# All Questions

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### Archimedes' Scheme to find $\pi$

Given an Archimedes' scheme $$a_{n+1}=\frac{2a_nb_n}{a_n+b_n}$$ $$b_{n+1}=\sqrt{a_{n+1}b_n}$$ with initial values $a_0=2\sqrt{3},b_0=3.$ How do I prove using Mathematica that this converges to ...
450 views

### Is there a method to send different Cell evaluation to different core?

I am running Mathematica on a computer with multi CPU and every CPU has multicore. I am wondering if there exist a method to send different cell evaluation to different core? So if I already have a ...
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### Force NDSolve to use finite difference

How to force NDSolve to use finite difference instead of FEM. I have the following code: ...
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### Mathematica doesn't save my work

When I save my work and close Mathematica, usually it's not saved, it won't save a my work,despite that it asks where to save the file. Sometimes it creates an empty notebook only.
173 views

### What's wrong with naming a rule?

Please have a look at the code below. The second Manipulate uses the name rl of the replacement rule given in the first line, ...
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### How to enlarge a specific part of a graph using Plot Command?

How to enlarge the closed curves of any Graph and Show them in a separate Graph within the ...
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### CompiledFunction::cfsa Argument x at position1 should be a machine-size real number [on hold]

I have a compiled function: g:=Compile[{{x, _Real}},...] and call g through an interim function: g2[x_?NumericQ] = g[x] If ...
42 views

### Why is FindCycle crashing for this graph?

I'm working with a directed graph, previously mentioned in Exporting a high-resolution GraphPlot of a very large graph (65,536 nodes). It can be generated with the following code: ...
70 views

### Evaluate pure function through round brackets

In have some matrices of pure functions or numbers which I multiply by other matrices or vectors. I would like the functions to be evaluated in the result, but all that I get is something like this: ...
62 views

### unordered lists with maximum dispersion [on hold]

As you can implement the following I have a list $$L = {p1, p2, p3, p4, p5 ........ pn}, n <50$$ I need cluttering and print this list 4 ...
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### Exporting a high-resolution GraphPlot of a very large graph (65,536 nodes)

Problem I have a very large graph of 65,536 vertices. GraphPlot yields: But the vertices are too dense to see in any detail, and attempting to use any of the ...
98 views

### Seeing coordinates in Graphics3D

I'm writing some structures built up from different strings that specify the coordinates of the lines. The code used to generate these is built up from a ton of user defined functions from my library, ...
228 views

### Find all roots of a function with parabolic cylinder functions in a range of the variable

I want to find all roots of a function involving Parabolic Cylinder Functions. In what follows, I define 2 variables $\xi1$ and $\xi2$, which in turn depend on $\omega$. My function is then defined as ...
115 views

### Definite integration in mathematica

I tried to integrate the following in Mathematica. $\int\limits_{-\infty}^\infty\cfrac{\text{e}^{\text{i}ax}}{x^2-b^2}\text{d}x$ where $a,b>0$ The analytical result is well known. ...
135 views

### Is it possible to get the (x, y) position of nodes in a Graph?

Given a graph... RandomGraph[{20,40}] ...is it possible to retrieve the (x, y) coordinates at which the nodes are drawn? ...
58 views

### Recreating a ContourPlot3D using points

Let's define a three-dimensional surface ...
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### PolynomialExtendedGCD in 2 variables

Consider a field $R$ and the ring $A=R[y]$. Consider two polynomials $g,h\in A[x]$. I want to obtain $d=\gcd(g,h)\in A[x]$ and two polynomials $s,t\in A[x]$ satisfying the Bézout relation: $sg+th=d$. ...