does not do this simplification because that would be wrong in some cases. For example: > subs({r=-1,b=-1,k=1/2}, (r/b)^k*r^(-k) = (1/b)^k); -I = I If you REALLY want Maple to do this, even if it could be wrong, you can use simplify symbolic: > simplify((r/b)^k*r^(-k),symbolic) A bit better would be to add some assumptions from your situation that will make it true: > simplify((r/b)^k*r^(-k)) assuming r>0, b>0; (-k) b > simplify((r/b)^k*r^(-k)) assuming k::integer; (-k) b -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: maple simplification question > Maple does not do this simplification because that would be wrong > in some cases. For example: > subs({r=-1,b=-1,k=1/2}, (r/b)^k*r^(-k) = (1/b)^k); > -I = I Hey, this is exactly the example I had in mind. ;-) > [...] > A bit better would be to add some assumptions from your situation that > will make it true: > simplify((r/b)^k*r^(-k)) assuming r>0, b>0; Note that 'assuming' was introduced in Maple 7. Users of older versions (like the original poster) will have to use the assume command. -- Thomas Richard Maple Support Scientific Computers GmbH http://www.scientific.de === Subject: Re: maple simplification question |>I am now dealing with a rather huge expression, one term of it |>(generated by Maple) is: |>(r/b)^k*r^(-k) |>which should equal (1/b)^k It should e.g. if k is an integer, or if r > 0 or b > 0. Not in general, e.g. try r=b=-1, k=1/2. |>I tried many things but Maple does not simplify it that way which is |>nasty as this term appears a lot of times. |>Is there a command to simplify it? |>(I am using Maple 6/Windows) > expr:= (r/b)^k*r^(-k): > assume(k,integer); simplify(expr); (-k~) b 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: maple simplification question > Maple does not do this simplification because that would be wrong > in some cases. For example: >>subs({r=-1,b=-1,k=1/2}, (r/b)^k*r^(-k) = (1/b)^k); > -I = I Oh. I did not see that... > A bit better would be to add some assumptions from your situation that > will make it true: >>simplify((r/b)^k*r^(-k)) assuming r>0, b>0; Fine, that is my case :-) Nils === Subject: residue in MAPLE Hi: Does anyone know how to convince MAPLE (version 6) to properly calculate the residue of a gamma function at a general negative integer? The following shows that it knows where the singularities are, but doesn't get the residue correctly. Neither will series(a,s=k) give the correct result. Of course residue(a,s=6); works correctly for any specific integer. So does 1/sin(pi*s) as shown below. Mike > restart;assume (k,posint); > b:=z^s/(s-k); > c:=1/sin(Pi*s); s s z b := ------ s - k~ 1 c := --------- sin(Pi s) > residue(a,s=k);residue(b,s=k);residue(c,s=k); 0 k~ z 1 --------- k~ Pi (-1) > singular(a,s);singular(b,s);singular(c,s); {s = -infinity}, {s = _N1~ - 1} {s = k~} {s = _Z1} === Subject: Re: residue in MAPLE |>Does anyone know how to convince MAPLE (version 6) to properly calculate |>the residue of a gamma function |>at a general negative integer? |>The following shows that it knows where the singularities are, but |>doesn't get the residue correctly. |>Neither will series(a,s=k) give the correct result. |>Of course residue(a,s=6); works correctly for any specific integer. |>> restart;assume (k,posint); ... |>> residue(a,s=k); Maple 8 and 9, btw, return unevaluated here, and have a division by zero if you use series. A work-around is to use the identity residue(ap,s=k); k~ k~ (-1) z - ------------ 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: saving 'worksheets' | MuPAD Light or Maxima Following from an earlier posting concerning 'free' symbolic maths packages, I'm still 'testing' MuPAD, and Maxima. Both have pros and cons (based on testing so far), but one thing that has me stumped is how to save 'worksheet's in either application, if at all possible (I know MuPAD Pro has a 'notebook' feature', but the free academic licensing only covers MuPAD Light). My students will be working with fairly long expressions, and it would be nice (translation: they won't hate me) if there is a way for them to store 'worksheets' such that when they want to re-start work on the project, they can simply open up the worksheet, and continue from where they left off (I'm referring to said file as a 'worksheet', reflecting my experiences with MAPLE). Is there any way to do this (or something analogous) in either MuPAD Light, or Maxima? I've read through the documentation as much as I can find, and most of the things I've tried using 'files' or 'fread' or various commands like same have failed miserably. couldn't find anything obvious. === Subject: Re: saving 'worksheets' | MuPAD Light or Maxima > Following from an earlier posting concerning 'free' symbolic maths packages, I'm > still 'testing' MuPAD, and Maxima. Both have pros and cons (based on testing so > far), but one thing that has me stumped is how to save 'worksheet's in either > application, if at all possible (I know MuPAD Pro has a 'notebook' feature', but > the free academic licensing only covers MuPAD Light). > My students will be working with fairly long expressions, and it would be nice > (translation: they won't hate me) if there is a way for them to store > 'worksheets' such that when they want to re-start work on the project, they can > simply open up the worksheet, and continue from where they left off (I'm > referring to said file as a 'worksheet', reflecting my experiences with MAPLE). > Is there any way to do this (or something analogous) in either MuPAD Light, or > Maxima? I've read through the documentation as much as I can find, and most of > the things I've tried using 'files' or 'fread' or various commands like same > have failed miserably. > couldn't find anything obvious. The best way I know to save worksheet under mupad is to save it as a text file. Then the Unix or cygwin command that keeps only the questions from the whole text session saved in the file MuPAD-last-session looks like awk 'BEGIN {FS =>> } ; { if (NF==2) { print $2 } }' MuPAD-last-session > session_`date +%d_%B_%Y_%Hh%M`.mu If you are searching for a free clone of maple, I would however recommend you to test my own GPL software giac/xcas, it has an interface that can save worksheets, and for simple scripts you can even import and run maple worksheets. More info at http://www-fourier.ujf-grenoble.fr/~parisse/giac.html N.B.: giac/xcas is a work in progress, there are certainly some bugs here and there, and the windows binaries are a little bit old (they will be updated at the beginning of September so that Windows user will benefit from a more user-friendly history). === Subject: Re: saving 'worksheets' | MuPAD Light or Maxima Personally I use emacs + maxima-mode, which I find a lot more convenient than worksheets .88 la Mathematica or Maple. However, I'm not sure whether this is an option (although it is certainly free and I recommend emacs anyway, since LaTeX is also very good to type in emacs. Also, there are interfaces for many, if not all CAS to emacs, so at least one has to know only one editor) A second option is texmacs, but I don't know anything about it, so I have to refer you to the maxima mailing list maxima@www.math.utexas.edu. A third possibility is to use save(filename,all); to save *everything* you did (including values - warning, might result in a big file) and to use load(filename); to restore it. However, it appears to be slightly broken currently. I asked already on the mailing list, whether a fix exists already - but in fact, I think it is not worth it. All the best Martin === Subject: Re: saving 'worksheets' | MuPAD Light or Maxima Here is the workaround: (due to Wolfgang Jenkner) A third possibility is to use load(nusum.mac); /* to workaround a bug */ save(filename,all); to save *everything* you did (including values - warning, might result in a big file) and to use load(filename); Martin Sample session: rubey$ maxima GCL (GNU Common Lisp) Version(2.5.0) Sun Nov 17 15:58:09 CET 2002 Licensed under GNU Library General Public License Contains Enhancements by W. Schelter Maxima 5.9.0rc3 http://maxima.sourceforge.net Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. This is a development version of Maxima. The function bug_report() provides bug reporting information. (C1) 2+2; (D1) 4 (C2) x:2; (D2) 2 (C3) load(nusum.mac); (D3) /usr/labri/rubey/share/maxima/5.9.0rc3/share/algebra/nusum.mac (C4) save(tmp,all); (D4) tmp (C5) quit(); rubey$ maxima GCL (GNU Common Lisp) Version(2.5.0) Sun Nov 17 15:58:09 CET 2002 Licensed under GNU Library General Public License Contains Enhancements by W. Schelter Maxima 5.9.0rc3 http://maxima.sourceforge.net Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. This is a development version of Maxima. The function bug_report() provides bug reporting information. (C1) load(tmp); (D4) tmp (C5) x; (D5) 2 (C6) c1; (D6) 4 === Subject: Re: saving 'worksheets' | MuPAD Light or Maxima You shouldn't have to save all, if you don't want to. You should be able to say save (filename, values, functions) and not save the labels, for example. or just specific items like save(filename,part1, x,w,result3); This save/load all is supposed to restore what you had in memory at the time of the save. This is perhaps not quite like restoring a worksheet, but if you type playback(); I think you will see all the previous inputs and outputs. The model in maxima (without a front end) is that you have in front of you a roll of paper on which you and the computer take turns typing. This part of the system was designed in 1968. RJF > Here is the workaround: (due to Wolfgang Jenkner) > A third possibility is to use > load(nusum.mac); /* to workaround a bug */ > save(filename,all); > to save *everything* you did (including values - warning, might result in a big > file) > and to use > load(filename); > Martin > Sample session: > rubey$ maxima > GCL (GNU Common Lisp) Version(2.5.0) Sun Nov 17 15:58:09 CET 2002 > Licensed under GNU Library General Public License > Contains Enhancements by W. Schelter > Maxima 5.9.0rc3 http://maxima.sourceforge.net > Distributed under the GNU Public License. See the file COPYING. > Dedicated to the memory of William Schelter. > This is a development version of Maxima. The function bug_report() > provides bug reporting information. > (C1) 2+2; > (D1) 4 > (C2) x:2; > (D2) 2 > (C3) load(nusum.mac); > (D3) /usr/labri/rubey/share/maxima/5.9.0rc3/share/algebra/nusum.mac > (C4) save(tmp,all); > (D4) tmp > (C5) quit(); > rubey$ maxima > GCL (GNU Common Lisp) Version(2.5.0) Sun Nov 17 15:58:09 CET 2002 > Licensed under GNU Library General Public License > Contains Enhancements by W. Schelter > Maxima 5.9.0rc3 http://maxima.sourceforge.net > Distributed under the GNU Public License. See the file COPYING. > Dedicated to the memory of William Schelter. > This is a development version of Maxima. The function bug_report() > provides bug reporting information. > (C1) load(tmp); > (D4) tmp > (C5) x; > (D5) 2 > (C6) c1; > (D6) 4 === Subject: Re: saving 'worksheets' | MuPAD Light or Maxima > My students will be working with fairly long expressions, and it would be nice > (translation: they won't hate me) if there is a way for them to store > 'worksheets' such that when they want to re-start work on the project, they can > simply open up the worksheet, and continue from where they left off (I'm In MuPAD, try write(save.mb) and later read(save.mb) -- +--+ +--+| |+-|+ Christopher Creutzig (ccr@mupad.de) +--+ Tel.: 05251-60-5525 === Subject: Re: saving 'worksheets' | MuPAD Light or Maxima > awk 'BEGIN {FS =>> } ; { if (NF==2) { print $2 } }' > MuPAD-last-session > session_`date +%d_%B_%Y_%Hh%M`.mu Note that this will loose all continuation lines, as in >> a+ &> b a + b I'd recommend perl -ne 'print if s/^(>> |&> )//;' MuPAD-last-session > session_`date +%d_%B_%Y_%Hh%M`.mu (untested) -- +--+ +--+| |+-|+ Christopher Creutzig (ccr@mupad.de) +--+ Tel.: 05251-60-5525 === Subject: substitution for negative constants in CAS what do you expect from substituting A for 1/2 in the expression below? sqrt(x+1/2) + 1/sqrt(x-1/2) Macsyma gives (x+a)^a +1/(x-a)^a Mathematica 4.1 gives 1/Sqrt[-1/2+x] +(a+x)^a Maple 7 gives 2*1/(sqrt(4*x-2))+(4*x+2)^a*a What does your favorite system do, and do you think it is correct? I think that Macsyma gets this one right, but maybe you disagree. (Arguably one could return other forms, since 2*a=1, and you can multiply by 1 all over the place.) RJF === Subject: Re: substitution for negative constants in CAS >what do you expect from > substituting A for 1/2 in the expression below? > sqrt(x+1/2) + 1/sqrt(x-1/2) >Maple 7 gives >2*1/(sqrt(4*x-2))+(4*x+2)^a*a (4*x+2)^a*a+2/(4*x-2)^(1/2) Maple stores the expression sqrt(x+1/2) + 1/sqrt(x-1/2) as (1/2)*(4*x+2)^(1/2)+2*(4*x-2)^(-1/2), since sqrt does some simplification. subs does a syntactic substitution: only operands that are literally 1/2 will be substituted. So in the 1/2*(4*x+2)^(1/2) there are two occurrences of 1/2, but in 2*(4*x-2)^(-1/2) there are none. 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: substitution for negative constants in CAS > what do you expect from > substituting A for 1/2 in the expression below? > sqrt(x+1/2) + 1/sqrt(x-1/2) Personally, I'd hope for Macsyma's answer. MuPAD currently returns >> subs(sqrt(x+1/2) + 1/sqrt(x-1/2), 1/2=A) A 1 (A + x) + ------------ 1/2 (x - 1/2) Just for output purposes, you can define an alias, which works better than subs: >> alias(a=1/2) >> sqrt(x+1/2) + 1/sqrt(x-1/2) 1 a -------- + (x + a) a (x - a) > What does your favorite system do, and do you think > it is correct? In a technical sense, MuPAD's answer is correct. I think I would prefer a different type of correctness, though. I'll have to think about this. > (Arguably one could return other forms, since 2*a=1, and > you can multiply by 1 all over the place.) Substituting 1/2 by a in 2*x should, in my opinion, not return x/a ... -- +--+ +--+| |+-|+ Christopher Creutzig (ccr@mupad.de) +--+ Tel.: 05251-60-5525 === Subject: Re: Symbolic calculus component May I suggest you try SymbMath.com? 17.5. Interface with Other Software You can run SymbMath from another software as a engine. Another software sends a text file to SymbMath, then run SymbMath in background, get result back from SymbMath. Please read its document for details. www.SymbMath.com > I'm looking for a symbolic calculus component for Windows development - i.e. > an ActiveX or a .net DLL that has somewhat like such a method (I call it > DoIt): > - DoIt(integrate(x,x)) returns a x^2/2 string > - DoIt(factor(x^2+2x+1)) returns a (x+1)^2 string > and so on. > I mean, the engine of programs such as Derive (or xMaxima) without > graphical interface. > Does such a thing exsist?