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Questions tagged [symbolic]

For questions about symbolic computation, as opposed to numerical computations.

146 questions with no upvoted or accepted answers
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121 views

Substitution of expressions using Groebner basis

I know this topic came up numerous times (most of the results are detailed in the comments of this link Is there a way to to substitute for symbols, simplify, and back-substitute?). However, I have ...
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102 views

Asymptotes of parabolic cylinder differential equations with boundaries at infinity

For context, I'm studying the paper Coulomb blockade in superconducting quantum point contacts by Averin from 1998. Specifically, I am trying to find how he obtains equation 11 from equation 10, which ...
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62 views

Define a new coordinate chart and do algebra/calculus in it

I've stumbled across a very nasty problem: define a toroidal coordinate chart and calculate Laplacian in it. As I'm going through it manually, I wonder if this can't be made in Mathematica. Sure, MMA ...
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434 views

how to obtain general solution for Laplace PDE in spherical coordinates using DSolve?

Can DSolve given a general solution to Laplace PDE in spherical coordinates without given boundary conditions? I tried, but not able to get a solution. Do I need ...
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73 views

Can substitution rules be compiled?

I am thinking of having a custom multiplication operation CenterDot[A,B] for non-commutative operators, and some rules that should commute the operators to a ...
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82 views

Convergent infinite sum fails to converge in Sum[…]

It looks like this. ...
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225 views

Solve resolves symbolic linear system in 20 seconds, LinearSolve just grinds on and on

I am repeatedly solving (related) systems of symbolic linear equations. Solve has worked reliably, but I expected LinearSolve to be faster. I ran into this case, which Solve resolves in ~20 seconds, ...
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146 views

Symbolic second variation (quadratic form matrix)

Mathematica has a calculus of variations package that can compute the first variational derivative symbolically, rather nicely. Does anyone know if there is a way to compute the quadratic form matrix ...
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79 views

Parallelizing code, any tips?

I have access to a Linux cluster and I'm trying to use Parallelize to run the above bellow faster, but whenever I try to place ...
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0answers
219 views

Replacement rule for summation with Kronecker delta

I want to perform some symbolic computations in index notation, without explicit reference to sums, so that in expressions of the type f[i,j]g[j,k] summation over <...
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235 views

Polynomial kernel expansion

I am trying to calculate the polynomial kernel expansion using Mathematica. I have tried the Expand and Simplify functions with ...
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344 views

Parallel evaluation of symbolic matrix eigenvalues

I'm trying to find eigenvalues of symbolic hermitian 40x40 block matrix. It is made from 20 2x2 matrices like this: ArrayFlatten[Table[M[m,n],{m,1,20},{n,1,20}]] ...
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99 views

Integrate with Subscript: does this crash your kernel too?

I encountered some strange behaviour running v10.0.1 on a Mac Pro, while working with Integrate and Subscript. Starting from a ...
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333 views

Symbolic Nullspace computation in parallel

I am trying to determine the nullspace of a large symbolic matrix. The single core evolution seems to take too long. I tried Parallelize[] on the commands ...
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104 views

Result of symbolic integration changed drastically by making assumptions

I would like to know the underlying reason for different outcomes for the two integration operation below. One of them includes a few assumptions, otherwise both have the same integrand: ...
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137 views

Getting long complex-valued integrals when simpler real-valued expressions exist

I have a long list of real-valued functions I'd like to integrate symbolically. For many of them, Mathematica gives me results with long complex-valued expressions involving weird functions such as <...
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979 views

specifying a list (vector) of arbitrary length

When trying to do symbolic calculations in mathematica involving a space of dimension n, which is arbitrary but fixed, I'd often like to work with vectors that have ...
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370 views

Find the values of parameters so that the matrix is symmetric positive definite

Good evening , I have a matrix 20x20 in symbolic form. The matrix depends on 5 parameters (a,b,c,d,e). I would like to get the interval of each parameters that ensures that the matrix S is symmetric ...
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294 views

Computing residues of matrix valued functions symbolically

I have a somewhat specific application in mind, but I've run into this kind of problem a few times and never found an elegant solution. Is there an efficient way to get Mathematica to recognize that ...
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786 views

Eigenvectors for a large symbolic matrix

I'm trying to compute the eigenvectors for a 42x42 symbolic matrix (with one variable) in Mathematica. I get the following error: Eigenvectors::eivec0: Unable to find all eigenvectors. >> and the ...
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245 views

(Symbolic) LinearSolve is slower/different after upgrading to Mathematica 9

Yesterday I upgraded from mathematica 8.0.4.0 to 9.0.1.0. Trying to run the same notebook I used many times before, it takes ages to evaluate a symbolic (linearsolve) expression which before was ...
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262 views

Problems with Simultaneous Equation Solving

Let me first explain what I am doing and then I will explain the problem that I can't figure out. I am basically trying to solve 2 equations for 2 unknowns (a1 and <...
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63 views

Solving a heat equation problem(DSolve)

I'm brand new to Mathematica. I am trying to solve a heat equation problem, but I keep getting back the input on the output line. The problem: In: ...
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62 views

Evaluating another symbolic sum

Here I asked about a symbolic sum, and received three very insightful replies (from: მამუკა ჯიბლაძე, Carl Woll and Dr. Wolfgang Hintze) which did the trick. (Thank you again!) Currently I am trying ...
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57 views

Defining second derivative boundary condition using DEigensystem

I tried to solve a fourth-order eigenvalue problem with boundary conditions on high order derivative. For example, the following equation, $$\frac{\partial d}{\partial t}+\frac{\partial^4 d}{\...
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1answer
128 views

Small error on symbolic eigenvalue of $2\times2$ matrix

I have some computation where I specifically define a 2x2 matrix to have a specific eigenvector v associated with an eigenvalue g, and a second eigenvalue l : ...
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48 views

Finding symbolic solution to constrained optimization question

The code below is my attempt to solve a constrained optimization problem: ...
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0answers
111 views

How to sum over the variable in partial derivative operator?

I need to use the partial derivative operator in Wolfram Mathematica within a summation, specifically to define the D'Alembertian operator of scalar fields. I am having trouble summing over the D ...
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144 views

Finding root of symbolic function

I'm trying to find a root of the following equation $$\theta^\frac{t}{s}-\theta-\sqrt{1-p},$$ where $0<t\leq1\leq s$ and $0<p<1$. I've tried FindRoot and Reduce, but somehow they don't ...
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1answer
108 views

Replacing one of the integrals in the multiple integral with an analytical solution

Problem consist in simplifying complicated multiple numerical integral, where I know analytical solution for a subset of them. Integrand is of the form ...
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0answers
70 views

Finding symbolic series coefficients

Is there any way to get the symbolic form of a series? For simple series this seems possible e.g. SeriesCoefficent[Exp[x],{x,0,n}] tells me that the general ...
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0answers
49 views

Symbolic differentiation on a function of matrices and vectors

Let $I_t$, $I$, $V$, $Z$ be vectors and $R$, $B$, $P$, $A$, $\mathcal{K}$, $\mathcal{P}$ be some matrices such that $$ \begin{eqnarray} S&=&-(R I+B^\top V)^\top \mathcal{R}(R I+B^\top V) ...
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53 views

Simplifying results of a vector function to be nested (SECOND UPDATE)

(Oddly enough, the title for another question that ended up dealing with an unrelated problem could have worked better here, but I didn't want to plagiarize.) Given a symbolic vector function ...
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47 views

Inverse Laplace transform of powers with an arbitrary index

Tried for Inverse Laplace transform (ILT) for the following: L[s] = (L /(L + s) w + Q /(Q + s) (1 - w))^n $L[s]$ can also be written as $$L[s]=\sum_{k=0}^n\...
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163 views

Computing symbolic form of trigonometric integral

To calculate symbolically this integrale $$I(s)= \int\limits_0^{\pi/2} \dfrac{\cos t}{\sin^2 t-R^2} \; e^{-s/\cos t}\; dt$$ which has already been asked Here, @yarchik has suggested to me to post ...
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102 views

Problems with DEigensystem

I have the following problem $\frac{c_p q_m}{A}\frac{\partial T(x,t)}{\partial t}+\rho c_p \frac{\partial T(x,t)}{\partial x}-\lambda \frac{\partial^2 T(x,t)}{\partial x^2}=0$ I want to find the ...
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51 views

Symbolic summation with variable bounds and variable number of indices

I wish to compute compute terms like Sum[f[t[j[1]],t[j[2]],...],{j[1],m},{j[2],n},...] for arbitrary positive integer n and any ...
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55 views

Finsler or Lagrange geometry package?

I was wondering if there exist any packages or examples of work on Finsler-Lagrange geometry. I need it to do symbolic calculations, as for example calculations of non-linear connection coefficients, ...
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91 views

How to work out sums symbolically?

Intro Consider these two equal expressions of the variance $$\frac{\sum _{i=1}^n x(i)^2}{n}-\frac{\left(\sum _{i=1}^n x(i)\right){}^2}{n^2}$$ and $$\frac{\sum _{i=1}^n \left(x(i)-\frac{\sum _{i=1}...
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116 views

Solve the Euler Angle equations

I'm trying to solve the system of equations, but I have no idea what wrong with my code. I wanna find out the relationship between $\alpha$, $\beta$, $\gamma$ and $\alpha1$, $\beta1$, $\gamma1$,$\...
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61 views

Solving this system of two algebraic equations

I'd like to find symbolically the common roots of two polynomial of second order in X and Y. Though this is not possible in general, with the present coefficients, MMA manages to output a result. <...
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299 views

Symbolic derivatives with vectors and matrices

I'm currently trying to solve some problems using symbolic vectors and matrices of arbitrary size. However, I have some problems with understanding and verifying the results: I defined the vectors as ...
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0answers
90 views

Convolve returns false result

Bug introduced in 9.0 or earlier and fixed in 10.0 I tried to convolve sin with sin and got this unexpected result: Convolve[Sin[x], Sin[x], x, y] (* 0 *) Now I ...
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294 views

Implementing Einstein's summation convention for a particular case

I know that there are few Q&A here regarding implementing summation convention and also other packages like xAct to do such things efficiently. But I was hoping for a very well cut-out technique ...
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32 views

How to understand if there is occurrence of a symbol in expression and make it be null if yes?

I have a table of frequences W={w1,w1,w2,w2} and a function E[i_]:=Exp[I*W[[i]]*t]. I'd really like to write such function that <...
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99 views

Noncommutative tensor product

I am using Mathematica 8. Is there any way to make a noncommutative tensor product calculation? For instance, I have the following relations : $XY=YX; \ Xt=qtX; \ Yt=qtY$. Is there any way to make a ...
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331 views

Can Mathematica solve Kuhn-Tucker Equations with arbitrary functional form (up to 2nd order derivative)

I am in a business of solving a 5-variables optimization with inequality constraints, and I would like to maintain the functional form as arbitrary as possible. So far, I am assuming that the ...
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103 views
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186 views

CharacteristicPolynomial returns 0

I have a following matrix. ...
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107 views

Computing symbolic surface normal of a surface point on a semialgebraic set

Consider a semialgebraic set; such as reg below: ...