Questions tagged [mathematica]
For questions concerning the popular computational software program published by Wolfram Research. (Note: you are more likely to get quicker and more accurate response if you ask the question on their user forum or on the Mathematica Stack Exchange site.)
222
questions with no upvoted or accepted answers
7
votes
0
answers
424
views
A generalization of Elon Musk's favorite interview question (Going 1km South, 1km West, then 1km North returns to the starting position).
This question concerns a generalization of the following problem (allegedly, in the early days of Tesla and SpaceX, Elon Musk would ask the following question to possible future employees):
Assume ...
- 15.4k
6
votes
2
answers
95
views
Optimal length of rope for sliding across a gap
I'm trying to solve a physics problem that I heard ~10 years ago in undergrad that was casually posed to me without a solution in mind; it has been bothering me ever since! Please let me know if this ...
- 262
6
votes
0
answers
120
views
Algorithm for FindSequenceFunction
What algorithm might Mathematica be using to compute FindSequenceFunction? Does anybody know if there is any online material on this topic?
- 328
6
votes
0
answers
2k
views
Choosing the branch of a logarithm
The problem: I am integrating complex logarithms over an angle $\phi$ over $[0,2\pi]$. It is quite complex (pun not intended) and I called Mathematica in to aid me. I am calculating an energy of a ...
- 599
5
votes
0
answers
118
views
Sampling from intersection of sphere and simplex
I need to isotropically sample vectors in $\mathbb{R}^d$ of given Euclidean norm $C$ with a restriction that components are positive and add up to 1. Can someone suggest a method to do it?
I tried ...
- 5,477
5
votes
0
answers
291
views
How to integrate $\left(1+\ln(x)\right)\sqrt{1+(x\ln(x))^2}$ with Risch algorithm?
How would you integrate
$\left(1 + \ln\left(x\right)\right)\,
\sqrt{1 + \left(x\ln\left(x\right)\right)^{2}\,}$
using the Risch algorithm?
I want to know this because Mathematica is using the Risch ...
- 2,579
4
votes
0
answers
144
views
Analysis of a sequence based on ratios of floors of consecutive powers of a real value
I am currently interested in the following sequence:
Fix a number $x$, and define a sequence $(a_n)_{n=0}^\infty = \lfloor x^n \rfloor$ and $(b_n)_{n=0}^\infty = \frac{a_{n+1}}{a_n}$
With a little ...
- 411
4
votes
0
answers
79
views
Closed form of A Log-Sine-Cosine Integral by Mathematica
By using the Mathematica 12.0, I found the numerical value of a Log-Sine-Cosine Integral that
$$\int_0^{\frac{\pi}{6}} \log^2(2\sin\theta)\log(\tan(\theta/2))d\theta=-4.39530911884935704937076725879.$$...
- 51
4
votes
0
answers
184
views
How Can I Visualize a PDE Boundary Condition?
In this question, the comment suggests that the integration bounds in the Fourier Series should be chosen to avoid discontinuities in the boundary conditions. I am trying to produce a nice visual to ...
- 1,922
4
votes
0
answers
167
views
Solving a difficult integral
I have been stuck on the following integral for some time:
$$
I = \int^{2 \pi}_0 \mathrm{d}\theta \frac{\cos \theta\left(x + \Delta\cos\theta\right)}{\sqrt{k + \left(x + \Delta\cos\theta\right)^2}} \...
4
votes
0
answers
95
views
Integrating Log function using Mathematica
Dear Stackexchange users,
I would like to integrate the following function using Mathematica as I don't have a way of doing this by hand:
$$\int_0^\pi \frac{\log(A-B\cos\theta)\sin^4\theta}{(A-B\cos\...
- 287
4
votes
0
answers
334
views
Approximate equation for tapered cycloid offset curve without cusps
Is it possible to create parametric equations to approximate a tapered cycloid offset curve without cusps, that does not require manual adjustment of values when the primary curve parameters are ...
- 41
4
votes
0
answers
495
views
The mathematics of anaglyph images
Note: I'm not quite sure whether this question properly belongs to the Mathematica or to the mathematics Stack Exchange. But because my question mainly concerns general mathematical principles rather ...
- 1,012
4
votes
0
answers
2k
views
SAGE vs. Mathematica for Lie algebras / groups?
What math software is better for working with Lie algebras and Lie groups, SAGE or Mathematica?
- 2,425
3
votes
0
answers
89
views
How to find eigenvalues of a linear operator consists of laplacian?
I have the following matrix of linear operator consists of Laplacian \begin{bmatrix}0&1&0\\\Delta&\Delta& 0\\0&0&\Delta\end{bmatrix}
acting on \begin{bmatrix}w\\w_t\\u\end{...
- 31