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0
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1answer
41 views

Comparing $f(x)$ and the $f\_approx(x)$ in Matlab, Octave or Mathematica/Wolfram

I have a function $f(x)$ and I wrote the approximation for $f(x)$ as $f\_approx(x)$ which is a simple algebraic formula with sums and products . I now want to study the 2 functions side by side and ...
0
votes
1answer
19 views

Simulating systems of SDEs in Mathematica and plotting solutions.

I would like to simulate the solution of the following system of SDE's: \begin{equation*}\begin{split} dX(t) &= - \frac{1}{2}X(t)\, dt - Y(t)\, dW(t)\\ dY(t) &...
2
votes
2answers
620 views

Computation of the minimal polynomial of a matrix in Mathematica

On the wolfram website, the following program is given for computing the minimal polynomial of a square matrix $a$ in the variable $x$: MatrixMinimalPolynomial[a_List?MatrixQ,x_]:=Module[ { ...
-1
votes
3answers
35 views

How many seats in the parliament? [closed]

In a particular country, there are two political parties, the red party and the blue party. Prior to last week's general election, the red party had 2 1/2 times as many representatives in the ...
3
votes
0answers
58 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 ...
1
vote
1answer
549 views

Newton backward interpolation in Mathematica

I have the following task: Create a function (in Wolfram Mathematica), called $\mathrm{NewtonBackward}$[n_,x0_,h_,f_] which interpolates backwards the function $f(x)$ with nodes {x_i = x_0 + $i$$\...
0
votes
2answers
546 views

Solve $4 A (L^{3/4}) - wL (((24 - L) w)^{-3/4}) = -(((24 - L) w)^{1/4})$ for L? Using Mathematica

I'm trying to solve $$4 A (L^{3/4}) - wL (((24 - L) w)^{-3/4}) = -(((24 - L) w)^{1/4})$$ for $L$ using Mathematica, and it spits the following out: ...
0
votes
0answers
21 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?
-2
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0answers
32 views

Verifying inequality in mathematica

I am trying to prove or disprove the flowing inequality : $0<a, b<1, a^2+b^2=1, 0<x<1/2, 0<y<1/2$ $\rightarrow$ $1-a^{2x-1}b^{2y-1}>0$?? For this I wrote ...
0
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0answers
33 views

how to calculate the implicit Cartesian equation from calabi yau threefold?

i find mathematica version about parametric form, how to calculate the implicit Cartesian equation from calabi yau threefold? ...
0
votes
1answer
23 views

Problem in trying to define an integrating function in Mathematica [closed]

I need to define a function that integrates a function in some interval and returns its numerical value. I am not allowed to use built in functions for integrating in Mathematica. This is my code ...
1
vote
1answer
92 views

Conversion of Hypergeometric functions from Maple to Mathematica

After a calculation I found in Maple an expression of the kind: $$f(x)=hypergeom\left(\left[\dfrac{a}{b},1\right],\left[c,d\right],h\right)$$ What is the equivalent notation in Mathematica which I ...
2
votes
1answer
38 views

How to prove an inequality or read Mathematica's proof

Given $0 < \alpha_1, \alpha_2 <1$ and $1/2 < p <1$, how to prove that the following expression is always non-negative? \begin{align*} (1 - \alpha_2)^2 p^2 (2 p -1) + \alpha_1^2 \, p\, \...
2
votes
3answers
207 views

How can I calculate OEIS A144311 efficiently?

I'm looking for a way to calculate OEIS A144311 efficiently. In one sense or another, this series considers the number between "relative" twin primes. What do I mean by this? Well, the number $77$ ...
1
vote
3answers
31 views

What is the difference between linear regression on y with x and x with y

I'm plotting the regression line of (GDP$\%$ Change, Poverty Rate$\%$)$\to (x,y)$ in Mathematica What would it mean if I were to switch the axis? (Poverty Rate $\%$, GDP change $%$) (GDP$\%$,Poverty$...
0
votes
0answers
17 views

How can I mark a specific point and vector in Mathematica?

How can I mark a specific point and vector in 3D in a Mathematica plot? I've draw a surface but I need to mark a point and vector on it. Thanks!
0
votes
0answers
32 views

Solving Quadratic Equation By Using Mathematica

I was bothered with the following very simple problem: Solving a quadratic equation $x^2+x+1=0$ in mathematica if I use "solve" function in mathematica as below: Solve[x^2 + x + 1 == 0, x] I ...
3
votes
1answer
2k views

A series solution of the differential equation: $\frac{d^2u(x)}{dx^2}+ u(x)^n = 0.$

Consider the differential equation $\frac{d^2u(x)}{dx^2}+ u(x)^n = 0.$ Let the solution be $u(x) = u_0(x) + p u_1(x) + p^2u_2(x) + \cdots +p^m u_m(x).$ Now we are interested in substituting the ...
0
votes
1answer
36 views

Formal expansion of matrices using Maple or Mathematica

I'd like to evaluate some powers of sum of matrices, say I would like to evaluate $\left(A+B\right)^{n}$ with $A$ and $B$ some matrices. Since I'd like to go to high order, I'd like to use Maple or ...
1
vote
1answer
42 views

Why is the right half of the output for the Plot[(-x)^(2/3), {x, -30, 30}] missing?

I want to get a figure for $(-x)^{\frac23}$. After using the following code, I found that only the left part of the function $(-x)^{\frac23}$ was plotted. ...
0
votes
0answers
28 views

Twin Prime Max Gaps

Ok, let's build a foundation here: A common way of testing primality, is dividing by all primes smaller than the number's square root. For instance, $97$ is prime because dividing by none of the ...
0
votes
1answer
11 views

MLE for Parameter Estimation using Mathematica

I am using Mathematica (MMA) 10.0.0.0 with MathStatica do determine parameters using MLE for several PDFs. I have tried the approach below for several PDFs but I keep getting messages that Mathematica ...
-1
votes
1answer
28 views

How to find the Limit of two variable using mathematica ?

I was wondering if there is a method to solve the limit of two variable using Mathematica , I try to do this Limit[(x^4+y^2)/(x^2+y^2),(x,y)->(0,0)] Limit[(x^4+y^2)/(x^2+y^2),x->0,y->0] but non of ...
0
votes
0answers
9 views

Dynamic array for defining function.

I wanted to define a function in mathematica.For example Shifted Schur function, so I wander if there is a way to define a dynamic array that is to take a vector $\lambda=(\lambda_1,\lambda_2,...,\...
0
votes
2answers
52 views

What does the terminology “characteristic polynomial” mean?

In the documentation of the command "MininimalPolynomial" in Mathematica it says "Find the characteristic polynomial of Sqrt[2] over the extension E^(I Pi/4). The code: MinimalPolynomial[Sqrt[2], x, ...
0
votes
0answers
21 views

How to obtain an analytic approximation of this wavelet-looking function?

I would like the approximating function to be infinitely differentiable. I have tried fitting (1) a polynomial and (2) a combination of sin, cos, and exp functions to approximate the function shown ...
1
vote
0answers
21 views

Symbolic Constrained Optimization in Matlab or Mathematica

I hope you are having a nice day. I am learning MATLAB at the moment and the best way for me to learn is to use it to tackle some of my problems. I am currently trying to solve the following problem ...
0
votes
0answers
15 views

Plotting data with error bars with gaussian distributed error

I want to fit a straight line model of the form $y_i = a+ b\ x_i$ to the list of $(x, y)$ pairs given below. How can I plot the data with error bars in both coordinates? ...
0
votes
0answers
40 views

One dimensional integration that Mathematica cannot do

I want to evaluate $$\int_{a+b-c}^s\,\text{d}x\, \frac{(-x+ab/c)^{\epsilon}}{(x+c-a-b)^{\epsilon+1} (a-x)},$$ where $a,b,c,\epsilon$ are real numbers, and to be treated as constants in the integration....
7
votes
3answers
957 views

Finding good approximation for $x^{1/2.4}$

I would like to a good (8 bits accuracy) approximation for $x^{1/2.4}$ in the range $[0, 1]$. This transform is used for converting linear intensities to SRGB compressed values, so it's important that ...
1
vote
0answers
49 views

ODE with Reflection

Some Background: I come from a computer science background and differential equations was not part of my course work. I'm still in contact with my professor that I ...
1
vote
1answer
59 views

What does the comma mean between two matrices represent?

For example [A,B] ? It has been many years since I needed to know.
1
vote
0answers
19 views

How do I extract the factor in Mathematica

If I get a equation $\left(\left(1-s_K\right) K^w+\left(1-s_L\right) L^w\right)\left(4 b a_m-4 a+2 b \tau +c \tau n^w-2 c n \tau \right)-\left(s_K K^w+s_L L^w\right)\left(4 b a_m-4 a+2 b \tau -c \...
0
votes
1answer
27 views

Double integral multivariable calculus

Consider the following integral $$\int_0^1 dx_1 \int_0^{1-x_1} dx_2 \, (1-x_1-x_2)^{-\epsilon-1} (-sx_2 - x_1p_1^2)^{-\epsilon-1}$$ where $s$ and $p_1^2$ are to be treated as constants throughout the ...
1
vote
2answers
59 views

Different eigenvectors obtained with Mathematica

Suppose that we have a matrix $$ \begin{pmatrix} a&c\\c&b \end{pmatrix}. $$ The eigenvalues of this matrix are given by $\lambda_1=(a+b-D)/2$ and $\lambda_1=(a+b+D)/2$, where $D=\sqrt{(a-b)^2+...
6
votes
1answer
135 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 u-...
3
votes
3answers
107 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 ...
0
votes
1answer
41 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
40 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
27 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 ...
5
votes
2answers
717 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) = \...
0
votes
0answers
32 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
31 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 ...
0
votes
1answer
71 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 ...
2
votes
1answer
547 views

How to use Mathematica to solve equations in a polynomial ring?

I am sorry. But I wonder whether it is fine to ask this question here. I need some help to solve some equations in a polynomial ring: Give the ring $\mathbb{F}_p [x ]/(x^2+x+1)$, where $p$ is a ...
0
votes
1answer
39 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
62 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
94 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
30 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 ...