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 StackExchange site.)

learn more… | top users | synonyms

6
votes
1answer
104 views

Improper integral: $\int_1^\infty\frac{\sin(\sqrt{x})}{\sqrt{x}}dx $.

mathematica is reporting that the improper integral $\int_1^\infty\frac{\sin(\sqrt{x})}{\sqrt{x}}dx $ coverges to $2\cos(1)$. However, when I try to confirm this by actually integrating it using ...
3
votes
3answers
56 views

Solution of the equation $\cot \theta = 2\cot 2\theta$

I've tried to solve the equation $\cot \theta = 2\cot 2\theta$ with the command 'Reduce' of Mathematica and obtained $\theta = n\pi$ as the solution with n an integer. But $\theta=n\pi$ is clearly a ...
1
vote
0answers
16 views

Integer solutions to a polynomial $f(x,y)$

How can I find the integer solutions of a polynomial $f(x,y)$ such that $a<|x|,|y|<A$ using Mathematica?
0
votes
1answer
24 views

How to find a pair of basis vectors for the plane given by the equation?

Find a pair of basis vectors for the plane given by the equation x+2y+3z=0 I was given the Hint: you can find points on the plane by choosing values for two variables and solving for the third I am ...
1
vote
2answers
42 views

Does the inverse of $f(x)=x^3$ have a non-negative domain to have a real output?

I'm not familiar with complex analysis. While playing with Mathematica (a mathematics software), I found that it keeps spitting out unexpected results, and the reason was that it considers differently ...
0
votes
1answer
29 views

Lattice Reduction in Mathematica

I have some trouble understanding the concept of lattice reduction. As I understand, an integer lattice $$\{ A k : k \in \mathbb{Z}^n \} \subset \mathbb{Z}^n $$ is defined by a regular matrix $A \in ...
0
votes
0answers
20 views

Convex Analysis - How To Find Non Convex Set

I have a problem regarding the following exercise (I considered to put this question on mathematica.stackexchange, but I changed my mind and though this was the right place for this particular ...
-1
votes
0answers
11 views

mathematica Linear programming with summation and product

I want to solve Linear programming in mathematica that have summation and products in objective function and in constraints. I ...
0
votes
0answers
25 views

Approximating a Riccati Differential Equation/Differential equation of two variables

I am currently really struggling to solve/approximate this Riccati equation $x'(t, v) = cv(1-x(t)) + \beta x(t)(1-x(t)) - \gamma x(t)$ st. $0 < c, \gamma, x_{0} < 1$ $ 0 \leq v \leq 1$ $ 0 ...
0
votes
1answer
32 views

How to find elements of a ring $\mathbb{Z}_n$ in Mathematica

How to find elements of a commutative ring with unity $\mathbb{Z}_n$, (under addition and multiplication modulo $n$) by using Mathimatica, which satisfying the following condition. Let $x, y \in R = ...
1
vote
1answer
55 views

Bug or feature? If statement inside double integrals [closed]

Generally speaking, $$ \int_c^a f(x) dx = \int_c^{a-b} f(x) dx + \int_{a-b}^a f(x) dx$$ However, consider the following Mathematica code: So apparently, the sum of the two sub-integrals $1/32 + 0 ...
1
vote
2answers
81 views

Revolution of fractal

How to find the volume and surface area of a shape which made from revolution of Koch Snowflake? (I think the surface area will be an infinity, because length of the Koch snowflake is infinity.) And ...
1
vote
1answer
25 views

Focal distance on a parabola

If focal distance of a point on the parabola $y = x^2 - 4$ is $25/4$ . And the points are of form $(\pm \sqrt{a}, b$ then how can we find $a , b$ or sum of these . I think the focus of parabola would ...
0
votes
1answer
30 views

Plotting a function around $0$ shows it is jumping around, although the limit as $x\to 0$ exists

My problem revolves around the function: $$ f(x) = \frac{\sin(\tan x) - \tan(\sin x)} {\arcsin(\arctan x) - \arctan(\arcsin x)} $$ The $\lim_{x\to 0}f(x)= 1$. However, whilst approaching 0, there is ...
11
votes
1answer
3k views

Fractional oblongs in unit square via the Paulhus packing technique

Oblongs of size $ \frac{1}{1} \times \frac{1}{2}$, $ \frac{1}{2} \times \frac{1}{3}$, $ \frac{1}{3} \times \frac{1}{4}$, $ \frac{1}{4} \times \frac{1}{5}$, ... have a total area of 1. ...
0
votes
0answers
30 views

How can I find $\int {\sqrt {{{\left[ 1 - {r k \cos \left( {(w - t )s + p} \right) } \right]}^2} + {{\left( {r w } \right)}^2}}} \mathrm{d}s$?

I have to integrate $$ \int {\sqrt {{{\left[ 1 - {r k \cos \left( {(w - t )s + p} \right) } \right]}^2} + {{\left( {r w } \right)}^2}}} \mathrm{d}s. $$ I have tried solving it with Mathematica, but ...
0
votes
1answer
20 views

How to alternate alternating negatives in a series (summation)?

Note: while this isn't a strictly Mathematica, I am using it to find my results. I have a problem where I integrate E^x x^n and I'm given results like ...
0
votes
1answer
24 views

Verifying general solution to differential equation

to the following differential equation: $y^{(6)}-2y'''+y=0$ I obtained the following general solution: $y=C_1e^x+C_2x ...
0
votes
1answer
27 views

efficient mathematica code to reduce computational time

I am trying to a code in Mathematica that is taking unacceptably long time (day) to run as it involves four summations. I am wondering is there any way to do some changes in the code so that it ...
1
vote
0answers
29 views

Creating a grid of coloured points

I wish to create a grid of $31\times31$ points with coordinates of the form $(\frac k{30};\frac n{30})$ within the unit square, and give each point a colour based on the 2-adic value of both its ...
1
vote
0answers
62 views

Minimize the number of non-zero elements of a matrix

I have a matrix A, which is huge, and all its elements are non-zero. I want to perform the operation: $ U_1\otimes U_2 \otimes U_3...\cdot A \cdot U_1^{\dagger}\otimes U_2^{\dagger}\otimes ...
5
votes
2answers
708 views

Should I trust Mathematica or numerous other sources on this Fourier transform

Assume $a>0$ So Mathematica claims $$F\{e^{-a|t|}\}(\omega) = \frac{a\sqrt{\frac{2}{\pi}}}{a^2+\omega^2}$$ However, I've read about another transform pair (page 3): $$F\{e^{-a|t|}\}(\omega) = ...
-3
votes
1answer
55 views

mathematica / maple

I have an expression of products and divisions of q-binomials. I want to check if the expression is always greater than 1. Is there a way I can do that with matlab/ mathematica/ maple?
0
votes
1answer
88 views

Why is it incorrect to integrate by $d(2x)$?

I tried to prove the volume of a cone. If you let the radius be $r$ and let the height be equal to the radius, then all you need to do is integrate the area of a circle with radius $r$ by $dr$. ...
0
votes
1answer
69 views

Visualising a 1-(50,15,15) design.

The problem I have is the visualisation of a 1-(50,15,15) design. That is a set of 50 points and 50 blocks (lines), so that each point is on 15 lines, and each line contains 15 points. My attempts ...
1
vote
0answers
33 views

What is following limit?

$\mathsf{Mathematica}$ evaluates $$\lim_{N\rightarrow\infty}\lim_{\epsilon\rightarrow0^+}\frac{\binom{N^{\frac{3}{2}}-N^{\frac{1}{2}}}{N^{1-8\epsilon}}}{\binom{N^{\frac{3}{2}}}{N^{1-8\epsilon}}}$$ to ...
-1
votes
1answer
58 views

Code Wolfram Mathematica [closed]

Sorry but I do not know English very well. The question is very simple, I hope someone knows the code that makes my case. In fact, writing: ...
2
votes
0answers
48 views

Is this system of inequalities (and equality) tractable?

I have some real parameters here. The $\mu_i$ - for $i=1,2,3,4,5$ - are 'convex coefficents' in that $\mu_i\geq 0$ and $\sum_{i}\mu_i=1$. The $x$ and $z$ are such that $x^2+z^2\leq 1$. The ...
1
vote
0answers
38 views

Convergence of a hypergeometric function

The hypergeometric function, ${}_{2}F_1(a,b,c;z)$ can be written in terms of a power series in $z$ as follows, $${}_{2}F_1(a,b,c;z) = \sum_{n=0}^{\infty} \frac{(a)_n (b)_n}{(c)_n} ...
0
votes
1answer
28 views

Problem with Solve a Differential Equation

I Have a little problem . I wrote this function ( function describe dynamics of ball-hoop system): ...
1
vote
0answers
42 views

Using Orthogonal Collocation to solve Coupled Ordinary Differential Equations

I am trying to solve six first order coupled ODE's, two of these are associated with a heat balance of a catalyst pellet, and four are mass balances. I have been trying to solve these equations using ...
3
votes
2answers
153 views

Solving $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$ (using wolfram/mathematica)

I would like to solve the following non-linear ordinary differential equation: $$\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$$ -I need an analytic solution. -I ...
3
votes
1answer
125 views

Fun/Frustration With Coding Coding Theory

it's time for practical coding theory. I am trying to write a simple program that will detected if a given binary code word is "correct" or not. If it is not correct, I want to detect/correct (since ...
0
votes
1answer
55 views

Mathematica - Searching a clever way to do a computation

I am solving this differential equation using Mathematica $$x ~y''(x)+\alpha ~ y'(x)+\frac{1-3\mu (x)}{(1-x) x}=0$$ where $\mu(x)$ is a polynomial: $$\mu ...
1
vote
1answer
84 views

Mathematical symbol for Symbolic Replacement

(Posted at mathematica.SE, as it might be better there) I'm searching for a mathematical symbol, that describes the symbolic replacement done for instance in Mathematica: ...
0
votes
1answer
125 views

How to plot a phase portrait for system of differential equations in mathematica or R?

Please, help me. I'd like the phase portrait for this system: If anyone can make this portrait and post a print screen here, I would thank you very much.
0
votes
1answer
58 views

How can i view solutions of Solve as multiples of pi in mathematica 10

i am new to Mathematica and can't find the option to show solutions of Equations like Solve[6.5 == 2 \[Pi]*r] as multiple of pi. I only get the numerical output ...
1
vote
1answer
131 views

How can I solve numerically this partial differential equation?

I am reading this paper and came across a system of differential equations with 4 ODEs and 1 PDE. The PDE is given below. My question is how to solve this numerically in MATLAB , Python or ...
0
votes
0answers
34 views

Closed form for a Bartlett's formula for AR(2)

Consider a stationary AR(2) process $$ Y_t=\phi_1Y_{t-1}+\phi_2Y_{t-2}+e_t $$ with $e_t$'s are i.i.d. with mean $0$ and variance $1$. Let $r_s$ be the $s$-th autocorrelation ...
0
votes
1answer
39 views

Graphing Fourier transforms on a frequency versus intensity plot (how to deal with complex numbers)

I am trying to understand how Fourier transforms are used to make HNMR plots. HNMR basically consists of hitting some molecules with some radiation and listening to the radio signal that results. ...
2
votes
1answer
93 views

Is the adjacency matrix of a given graph (OR any graphs isomorphic to a given graph) a Kronecker product, and if so what are the factors?

I have a few triangular grid graphs that I am trying to express as the direct products of smaller graphs, if possible. ...
0
votes
2answers
88 views

Techniques to solve nonlinear first-order ODEs

I am trying to solve the following nonlinear ODE: $$\frac{dy}{dx} = \frac{1}{x(ayx-b)},$$ where $a, b$ are constants and $a>0$. Moreover, you may assume that $b \neq 0$ if necessary. This ...
11
votes
2answers
341 views

Twilight Zelda Guardian Puzzle : Shortest Path (UPDATE: ADDED RULES)

I'm playing a video game right now and in it is a puzzle (see here). There are solutions to solving it (see here) on the Internet, but I'd like to know if this path is the shortest path (least amount ...
3
votes
1answer
191 views

Help me understand Gröbner basis result please

I'm practicing a bit with Gröbner bases but I'm not understanding the following result I obtain from Mathematica: ...
0
votes
1answer
57 views

Summation giving incorrect value (I think) in Mathematica

I have the problem $\displaystyle\sum\limits_{x=2}^4 \dfrac{1}{x^2}$. I know the answer to this problem should be $\dfrac{61}{144}$. When I type the problem into Wolfram Mathematica, I get the answer ...
1
vote
0answers
71 views

What is $\int (1-e^{-x})^n dx$?

For my purposes, $n$ is a non-negative integer, and $x > 0$. I didn't know how to evaluate this integral, so I plugged it into Mathematica. It told me the solution is $(-1)^n B(e^x; -n, n+1)$ I ...
1
vote
0answers
42 views

Precision of starting values in FindMinimum

I am currently working on an optimization of chemical kinetic model. Starting points for FindMinimum is defined as: k10 = 2.45*10^-1 and k20 = 8.65*10^-11. The step monitor is used to show calculated ...
1
vote
2answers
60 views

Solving differential equations with Wolfram Mathematica

So I saw this differential equations in my textbook $$\frac{{{d^4}\omega }}{{d{x^4}}} + 4{\lambda ^4}\omega = 0$$ and I figured why not solve it with majestic Wolfram Mathematica. So I wrote this ...
1
vote
1answer
62 views

Dual curve of the lemniscate of Bernoulli?

Does anybody happen to know the homogeneous equation $F(u,v,w) = 0$ for the algebraic curve dual to the lemniscate of Bernoullli: $$ F(x,y,x) = (x^2 + y^2)^2 - A (x^2 -y^2)z^2 = 0?$$ I looked at the ...
2
votes
0answers
31 views

Finding feasible solution of inequalities in math software

I have a Math problem where I have some true statements, and I want to know if there is a feasible solution to an equation. I would like to know how to do that in either Matlab or Mathematica. The ...