Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,205
questions
0
votes
0answers
52 views
Solve method in Mathematica, symbolically solving method
I am looking for a way to solve this equation symbolically with Mathematica.
...
1
vote
1answer
74 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
79 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
149 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
39 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
62 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:
...
1
vote
2answers
57 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
27 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
78 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
39 views
NonCommutativeMultiply question- syntax question
if I define id as:
id /: NonCommutativeMultiply[id, x_] := x
id /: NonCommutativeMultiply[y_, id] := y
then ...
3
votes
3answers
277 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
57 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
84 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
118 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
31 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
66 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
26 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
...
8
votes
1answer
129 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
87 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
53 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
584 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
86 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
47 views
TensorExpand, TensorProduct and Distribution over Scalars
Consider:
TensorExpand[( b1 x )\[TensorProduct] (b1 x + b2),
Assumptions -> x ā Reals]
(*x^2 b1\[TensorProduct]b1 + x b1\[TensorProduct]b2*)
This works as ...
2
votes
2answers
78 views
Solving Simultaneous equations of matrices
I am in a precarious situation where I have two equations:
eq1 = Ī±1 + Ī±t12.t1 + Ī±r11.r1 == 0;
eq2 = Ī³1 + Ī³t12.t1 + Ī³r11.r1 == 0;
Where each variable is a 3x3 ...
4
votes
3answers
93 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
241 views
0
votes
0answers
35 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
51 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
73 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 ...
2
votes
1answer
66 views
How &@ and &/@works?
I have the following expression:
(Join[#, Reverse[#, {2}]] &@Partition[#, 2, 1, 1]) & /@ Vec
(* where: *)
Vec={{2,0},{1,1},{0,2}},
but I am not sure how ...
0
votes
0answers
26 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
151 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
175 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
63 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
66 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
54 views
Substitution of expressions in a symbolic expression
I define tables of symbolic variables in the following form (for convenience)
...
2
votes
1answer
50 views
Plotting symbolic functions
I want to plot the following Gaussian function
Is there a way that I can do this symbolically without giving values to the constants.
4
votes
3answers
126 views
The symbolic result does not give a proper answer when inputs are specified
Define F by
F[m_, k_, i_, j_] := (-1)^(m+k)/(m!*k!)*2^m*Binomial[m, i]*Binomial[k+1,j]
I am trying to find this sum:
...
0
votes
1answer
46 views
Symbolically evaluating jump conditions of expressions across interfaces
I am dealing with a problem in electromagnetism involving problems in different regions, and there is something that I haven't been able to figure out yet. What I would like to be able to do is take ...
0
votes
0answers
36 views
Simplifying symbolic products of matrices
(This is probably a trivial question, but I could not find the answer in the documentation.)
I would like to be able to use (functions similar to) Simplify, ...
1
vote
1answer
87 views
Symbolic solution of system of equations 12x12 takes very long time and the answer is complex too
I am trying to solve a system of equation symbolically. It works fine for 6x6, however for 12x12 system it takes very long and the answers are complex. I am using "Solve" or "Reduce&...
3
votes
2answers
91 views
Creating an Array with Subscripts and Superscripts
I would like to figure out how to construct an array using subscripts and superscripts based on the following info:
...
0
votes
0answers
82 views
Why does Mathematica give the wrong answer for this integral, and how can I correct it?
Mathematica is getting the following integral completely wrong:
$Assumptions = a > 0;
Integrate[1/k (E^-(k + a)^2 - E^-(k - a)^2), {k, 0, ā}]
(* I E^-a^2 Ļ *)
...
2
votes
1answer
127 views
Bug in DSolve when solving a system of two second order PDEs?
I'm solving a simple system of PDEs in Mathematica 11.1:
DSolve[{D[f[x, y], x, y] == 0, D[g[x, y], x, y] == 0}, {f[x, y], g[x, y]}, {x, y}]
This gives:
...
6
votes
2answers
186 views
DSolve does not return solution to simple system of second order PDEs
I'm trying to solve a simple system of second order PDEs with Mathematica 11.1.
Here is the system:
...
2
votes
1answer
62 views
Concatenation of Distributions
I would like to calculate mean, variance, ... of a concatenation of distributions (is this the correct technical term?). For an easy example I am trying to calculate the mean of a PoissonDistribution ...
