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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 ...
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 ...
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 ...
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 ...
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 ...
82 views

### Convergent infinite sum fails to converge in Sum[…]

It looks like this. ...
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, ...
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 ...
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 ...
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 <...
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 ...
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}]] ...
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 ...
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 ...
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: ...
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 <...
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 ...
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 ...
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 ...
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 ...
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 ...
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 <...
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: ...
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 ...
57 views

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### 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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### 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 ...
103 views

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