Questions tagged [symbolic]

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

Filter by
Sorted by
Tagged with
0
votes
1answer
65 views

DSolve doesn't respond

So I am trying to use DSolve to solve the following system of equations: ...
2
votes
1answer
79 views

Can Limit take limits of unknown functions?

For example, when I input this f[0] = 0; Limit[f[x], x -> 0] , it does not output 0. Is there a way to get it to output <...
1
vote
0answers
42 views

Symbolically solving linear program [closed]

I have been surprised that Mathematica cannot solve a linear program. Specifically, I have tried to solve the following problem: ...
0
votes
0answers
61 views

Solving partial differential equation

I am new to mathematica and I want to solve the following pde. I have two boundary conditions and one initial condition. I have tried the following code but the output is not the solution and it's ...
7
votes
1answer
248 views

Problems with DSolve and NDSolve for Dirichlet problem on an annulus

To solve the Dirichlet problem on an annulus, I do the following in 12.2 on Windows 10 Pro ...
1
vote
1answer
69 views

Symbolic Integration with trigonometric functions

I have this trigonometric integral which takes forever to evaluate $\int dx \frac{4 \left(\cos \left(p_1 x\right)-\frac{\sin \left(p_1 x\right)}{p_1 x}\right) \left(\cos \left(p_2 x\right)-\frac{\...
1
vote
0answers
39 views

Take overall minus sign in front in dot product with symbolic variables

I have the following as the output of a calculation a.b+(-a).b and I would like Mathematica to evaluate this to zero. Is there a way to specify that for my ...
1
vote
1answer
54 views

DSolve a partial differential equation with two boundary conditions

While trying to solve: $$ z \frac{\partial}{\partial z} (z G(s,z))=z \cosh (s) \frac{\partial}{\partial z} G(s,z)-\frac{1}{2} \sinh (s) \frac{\partial}{\partial s} G(s,z) $$ using DSolve it gives a ...
0
votes
0answers
50 views

Equations with Tensor product and Ket in Mathematica:

I tried to express this equation in Mathematica: I defined necessary things: ...
1
vote
1answer
57 views

Understand a result of FullSimplify

FullSimplify[((Sqrt[5] - 1)/(2*2^(1/4)))*Sqrt[Sqrt[2]*5^(1/4) - Sqrt[Sqrt[5] - 1]]] returns ...
1
vote
1answer
144 views

How can I solve a system of PDEs with constraints but having unknown boundary conditions

I have a 1st order system of two PDEs with two independent variables and two dependent variables. ...
0
votes
0answers
53 views

Solve method in Mathematica, symbolically solving method

I am looking for a way to solve this equation symbolically with Mathematica. ...
1
vote
1answer
76 views

How to get Mathematica to return more accurate symbolic eigenvectors

This code: Eigenvectors[{{Cos[t], Sin[t]}, {Sin[t], -Cos[t]}}] returns this output: ...
0
votes
1answer
80 views

speed up symbolic summation

I have the following summation L=24; sind=Range[-Pi,Pi,2*Pi/L]; Sum[f, {x, sind}, {y, sind}, {x1, sind}, {y1, sind}, {x2, sind}, {y2, sind}] where ...
4
votes
3answers
169 views

Initial-boundary value problem of 2nd order linear PDE with variable coefficient

Today I was studying partial differential equations and I tried to check if my solution was correct, I thought Mathematica code would be easy, but it wasn't. Here is my problem: Solve $u_{xx}-2tu-u_t=...
1
vote
1answer
43 views

Normal ordering of operators multiplied by scalars

I have the following code for normal ordering of two Boson operators $a(x),\,b(y)$: ...
3
votes
1answer
89 views

Extracting von Neumann neighbors from a list of lists [duplicate]

I want to be able to implement a rule that extracts the von Neumann neighbors from a given list of lists, that act as the entries of a rectangular matrix. Say a list of lists is given: ...
2
votes
2answers
136 views

Creating a Symbolic Matrix

Probably very simple, but I don't know where to start with this. How do I go about creating a symbolic matrix, such as the one below? I want to be able to use this so that any list of lists that are ...
0
votes
1answer
32 views

Expand product of symbolic sums (with identically named indices)

I have an expression that is a product of two symbolic sums. Sum[a[k], {k, 1, n}]*Sum[b[k], {k, 1, n}] How can I expand this expression? I want to see something ...
1
vote
0answers
80 views

How reliable is AsymptoticIntegrate?

In new mathematica 12 there is a new function AsymptoticIntegrate. However, it seems that it gives me incorrect results in some cases. To be completely honest, it ...
2
votes
1answer
42 views

NonCommutativeMultiply question- syntax question

if I define id as: id /: NonCommutativeMultiply[id, x_] := x id /: NonCommutativeMultiply[y_, id] := y then ...
3
votes
3answers
338 views

Solving a Sturm-Liouville problem

Ello, I would like to reproduce the analytical solution of the following eigenvalue problem, or at the least confirm them numerically (especially the eigenvalues): $$ - \frac{1}{2} y^{\prime \prime} ...
0
votes
0answers
29 views

summation involving Kronecker Deltas

I see that: Sum[u[q] u[k] v[k1] v[k + k1 + q] KroneckerDelta[k1 - q], {k1, -\[Infinity], \[Infinity]}] produces the correct result: ...
1
vote
2answers
60 views

Better way to do a replacement to define a function

I have a long analytical process where I have defined a stand in function Int[] to act as a placeholder for either NIntegrate[] ...
2
votes
1answer
91 views

Game of Life (GoL) in 3D cellular automaton and its rule numbers

I walked through How to calculate CellularAutomaton rule numbers in higher dimensions? to produce the following code for the Advent of Code, day 17, which asks for "Life, but in 3D". More ...
1
vote
3answers
132 views

How do I solve this integral in Mathematica?

I am trying to solve this integral in Mathematica $$ I=\int_{0}^{1} d x e^{iax} K_{0}\left(\sqrt{\left[q x(1-x)+m\right] b}\right) $$ where $a$, $b$, $m$, and $q$ are real positive constants. I want ...
0
votes
0answers
38 views

Symbolic min max optimization

I have the following seemingly simple optimization problem Minimize[{Max[p^(c - 3) , a p^(c - 1) , b p^c], d <= p <= 1}, p] but the Mathematica does nothing. ...
4
votes
0answers
67 views

How to get an asymptotic of the real-valued branch of the inverse function?

Consider function $f:\mathbb R^+\to\mathbb R^+$, defined as $f(x) = x + x^2\left(1 + \log x\right)$. I need to find an asymptotic approximation of its inverse function $f^{\small(-1)}\!:\mathbb R^+\to\...
1
vote
0answers
31 views

Importing equations generated in subpackage to be solved in another subpackage

I have a package which contains two subpackages: one ("`MOTSimulator`MOTGenerator") which generates a systems of differential equations of the form ...
9
votes
1answer
151 views

Nice use case for symbolic tensors?

I come from before the times of symbolic tensors in Mathematica, and am used to working with concrete tensors and custom commands to contract them using Transpose, Dot, etc. I recently realized that ...
1
vote
1answer
95 views

How to perform symbolic integration of six variable function?

I have a function of six variables in total - x1, x2, x3, x11, x22, x33 and I need to perform symbolic integration to get a symbolic expression. Before showing my ...
1
vote
0answers
58 views

Implementing the symbolic identity matrix $I$

I am working with symbolic tensors within Mathematica and I wanted to ask if there is a way to have a symbolic identity tensor.
2
votes
2answers
614 views

Three coupled PDEs to be solved semi-analytically/analytically

I have been trying to solve the following three coupled PDEs where the final objective is to find the distributions $\theta_h, \theta_c$ and $\theta_w$: $x\in[0,1]$ and $y\in[0,1]$ $$\frac{\partial \...
0
votes
1answer
88 views

Having problem in evaluating the eigenvalues of an $11\times11$ symmetric matrix in Mathematica [closed]

I am solving an $11\times11$ matrix in Mathematica. I am facing problem when I try to find the determinant or eigenvalues of this matrix. The error (Det::matsq/<...
1
vote
3answers
65 views

Solve function used symbolic computation yields all the coefficients value zeros

I am trying to compute the symbolic coefficients of using Solve function. But this is yielding all the coefficients values zeros. What are the other ways to find ...
2
votes
2answers
94 views

Can't compute the Integral

I tried to calculate an integral with the function Integrate, but it runs for a long long time without any answer. I have been checking the integrand and it seems ...
3
votes
1answer
52 views

TensorExpand, TensorProduct and Distribution over Scalars

Consider: TensorExpand[( b1 x )\[TensorProduct] (b1 x + b2), Assumptions -> x ∈ Reals] (*x^2 b1\[TensorProduct]b1 + x b1\[TensorProduct]b2*) This works as ...
2
votes
2answers
104 views

Solving Simultaneous equations of matrices

I am in a precarious situation where I have two equations: eq1 = α1 + αt12.t1 + αr11.r1 == 0; eq2 = γ1 + γt12.t1 + γr11.r1 == 0; Where each variable is a 3x3 ...
4
votes
3answers
96 views

Table over array indices

I want to generalize the following table to a summation over $s[1], \ldots, s[N]$ and $t[1], \ldots t[N]$, where each variable sums over $\{-1, 1\}$. ...
3
votes
3answers
244 views

A question on the exact value [closed]

Could anyone help me find the exact value of ...
0
votes
0answers
37 views

How to define function in Mathematica

I have a 3 by 3 symbolic matrix M(x,y,z). Question:1 First, I want to find its eigenvalues and eigenvectors. After that I want to make each eigenvalue and eigenvector a function of x,y, and z i.e. <...
0
votes
2answers
57 views

How to make calculations involving symbolic summation?

I want to minimize a function involving the sum of $n$ fixed (but indetermined) $x$ values, for example: Minimize[Sum[(x[i] - a)^2, {i, 1, n}], a] Expected answer: ...
0
votes
0answers
86 views

Symbolic equation solving: Inverse functions are being used by Solve

I'm quite new to mathematica, so apologies if the question it soo trivial. I'm trying to symbolically solve an equation for R, and would like at the same time to mix in a second equation. What I've ...
0
votes
0answers
35 views

Is there any formula to get the IRR from the slope of the Cumulative Cash Flow?

I've simulated a monthly regular cash flow with Excel, and the Internal Rate of Return (IRR) calculated from the first date to the current row. The curve of the IRR is very similar to the Transfer ...
5
votes
2answers
163 views

Trying to solve transient semi-infinite 1D Fick's Law with decay, getting constant for answer

I'm trying to find the solution to $$\frac{\partial f(x,t)}{\partial t} = a\frac{\partial^2 f(x,t)}{\partial x^2} - bf(x,t)$$ where $$f(0,t)=1, \lim_{x\to\infty}f(x,t)=0,f(x,0)=0.$$ I tried: ...
6
votes
1answer
180 views

Why can't this simple second-order differential equation be solved?

I'm trying to solve the following partial differential equation: $$ f(x,y) = \partial_x^2f(x,y)-\partial_y^2f(x,y) $$ for which one obvious solution would be: $$ f(x,y)=e^{2x+\sqrt{3}y} $$ An even ...
0
votes
0answers
18 views

Is substitution of symbolic expressions for JordanDecomposition correct?

Is it correct if I substitute letters A-Z for 25 expressions that are in a 5x5 matrix, run JordanDecomposition and then substitute expressions back? The process makes no progress after a day with ...
2
votes
1answer
73 views

Trouble evaluating this definite integral, either directly or with indefinite + limits

I have the function $$ \Sigma(x) = \frac{\sqrt{R^2-x^2}(\left| R\right| -1)}{\left(R^2-1\right) \left(x^2-1\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{R^2-x^2}}{\sqrt{R^2 \left(1-x^2\right)}}\right)-\...
0
votes
0answers
71 views

Very slow (days…) computation of JordanDecomposition of symbolic matrix

I am aware there may exist a similar topic, but I haven't found anything. Is there any way to speed up computation of JordanDecomposition for a symbolic 5x5 matrix with about symbolic variables? After ...
1
vote
1answer
65 views

Substitution of expressions in a symbolic expression

I define tables of symbolic variables in the following form (for convenience) ...

1
2
3 4 5
26