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  • Mathematica 8 crashes Ubuntu 13.10

    - by Georgy Ivanov
    I have Mathematica 8 installed on my Ubuntu laptop since 2011. I updated Ubuntu several times, and experienced no problems with Mathematica. It also worked smoothly after I updated Ubuntu to 13.10 (it worked for sure for a week after update). When I tried to start Mathematica today by executing a .sh-file, the screen went black, I was logged out from the session and thrown back to the login screen. Typing mathematica in the terminal produced the same effect. Typing mathematica -cleanstart or mathematica -mesa did not help. Starting Gnome session with or without effects did not help Launching mathematica under another user account did not help. I still can run text-only version of mathematica by typing math in the terminal. I don't remember making any changes to my configuration except for installing updates. Is there any quick way to fix this behavior? How can I know which component exactly crashed? Where should I look for crash logs?

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  • What is in your Mathematica tool bag?

    - by Timo
    We all know that Mathematica is great, but it also often lacks critical functionality. What kind of external packages / tools / resources do you use with Mathematica? I'll edit (and invite anyone else to do so too) this main post to include resources which are focused on general applicability in scientific research and which as many people as possible will find useful. Feel free to contribute anything, even small code snippets (as I did below for a timing routine). Also, undocumented and useful features in Mathematica 7 and beyond you found yourself, or dug up from some paper/site are most welcome. Please include a short description or comment on why something is great or what utility it provides. If you link to books on Amazon with affiliate links please mention it, e.g., by putting your name after the link. Packages: LevelScheme is a package that greatly expands Mathematica's capability to produce good looking plots. I use it if not for anything else then for the much, much improved control over frame/axes ticks. David Park's Presentation Package ($50 - no charge for updates) Tools: MASH is Daniel Reeves's excellent perl script essentially providing scripting support for Mathematica 7. (This is finally built in as of Mathematica 8 with the -script option.) Resources: Wolfram's own repository MathSource has a lot of useful if narrow notebooks for various applications. Also check out the other sections such as Current Documentation, Courseware for lectures, and Demos for, well, demos. Books: Mathematica programming: an advanced introduction by Leonid Shifrin (web, pdf) is a must read if you want to do anything more than For loops in Mathematica. Quantum Methods with Mathematica by James F. Feagin (amazon) The Mathematica Book by Stephen Wolfram (amazon) (web) Schaum's Outline (amazon) Mathematica in Action by Stan Wagon (amazon) - 600 pages of neat examples and goes up to Mathematica version 7. Visualization techniques are especially good, you can see some of them on the author's Demonstrations Page. Mathematica Programming Fundamentals by Richard Gaylord (pdf) - A good concise introduction to most of what you need to know about Mathematica programming. Undocumented (or scarcely documented) Features: How to customize Mathematica keyboard shortcuts. See this question. How to inspect patterns and functions used by Mathematica's own functions. See this answer How to achieve Consistent size for GraphPlots in Mathematica? See this question.

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  • Debugging a working program on Mathematica 5 with Mathematica 7

    - by Neuschwanstein
    Hi everybody, I'm currently reading the Mathematica Guidebooks for Programming and I was trying to work out one of the very first program of the book. Basically, when I run the following program: Plot3D[{Re[Exp[1/(x + I y)]]}, {x, -0.02, 0.022}, {y, -0.04, 0.042}, PlotRange -> {-1, 8}, PlotPoints -> 120, Mesh -> False, ColorFunction -> Function[{x1, x2, x3}, Hue[Arg[Exp[1/(x1 + I x2)]]]]] either I get a 1/0 error and e^\infinity error or, if I lower the PlotPoints options to, say, 60, an overflow error. I have a working output though, but it's not what it's supposed to be. The hue seems to be diffusing off the left corner whereas it should be diffusing of the origin (as can be seen on the original output) Here is the original program which apparently runs on Mathematica 5 (Trott, Mathematica Guidebook for Programming): Off[Plot3D::gval]; Plot3D[{Re[Exp[1/(x + I y)]], Hue[Arg[Exp[1/(x + I y)]]]}, {x, -0.02, 0.022}, {y, -0.04, 0.042}, PlotRange -> {-1, 8}, PlotPoints -> 120, Mesh -> False] Off[Plot3D::gval]; However, ColorFunction used this way (first Plot3D argument) doesn't work and so I tried to simply adapt to its new way of using it. Well, thanks I guess!

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  • Keyboard shortcut to Un/Comment out code in Mathematica 7?

    - by dbjohn
    A keyboard shortcut to comment/uncomment out a piece of code is common in other programming IDE's for languages like Java, .Net. I find it a very useful technique when experimenting through trial and error to temporarily comment out and uncomment lines, words and parts of the code to find out what is and isn't working. I cannot find any such keyboard shortcut on the Mathematica front end in version 7. I know that it is possible to comment out code by selecting the code, right mouse click and select Un/Comment from the menu that appears but this is too slow while coding. I tried to access this using the menu key Menu on the keyboard but Mathematica frontend doesn't respond to or recognise this key unlike other applications, this could have allowed a key combination for commenting. Can someone else verify that this isn't unique to my machine and that the key isn't recognised by mathematica. I looked at this question and looked in the KeyEventTranslations.tr file but I don't think there is any way to create a shortcut to do this(?). Should I just live with it? Any other suggestions? (I have seen there is an Emacs version of mathematica, I have never tried Emacs or this Mma version and imagine that it would have this ability but would prefer not to go to the trouble and uncertainty of installing it. Also I would guess that the Wolfram Workbench could do this, but that may not be worth the investment just for this.)

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  • Running Mathematica-5 remotely

    - by oxinabox.ucc.asn.au
    I have Mathematica 5 - a powerful CAS. I have a cheap netbook (running Windows XP), wich not only is too slow to run mathmatica on, I doubt it has the harddrive space. I do however have remote access to a number of very powerful computers, (most of wich run variose Linuxes, but one of which is Windows Server 2008, though I'ld rather not use this one*). Mostly over SSH but other protocols can be arraged for some, I'm sure. So I'ld like to install Mathematica onto one of these machine and then run it remotely. Either from the command line via Putty or via some other method. I glanced through the mathematical documentation and read something about using some MathLink program, which links the front end installed on my computer to a remote kernel. Anyone have any experience with this? I'm not sure if this belongs here or in SuperUser. At the moment, it's being tinkered with, and when the tinkering stops it'll likely be used to run multiple thin terms. As compared to the Linux machines: I have access to a dual 2.4 Xeon with 3GB RAM, which the rest of the world seems to have completely forgotten about (runs freeBSD!).

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  • Mathematica Programming Language–An Introduction

    - by JoshReuben
    The Mathematica http://www.wolfram.com/mathematica/ programming model consists of a kernel computation engine (or grid of such engines) and a front-end of notebook instances that communicate with the kernel throughout a session. The programming model of Mathematica is incredibly rich & powerful – besides numeric calculations, it supports symbols (eg Pi, I, E) and control flow logic.   obviously I could use this as a simple calculator: 5 * 10 --> 50 but this language is much more than that!   for example, I could use control flow logic & setup a simple infinite loop: x=1; While [x>0, x=x,x+1] Different brackets have different purposes: square brackets for function arguments:  Cos[x] round brackets for grouping: (1+2)*3 curly brackets for lists: {1,2,3,4} The power of Mathematica (as opposed to say Matlab) is that it gives exact symbolic answers instead of a rounded numeric approximation (unless you request it):   Mathematica lets you define scoped variables (symbols): a=1; b=2; c=a+b --> 5 these variables can contain symbolic values – you can think of these as partially computed functions:   use Clear[x] or Remove[x] to zero or dereference a variable.   To compute a numerical approximation to n significant digits (default n=6), use N[x,n] or the //N prefix: Pi //N -->3.14159 N[Pi,50] --> 3.1415926535897932384626433832795028841971693993751 The kernel uses % to reference the lastcalculation result, %% the 2nd last, %%% the 3rd last etc –> clearer statements: eg instead of: Sqrt[Pi+Sqrt[Sqrt[Pi+Sqrt[Pi]]] do: Sqrt[Pi]; Sqrt[Pi+%]; Sqrt[Pi+%] The help system supports wildcards, so I can search for functions like so: ?Inv* Mathematica supports some very powerful programming constructs and a rich function library that allow you to do things that you would have to write allot of code for in a language like C++.   the Factor function – factorization: Factor[x^3 – 6*x^2 +11x – 6] --> (-3+x) (-2+x) (-1+x)   the Solve function – find the roots of an equation: Solve[x^3 – 2x + 1 == 0] -->   the Expand function – express (1+x)^10 in polynomial form: Expand[(1+x)^10] --> 1+10x+45x^2+120x^3+210x^4+252x^5+210x^6+120x^7+45x^8+10x^9+x^10 the Prime function – what is the 1000th prime? Prime[1000] -->7919 Mathematica also has some powerful graphics capabilities:   the Plot function – plot the graph of y=Sin x in a single period: Plot[Sin[x], {x,0,2*Pi}] you can also plot 3D surfaces of functions using Plot3D function

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  • Lexical and dynamic scoping in Mathematica: Local variables with Module, With, and Block

    - by dreeves
    The following code returns 14 as you'd expect: Block[{expr}, expr = 2 z; f[z_] = expr; f[7]] But if you change that Block to a Module then it returns 2*z. It seems to not matter what other variables besides expr you localize. I thought I understood Module, Block, and With in Mathematica but I can't explain the difference in behavior between Module and Block in this example. Related resources: Tutorial on Modularity and the Naming of Things from the Mathematica documentation Excerpt from a book by Paul R. Wellin, Richard J. Gaylord, and Samuel N. Kamin Explanation from Dave Withoff on the Mathematica newsgroup

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  • How to make external Mathematica functions interruptible?

    - by Szabolcs
    I had an earlier question about integrating Mathematica with functions written in C++. This is a follow-up question: If the computation takes too long I'd like to be able to abort it using Evaluation Abort Evaluation. Which of the technologies suggested in the answers make it possible to have an interruptible C-based extension function? How can "interruptibility" be implemented on the C side? I need to make my function interruptible in a way which will corrupt neither it, nor the Mathematica kernel (i.e. it should be possible to call the function again from Mathematica after it has been interrupted)

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  • Sprintf equivalent in Mathematica?

    - by jxy
    I don't know why Wikipedia lists Mathematica as a programming language with printf. I just couldn't find the equivalent in Mathematica. My specific task is to process a list of data files with padded numbers, which I used to do it in bash with fn=$(printf "filename_%05d" $n) The closest function I found in Mathematica is PaddedForm. And after some trial and error, I got it with "filename_" <> PaddedForm[ Round@#, 4, NumberPadding -> {"0", ""} ]& It is very odd that I have to use the number 4 to get the result similar to what I get from "%05d". I don't understand this behavior at all. Can someone explain it to me? And is it the best way to achieve what I used to in bash?

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  • Mathematica & J/Link: Memory Constraints?

    - by D-Bug
    I am doing a computing-intensive benchmark using Mathematica and its J/Link Java interface. The benchmark grinds to a halt if a memory footprint of about 320 MB is reached, since this seems to be the limit and the garbage collector needs more and more time and will eventually fail. The Mathematica function ReinstallJava takes the argument command line. I tried to do ReinstallJava[CommandLine -> "java -Xmx2000m ..."] but Mathematica seems to ignore the -Xmx option completely. How can I set the -Xmx memory option for my java program? Where does the limit of 320 MB come from? Any help would be greatly appreciated.

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  • how to write the code for this program specially in mathematica? [closed]

    - by asd
    I implemented a solution to the problem below in Mathematica, but it takes a very long time (hours) to compute f of kis or the set B for large numbers. Somebody suggested that implementing this in C++ resulted in a solution in less than 10 minutes. Would C++ be a good language to learn to solve these problems, or can my Mathematica code be improved to fix the performance issues? I don't know anything about C or C++ and it should be difficult to start to learn this languages. I prefer to improve or write new code in mathematica. Problem Description Let $f$ be an arithmetic function and A={k1,k2,...,kn} are integers in increasing order. Now I want to start with k1 and compare f(ki) with f(k1). If f(ki)f(k1), put ki as k1. Now start with ki, and compare f(kj) with f(ki), for ji. If f(kj)f(ki), put kj as ki, and repeat this procedure. At the end we will have a sub sequence B={L1,...,Lm} of A by this property: f(L(i+1))f(L(i)), for any 1<=i<=m-1 For example, let f is the divisor function of integers. Here I put some part of my code and this is just a sample and the question in my program could be more larger than these: «««««««««««««««««««««««««««««««««««« f[n_] := DivisorSigma[0, n]; g[n_] := Product[Prime[i], {i, 1, PrimePi[n]}]; k1 = g[67757] g[353] g[59] g[19] g[11] g[7] g[5]^2 6^3 2^7; k2 = g[67757] g[353] g[59] g[19] g[11] g[7] g[5] 6^5 2^7; k3 = g[67757] g[359] g[53] g[19] g[11] g[7] g[5] 6^4 2^7; k4 = g[67759] g[349] g[53] g[19] g[11] g[7] g[5] 6^5 2^6; k5 = g[67757] g[359] g[53] g[19] g[11] g[7] g[5] 6^4 2^8; k6 = g[67759] g[349] g[53] g[19] g[11] g[7] g[5]^2 6^3 2^7; k7 = g[67757] g[359] g[53] g[19] g[11] g[7] g[5] 6^5 2^6; k8 = g[67757] g[359] g[53] g[19] g[11] g[7] g[5] 6^4 2^9; k9 = g[67757] g[359] g[53] g[19] g[11] g[7] g[5]^2 6^3 2^7; k10 = g[67757] g[359] g[53] g[19] g[11] g[7] g[5] 6^5 2^7; k11 = g[67759] g[349] g[53] g[19] g[11] g[7] g[5]^2 6^4 2^6; k12 = g[67757] g[359] g[53] g[19] g[11] g[7] g[5]^2 6^3 2^8; k13 = g[67757] g[359] g[53] g[19] g[11] g[7] g[5]^2 6^4 2^6; k14 = g[67757] g[359] g[53] g[19] g[11] g[7] g[5]^2 6^3 2^9; k15 = g[67757] g[359] g[53] g[19] g[11] g[7] g[5]^2 6^4 2^7; k16 = g[67757] g[359] g[53] g[23] g[11] g[7] g[5] 6^4 2^8; k17 = g[67757] g[359] g[59] g[19] g[11] g[7] g[5] 6^4 2^7; k18 = g[67757] g[359] g[53] g[23] g[11] g[7] g[5] 6^4 2^9; k19 = g[67759] g[353] g[53] g[19] g[11] g[7] g[5] 6^4 2^6; k20 = g[67763] g[347] g[53] g[19] g[11] g[7] g[5] 6^4 2^7; k = Table[k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, k18, k19, k20]; i = 1; count = 0; For[j = i, j <= 20, j++, If[f[k[[j]]] - f[k[[i]]] > 0, i = j; Print["k",i]; count = count + 1]]; Print["count= ", count] ««««««««««««««««««««««««««««««««««««

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  • Closest to “Mathematica Graphics[]" drawing environment for Python

    - by 500
    Being only familiar with Mathematica and its Graphics, I have now to learn to draw Graphics using Python for a server. Mostly conditional combination of simple shape. What would be a package for Python that make drawing Graphics as close as possible as the Mathematica Graphics environment ? For Example, I would need to do such thing as in : http://mathematica.stackexchange.com/questions/1010/2d-gaussian-distribution-of-squares-coordinates#comment2475_1010

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  • Mathematica equivalent of Ruby's inject

    - by Ben Alpert
    Is there a Mathematica function like inject in Ruby? For example, if I want the product of the elements in a list, in Ruby I can write: list.inject(1) { |prod,el| prod * el } I found I can just use Product in Mathematica: Apply[Product, list] However, this isn't general enough for me (like, if I don't just want the product or sum of the numbers). What's the closest equivalent to inject?

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  • Using Mathematica to generate crystal lattices

    - by lavabo
    How do you generate a 3x3x3 lattice in Mathematica? Is it possible to color some of the lattice points? It seems that it is possible but I cannot get it to work so far http://reference.wolfram.com/mathematica/ref/LatticeData.html What I mean by 3x3x3 is something like figure (c) on the right:http://physics.ucsd.edu/was-sdphul/labs/2dl/exp6/exp63.gif

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  • Mathematica regular expressions on unicode strings.

    - by dreeves
    This was a fascinating debugging experience. Can you spot the difference between the following two lines? StringReplace["–", RegularExpression@"[\\s\\S]" -> "abc"] StringReplace["-", RegularExpression@"[\\s\\S]" -> "abc"] They do very different things when you evaluate them. It turns out it's because the string being replaced in the first line consists of a unicode en dash, as opposed to a plain old ascii dash in the second line. In the case of the unicode string, the regular expression doesn't match. I meant the regex "[\s\S]" to mean "match any character (including newline)" but Mathematica apparently treats it as "match any ascii character". How can I fix the regular expression so the first line above evaluates the same as the second? Alternatively, is there an asciify filter I can apply to the strings first? PS: The Mathematica documentation says that its string pattern matching is built on top of the Perl-Compatible Regular Expressions library (http://pcre.org) so the problem I'm having may not be specific to Mathematica.

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  • Targeted Simplify in Mathematica

    - by Timo
    I generate very long and complex analytic expressions of the general form: (...something not so complex...)(...ditto...)(...ditto...)...lots... When I try to use Simplify, Mathematica grinds to a halt, I am assuming due to the fact that it tries to expand the brackets and or simplify across different brackets. The brackets, while containing long expressions, are easily simplified by Mathematica on their own. Is there some way I can limit the scope of Simplify to a single bracket at a time? Edit: Some additional info and progress. So using the advice from you guys I have now started using something in the vein of In[1]:= trouble = Log[(x + I y) (x - I y) + Sqrt[(a + I b) (a - I b)]]; In[2]:= Replace[trouble, form_ /; (Head[form] == Times) :> Simplify[form],{3}] Out[2]= Log[Sqrt[a^2 + b^2] + (x - I y) (x + I y)] Changing Times to an appropriate head like Plus or Power makes it possible to target the simplification quite accurately. The problem / question that remains, though, is the following: Simplify will still descend deeper than the level specified to Replace, e.g. In[3]:= Replace[trouble, form_ /; (Head[form] == Plus) :> Simplify[form], {1}] Out[3]= Log[Sqrt[a^2 + b^2] + x^2 + y^2] simplifies the square root as well. My plan was to iteratively use Replace from the bottom up one level at a time, but this clearly will result in vast amount of repeated work by Simplify and ultimately result in the exact same bogging down of Mathematica I experienced in the outset. Is there a way to restrict Simplify to a certain level(s)? I realize that this sort of restriction may not produce optimal results, but the idea here is getting something that is "good enough".

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  • Performance difference between functions and pattern matching in Mathematica

    - by Samsdram
    So Mathematica is different from other dialects of lisp because it blurs the lines between functions and macros. In Mathematica if a user wanted to write a mathematical function they would likely use pattern matching like f[x_]:= x*x instead of f=Function[{x},x*x] though both would return the same result when called with f[x]. My understanding is that the first approach is something equivalent to a lisp macro and in my experience is favored because of the more concise syntax. So I have two questions, is there a performance difference between executing functions versus the pattern matching/macro approach? Though part of me wouldn't be surprised if functions were actually transformed into some version of macros to allow features like Listable to be implemented. The reason I care about this question is because of the recent set of questions (1) (2) about trying to catch Mathematica errors in large programs. If most of the computations were defined in terms of Functions, it seems to me that keeping track of the order of evaluation and where the error originated would be easier than trying to catch the error after the input has been rewritten by the successive application of macros/patterns.

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  • How to reshape matrices in Mathematica

    - by speciousfool
    When manipulating matrices it is often convenient to change their shape. For instance, to turn an N x M sized matrix into a vector of length N X M. In MATLAB a reshape function exists: RESHAPE(X,M,N) returns the M-by-N matrix whose elements are taken columnwise from X. An error results if X does not have M*N elements. In the case of converting between a matrix and vector I can use the Mathematica function Flatten which takes advantage of Mathematica's nested list representation for matrices. As a quick example, suppose I have a matrix X: With Flatten[X] I can get the vector {1,2,3,...,16}. But what would be far more useful is something akin to applying Matlab's reshape(X,2,8) which would result in the following Matrix: This would allow creation of arbitrary matrices as long as the dimensions equal N*M. As far as I can tell, there isn't anything built in which makes me wonder if someone hasn't coded up a Reshape function of their own.

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  • Mathematica - Import CSV and process columns?

    - by Casey
    I have a CSV file that is formatted like: 0.0023709,8.5752e-007,4.847e-008 and I would like to import it into Mathematica and then have each column separated into a list so I can do some math on the selected column. I know I can import the data with: Import["data.csv"] then I can separate the columns with this: StringSplit[data[[1, 1]], ","] which gives: {"0.0023709", "8.5752e-007", "4.847e-008"} The problem now is that I don't know how to get the data into individual lists and also Mathematica does not accept scientific notation in the form 8.5e-007. Any help in how to break the data into columns and format the scientific notation would be great. Thanks in advance.

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  • Bug in Mathematica's Integrate with PrincipalValue->True

    - by Janus
    It seems that Mathematica's handling of principal value integrals fails on some corner cases. Consider these two expressions (which should give the same result): Integrate[UnitBox[x]/(x0 - x), {x, -Infinity, Infinity}, PrincipalValue -> True, Assumptions -> {x0 > 0}] /. x0 -> 1 // Simplify Integrate[UnitBox[x]/(x0 - x) /. x0 -> 1, {x, -Infinity, Infinity}, PrincipalValue -> True] In Mathematica 7.0.0 I get I Pi+Log[3] Log[3] Has this been fixed in later versions? Does anybody have an idea for a (more or less) general workaround?

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  • Version control of Mathematica notebooks

    - by Etaoin
    Mathematica notebooks are, of course, plaintext files -- it seems reasonable to expect that they should play nice with a version-control system (git in my case, although I doubt the specific system matters). But the fact is that any .nb file is full of cache information, timestamps, and other assorted metadata. Scads of it. Which means that limited version control is possible -- commits and rollbacks work fine. Merging, though, is a disaster. Mathematica won't open a file with merge markers in it, and a text editor is no way to go through a .nb file. Has anyone had any luck putting a notebook under version control? How?

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  • Initial conditions with a non-linear ODE in Mathematica

    - by buggy
    Hi, I'm trying to use Mathematica's NDSolve[] to compute a geodesic along a sphere using the coupled ODE: x" - (x" . x) x = 0 The problem is that I can only enter initial conditions for x(0) and x'(0) and the solver is happy with the solution where x" = 0. The problem is that my geodesic on the sphere has the initial condition that x"(0) = -x(0), which I have no idea how to tell mathematica. If I add this as a condition, it says I'm adding True to the list of conditions. Here is my code: s1 = NDSolve[{x1''[t] - (x1[t] * x1''[t] + x2[t] * x2''[t] + x3[t]*x3''[t]) * x1[t] == 0, x2''[t] - (x1[t] * x1''[t] + x2[t] * x2''[t] + x3[t]*x3''[t]) * x2[t] == 0, x3''[t] - (x1[t] * x1''[t] + x2[t] * x2''[t] + x3[t]*x3''[t]) * x3[t] == 0, x1[0] == 1, x2[0] == 0, x3[0] == 0, x1'[0] == 0, x2'[0] == 0, x3'[0] == 1} , { x1, x2, x3}, {t, -1, 1}][[1]] I would like to modify this so that the initial acceleration is not zero but -x(0). Thanks

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  • Wolfram Workbench and Mathematica Help System

    - by belisarius
    I find the Wolfram Workbench a nice environment for Mathematica development. However, as I program in Mathematica, I need to navigate the Help System very often. The Workbench provides a tooltip tool that shows a very basic help for the Mma functions (just the usage messages), and is not enough for my usual needs. So: Is there a way to bring up and navigate the whole Mma Help System from inside the Workbench? Alternative solutions are also welcome. Re-entering the function name in a notebook and pressing F1 is not :)

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  • output with "Private`" Content in Mathematica Package

    - by madalina
    Hello everyone, I am trying to solve the following implementation problem in Mathematica 7.0 for some days now and I do not understand exactly what is happening so I hope someone can give me some hints. I have 3 functions that I implemented in Mathematica in a source file with extension *.nb. They are working okay to all the examples. Now I want to put these functions into 3 different packages. So I created three different packages with extension .*m in which I put all the desired Mathematica function. An example in the "stereographic.m" package which contain the code: BeginPackage["stereographic`"] stereographic::usage="The package stereographic...." formEqs::usage="The function formEqs[complexBivPolyEqn..." makePoly::usage="The function makePoly[algebraicEqn] ..." getFixPolys::usage="The function..." milnorFibration::usage="The function..." Begin["Private`"] Share[]; formEqs[complex_,{m_,n_}]:=Block[{complexnew,complexnew1, realeq, imageq, expreal, expimag, polyrealF, polyimagF,s,t,u,v,a,b,c,epsilon,x,y,z}, complexnew:=complex/.{m->s+I*t,n->u+I*v}; complexnew1:=complexnew/.{s->(2 a epsilon)/(1+a^2+b^2+c^2),t->(2 b epsilon)/(1+a^2+b^2+c^2),u->(2 c epsilon)/(1+a^2+b^2+c^2),v->(- epsilon+a^2 epsilon+b^2 epsilon+c^2 epsilon)/(1+a^2+b^2+c^2)}; realeq:=ComplexExpand[Re[complexnew1]]; imageq:=ComplexExpand[Im[complexnew1]]; expreal:=makePoly[realeq]; expimag:=makePoly[imageq]; polyrealF:=expreal/.{a->x,b->y,c->z}; polyimagF:=expimag/.{a->x,b->y,c->z}; {polyrealF,polyimagF} ] End[] EndPackage[] Now to test the function I load the package Needs["stereographic`"] everything is okay. But when I test the function for example with formEqs[x^2-y^2,{x,y}] I get the following ouput: {Private`epsilon^2 + 2 Private`x^2 Private`epsilon^2 + Private`x^4 Private`epsilon^2 - 6 Private`y^2 Private`epsilon^2 + 2 Private`x^2 Private`y^2 Private`epsilon^2 + Private`y^4 Private`epsilon^2 - 6 Private`z^2 Private`epsilon^2 + 2 Private`x^2 Private`z^2 Private`epsilon^2 + 2 Private`y^2 Private`z^2 Private`epsilon^2 + Private`z^4 Private`epsilon^2, 8 Private`x Private`y Private`epsilon^2 + 4 Private`z Private`epsilon^2 - 4 Private`x^2 Private`z Private`epsilon^2 - 4 Private`y^2 Private`z Private`epsilon^2 - 4 Private`z^3 Private`epsilon^2} Of course I do not understand why Private` appears in front of any local variable which I returned in the final result. I would want not to have this Private` in the computed output. Any idea or better explanations which could indicate me why this happens? Thank you very much for your help. Best wishes, madalina

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  • Two strange efficiency problems in Mathematica

    - by Jess Riedel
    FIRST PROBLEM I have timed how long it takes to compute the following statements (where V[x] is a time-intensive function call): Alice = Table[V[i],{i,1,300},{1000}]; Bob = Table[Table[V[i],{i,1,300}],{1000}]^tr; Chris_pre = Table[V[i],{i,1,300}]; Chris = Table[Chris_pre,{1000}]^tr; Alice, Bob, and Chris are identical matricies computed 3 slightly different ways. I find that Chris is computed 1000 times faster than Alice and Bob. It is not surprising that Alice is computed 1000 times slower because, naively, the function V must be called 1000 more times than when Chris is computed. But it is very surprising that Bob is so slow, since he is computed identically to Chris except that Chris stores the intermediate step Chris_pre. Why does Bob evaluate so slowly? SECOND PROBLEM Suppose I want to compile a function in Mathematica of the form f(x)=x+y where "y" is a constant fixed at compile time (but which I prefer not to directly replace in the code with its numerical because I want to be able to easily change it). If y's actual value is y=7.3, and I define f1=Compile[{x},x+y] f2=Compile[{x},x+7.3] then f1 runs 50% slower than f2. How do I make Mathematica replace "y" with "7.3" when f1 is compiled, so that f1 runs as fast as f2? Many thanks!

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