# Tagged Questions

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.)

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### 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 ...
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### 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) &...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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? ...
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### 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 ...
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### 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\, \...
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### 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 $77$ ...
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### 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, ...
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### 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 ...
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### 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 ...
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### 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? ...
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### 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....
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### What does the comma mean between two matrices represent?

For example [A,B] ? It has been many years since I needed to know.
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### 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-...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...