What is Mathematica: Definition and 1000 Discussions

Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow symbolic computation, manipulating matrices, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in Mathematica.

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  1. K

    Mathematica Is Mathematica more incomplete than the other math solver software packages?

    I only have access to mathematica currently. Regarding specifically its power to solve integrals, is it more unable to solve integrals than others like Maple? If the answer is yes, then I will move to purchase Maple.
  2. Wi_N

    Solving a min max problem in 2 variables using Mathematica

    Drawing the graph in 3d you see endless "mountains and valleys" which logic tells me there will also be infinite max min points in 2d regardless of where you slice the graph. apparently this is wrong and there is a finite max/min points in R^2/2D. Please note this problem does not have a domain...
  3. JD_PM

    Mathematica Is Mathematica the best option to compute the eigenvalues?

    I am wondering what's the best option to compute the eigenvalues for such a determinant$$\begin{vmatrix} \sin \Big( n \frac{\omega}{v_1} \theta \Big) & \cos \Big( n \frac{\omega}{v_1} \theta \Big) & 0 & 0 \\ 0 & 0 & \sin \Big( n \frac{\omega}{v_2} (2 \pi - \theta) \Big) & \cos \Big( n...
  4. S

    A Calculating the Gravitational wave spectrum with Inflation as a source

    I am interested in knowing how to calculate the gravitational wave (GW) spectrum with inflation as a source, I have some background in inflation but I am not so familiar about calculating the GW spectrum. I am reading a paper (https://arxiv.org/abs/0804.3249) about it, however, a big part of it...
  5. C

    Mathematica Defining a piecewise function in Mathematica

    Hello everyone. I am trying to do a 2D Shannon interpolation, but I cannot use a sinc because later on this expression goes in an optimization software that doesn't recognize it. I have defined my own version of sinc as: sincC = Piecewise[{(Sin[Pi* #]/(Pi*(#))), # >= 1}, {1 - (#^2)/6 +...
  6. M

    Mathematica Plotting k^2 in Mathematica - Output Not 1?

    Can anyone confirm if the following in Mathematica gives an output that is not 1? I'm getting some sort of sinusoid, but I should get 1. k = 2; Plot[k^2 JacobiSN[t, k]^2 + JacobiDN[t, k]^2, {t, 0, 10}] Thanks!
  7. P

    What specs should I look for in a laptop

    After completing my sophomore year at college as a Physics major and I realized that the laptop I currently have is not able to keep up with the demand I put it under for school. The laptop I currently have has a <2 hour battery life and has been known to crap out (didn't know how else to...
  8. S

    Mathematica Solving 2-D partial integro-differential equation

    While reproducing a research paper, I came across the following equation, ∂f/∂t−(H(f)(∂f/∂x)=0 where [H(f)] is hilbert transform of 'f.' and f=f(x,t) and initial condition is f(x,0)=cos(x) and also has periodic boundary conditions given by F{H{f(x′,t)}}=i⋅sgn(k)F{f(x,t)}, where F(f(x,t) is...
  9. Ackbach

    Wolfram releases the free Wolfram Engine for Developers

    Wolfram made what I would call a gigantic move: they released the Wolfram Engine for Developers - for zero cost! The idea of the Engine is primarily that you can call and run Wolfram Langauge commands from lots of different sources. I am not the kind of person to automate Mathematica, although...
  10. M

    Quadratic eigenvalue problem and solution (solved in Mathematica)

    Hi PF! Given the quadratic eigenvalue problem ##Q(\lambda) \equiv (\lambda^2 M + \lambda D + K)\vec x = \vec 0## where ##K,D,M## are ##n\times n## matrices, ##\vec x## a ##1\times n## vector, the eigenvalues ##\lambda## must solve ##\det Q(\lambda)=0##. When computing this, I employ a...
  11. A

    Mathematica Calculating traces with FeynCalc

    Hello everybody! I need a little help with FeynCalc. I think the problem is really simple but I can't find how to fix it. I want to evaluate a trace coming from a Feynman diagram. Since the particles are all massless, I want to impose the condition on the momentum ##p^2=k^2=p'^2=0##. I've...
  12. Z

    Solve for x(t) and v(t) given a Force equation using Mathematica

    Homework Statement Homework Equations F= ma or F= md^2x/dt^2 The Attempt at a Solution I know that this second order differential is non linear. I attempted to solve the problem as -k/x^2 = md^2x/dt^2 but I'm getting trouble since it is a second order ODE and I haven't learned how to solve...
  13. F

    Mathematica Problem with line integrals in Mathematica

    Hello everyone. I am testing mathematica to work with some line integrals. I want to go from the point (0,0) to (2, 3) over a straight line. I do it with 3 different parametrizations. The problem is that each one offers me a different result. The original problem is a two dimensional gaussian...
  14. B

    Mathematica Equation of motion in Mathematica

    I have a question to a physical task in Mathematica. We have this equation of motion: For energy of masspoint there is the condition : I have to write a procedure that uses the law of the conservation of energy for the potential V(x) to calculate t(x_1) - t(x_0) when there are given two...
  15. dRic2

    MATLAB Compare MatLab vs Mathematica for CFD | Ric

    I know a little bit of MatLab (for example I can solve simple, well conditioned, systems of 1st and 2nd order ODE), but I know nothing about Mathematica. I don't know whether or not start to learn how to code in Mathematica or keep studying MatLab. For example, for CFD (computational fluid...
  16. A

    Solution: Plotting Mathematica Homework w/ Recursion Limit Error

    Homework Statement Homework Equations E= kq/r^2 * r-hat where q= +/-(1.6*10^-19) The Attempt at a Solution x= (1.6*10^-19)*x/(x^2+y^2+(z+1)^2)^(3/2) - (1.6*10^-19)*x/(x^2+y^2+(z-1)^2)^(3/2)y= (1.6*10^-19)*y/(x^2+y^2+(z+1)^2)^(3/2) - (1.6*10^-19)*y/(x^2+y^2+(z-1)^2)^(3/2) z=...
  17. A

    Using Mathematica to solve an ODE

    Homework Statement Homework Equations The Attempt at a Solution I used the NDSolve function from mathematic but its giving me problems. What is the correct way to enter the equation?[/B] soln = NDSolve[{y''[t] = (-9.8/5)*sin (t), y[0] = 20, y, {x, 0, 12}}]
  18. topsquark

    Mathematica Non-commutative multiplication in Mathematica

    Does anyone know if it's possible to tell Mathematica to do calculations with non-Abelian groups, such as the quaternions? For example, how do you tell it to do (3 + j)(4 - i)? I would like to extend this beyond quaternions so is there is a way to define arbitrary group definitions? Thanks! -Dan
  19. M

    Mathematica Why Does a Polar Plot of a Circle Only Show One Side of the Unit Circle?

    Why is it when I plot a circle from ##\theta \in [\pi/2,-\pi/2]## I get the right side of the unit circle: PolarPlot[1, {\[Theta], \[Pi]/2, -\[Pi]/2}] ? Shouldn't I get the left side?
  20. A

    DFT for Helium using Mathematica

    I'm trying to solve this problem with Mathematica. Im not a Mathematica expert, but my program works perfect when vhartree={0,0,..,0}. This is the program I wrote: Clear[u, poisson, vhartree] h = 10^(-2);(*step integration*) rmax = 20; rmin = 10^(-30); Z = 2; (*atomic number*) points =...
  21. M

    Mathematica Why does Mathematica frequently crash on Mac OS?

    Hi PF I have Mathematica 10.1.0.0 Student version running on mac OS High Sierra 10.13.5. Mathematica frequently crashes. Also, every time I minimize a sheet or "save selection as" it brings up a dark window that I either have to close, or if it doesn't let me close I have to quit the program...
  22. F

    MATLAB Translating from Mathematica to Matlab

    Hello everyone. I was wondering if someone could tell me how to write the next line of Mathematica code in Matlab. x = Sum [ Sqrt [ vals[ [ j ] ] ] * vecs [ [ j, All ] ] * z [ [ j ] ] , {j,1,10} vals is a eigenvalues vector, vecs is a eigenvector matrix and z is a vector of random variables...
  23. MidgetDwarf

    Anyone familiar with this Mathematica textbook?

    I am wondering if any PF member is familiar with this textbook on Mathematica. Mathematica by Example, Fifth Edition, by Martha L.L. Abell. The amazon link is https://www.amazon.com/dp/0128124814/?tag=pfamazon01-20 The course description: MATH 2110 with grade C or better. Introduction to...
  24. C

    Mathematica Efficiently Store Mathematica Output as Vector: A How-To Guide

    Hi. I want to store the output of Roots[LegendreP[3.0, x] == 0, x] as a vector. Can someone help me? Thanks
  25. M

    MATLAB Exporting Multiple Variables from Mathematica to MATLAB - Quick and Easy Guide

    Hi PF! I'm trying to export two matrices ##A## and ##B## from Mathematica into MATLAB. I can export one just fine; so far what I write is SetDirectory[NotebookDirectory[]] Export["data.mat", {A}] Do you know how I can export two variables at a time and then how I can export directly into...
  26. C

    Mathematica Cannot do the integral of the Hyper-geometric function?

    Dear friends: It's strange that Mathematica can do the integral of ##\int_0^\infty dx~x~_2F_1(a,b,c,1-x^2)##, however, fails when it's changed to ##\int_0^\infty dx~x~_2F_1(a,b,c,1-x-x^2)##. Are there any major differences between this two types? Is it possible to do the second kind of integral...
  27. M

    Mathematica Cannot Plot This Function in Mathematica

    Hi PF! I have the following in Mathematica. Notice h[2,x,0.5] gives me an output in terms of x, but when I try to plot this I get errors. Anyone know why this is? I read the error messages but am still unsure why I am not getting a clean output.
  28. M

    Mathematica Using While Loops in Mathematica for Iterative Computations

    Hi PF! I'm trying to compute $$\phi_n(x)=\pi x^2+\int_0^{\pi} 3(0.5 \sin (3x)-tx^2)\phi_{n-1}(t)\,dt$$ given ##\phi_0 = 0##. I'd like to iterate this computation until ##\sqrt{\int(\phi_{n+1}-\phi_n)^2}< 0.1##. I've never used the while loop in Mathematica, tried reading the documentation but...
  29. M

    Mathematica Real Part in Mathematica: How to Extract the Real Values from Fractions

    Hi PF! I have some variables that are all real, and I have a few ##i##s, all in a fraction. When I ask Mathematica to give me the real part of the entire fraction, ##Re[]##, it simply echoes my input, not giving me anything useful. Any help is greatly appreciated.
  30. M

    Mathematica Labeling Plots in Mathematica 10.1.0.0 Student Edition

    Hi PF! I am using an older version of Mathematica: 10.1.0.0, the student edition. I am trying to label plots within the Plot function using the command "PlotLegend ->" but when running, first I get a message that this is outdated, and when I suppress, I get a legend that does not work with the...
  31. L

    Linear Algebra - Find an orthogonal matrix P

    A problem that I have to solve for my Linear Algebra course is the following We are supposed to use Mathematica. What I have done is that I first checked that A is symmetric, i.e. that ##A = A^T##. Which is obvious. Next I computed the eigenvalues for A. The characteristic polynomial is...
  32. C

    Polynomial expansion from Python to Mathematica

    Hi everybody. In Python there is a library called chaospy. One useful command is cp.orth_ttr which generates a polynomial expansion, e. g. a series of orthogonal polynomials or orders zero, one, two... for a random variable e.g normal, uniform... For more information see...
  33. C

    Mathematica Is this a bug in Mathematica 11 ?

    I calculated a simple complex function integration using Mathematica 11. As the screenshot shows, the only difference between the two inputs is that I set a = 1 in the second one. However, the two outputs differ by a factor of 2. What's wrong? Is this a bug?
  34. Necmi

    Mathematica Solve Perturbation problem with mathematica

    u'(1-epsilon(u')^2)=-y uo(1)=0 u1(1)=0 I need solve this problem with mathematica.
  35. S

    Can Wolfram Mathematica be wrong on this Integration?

    Homework Statement Mathematica vs (Symbolab + my brain) Homework EquationsThe Attempt at a Solution I think this integral calculation in Mathematica is wrong. Open pictures below. Please help me. Graphs (the red one is under the blue and the green): https://ibb.co/bACa3G Wolfram Mathematica...
  36. J

    Mathematica Number of extensions with Free Trial of Mathematica

    I have just started a free trial with Mathematica. Does anyone know how many times one can request the extension of the free trial?
  37. C

    Analytic Continuation of DiLog in Mathematica

    I have obtained the Dilog function in some output and was just wondering if anyone knew how to interpret its meaning. The mathematica notes tell me that ##\text{DiLog}(x,\alpha)## gives the dilogarithm function, which for real ##x>1## evaluates on the side of the branch prescribed by...
  38. RicardoMP

    Mathematica How to append functions to a list of functions?

    My objective is to make a list of functions and afterwards be able to make operations with those functions. Hyfield[list_, bits_] := Module[{i, auxList, Hy}, auxList[a_] := List[]; For[i = 1, i <= bits*2, i++, auxList[a] = Append[auxList[a]...
  39. DeathbyGreen

    Mathematica Eigenvectors 4x4 Matrix in Mathematica

    Hi, I'm trying to calculate the eigenvectors of a 4x4 matrix, but I don't want the actual eigenvalues included in the solution, I simply want them listed as a variable. For example, I have the matrix: H_F = \left[ \begin{array}{cccc} \hbar\Omega&\hbar v_fk_- &0&0\\ \hbar...
  40. M

    Mathematica How can I optimize Mathematica computation time for functional definitions?

    Hi PF! I am using the following code in Mathematica mat = {{1, Cos[2], Cos[4], Sin[2], Sin[4}, {1, 1, 1, 0, 0}}; Li[x_] := Transpose[ NullSpace[ mat].{{1}, {Cos[x}, {Cos[ 2 x]}, {Sin[x]}, {Sin[2 x]}}]; Li1[x_] := Li[x].{{1}, {0}, {0}}; f[x_] :=...
  41. W

    Mathematica Is the integral for current correct?

    Hi, I am using Mathematica to calculate density of states and current of the Green's function times self energy in most simple form. I am not sure if I am getting current integral over energy implemented correctly. Shouldnt first current plot be a line with a slope? Below is my code...
  42. M

    Mathematica Mathematica Plot Real Portion (Contour Plot)

    Hi PF! In Mathematica and given the code below, I am trying to the real part of ##\sigma##, ##Re(\sigma)##, in stead of simply ##\sigma##. Any help would be awesome! Here's what I have: n = 3; ContourPlot[(\[Sigma]^2 - 2 (n - 1) (2 n + 1) \[Epsilon] \[Sigma] + (n - 1) n (n + 2)) ((...
  43. Pushoam

    Minkowski Diagram and Mathematica

    Homework Statement [/B]Homework Equations Mathematica The Attempt at a Solution I want to plot the diagram using Mathematica. I saw on the net there is some kind of programming needed for this. Do I need to learn programming for doing this? If yes, how to learn it?
  44. W

    Mathematica Add a rectangle to a plot to indicate range

    I have some data points that I want to plot and suppose I have the function ##f(x) = x##, with the domain having the range ##0\leq x \leq 10##. Assume that the experimental values lies in the range ##4\leq x \leq 7##, how can I put a rectangular region to cover this range behind my plot so as to...
  45. M

    A EoM in Schwarzschild geometry: geodesic v Hamilton formalism

    Hi there guys, Currently writing and comparing two separate Mathematica scripts which can be found here and also here. The first one I've slightly modified to suit my needs and the second one is meant to reproduce the same results. Both scripts are attempting to simulate the trajectory of a...
  46. hbz88

    Mathematica For looping problem not getting answer

    Hi, I need some helps. I try to run the code below but its keep give me the value of intial value. Q = 1415; \[Mu] = 1000; \[Sigma] = 500; double dx; double x; double fx; double fxplusdx; double I1; double I2; I1 = 0; I2 = 0; For[x = 0, x <= Q - dx, dx += 0.01, fx = PDF[NormalDistribution[0...
  47. Q

    Mathematica Mathematica: Convolution Integral

    Hi all! I'm new to Mathematica. I have written a code for performing a convolution integral (as follows) but it seems to be giving out error messages: My code is: a[x_?NumericQ] := PDF[NormalDistribution[40, 2], x] b[k_?NumericQ, x_?NumericQ] := 0.0026*Sin[1.27*k/x]^2 c[k_?NumericQ...
  48. A

    Mathematica Mathematica: Mapping a Four Color Rectangle to a Four Color Torus

    Hi, I was wondering if someone could help me understand the grid command in the following Mathematica code that transforms a rectangle to a torus like in this video below. My problem is I want the blue rectangle in the Mathematica code to look like the four color rectangle in the plot below...
  49. W

    Mathematica Rescaling equations in Mathematica

    Suppose I have a differential equation $$\ddot \phi + 3H (1+Q) \dot \phi + V_{,\phi} = 0$$ where ##\phi## is the inflaton field. ##H## is the Hubble parameter, ##Q## is just a number, ##V_{,\phi}## is the derivative with respect to ##\phi##, and initial conditions given by ##\phi[0] = 2...
  50. W

    Mathematica Cosmic inflation using mathematica

    In cosmic inflation, we have the equation of motion for the inflaton given by, $$\ddot\phi + 3H(1 + Q)\dot\phi + V_\phi = 0$$ the Friedman equation is given by $$H^2 = \frac{1}{3 M_p^2}(\frac{1}{2} \dot\phi^2 + V + \rho_r)$$ where ##M_p## is the reduced Planck mass. The differential equation...
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