# Tagged Questions

This tag concerns computational problems central to mathematical and scientific computating. The scope includes algorithms, numerical analysis, optimization, and linear algebra, computational topology, computational geometry, symbolic methods, and inverse problems.

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### Even natural numbers are sums of two primes with twins or of two primes without twins

I seems to be very few even numbers that can't be written as a sum of two primes with twins or as a sum of two primes without twins. That is, suppose that $\mathbb P'$ is the set of the primes not ...
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### Finding all real roots of an equation

I am looking for a computational method to find real roots of a function. The function looks like this: $$F(x) = \sum_{i=0}^n \frac{k_i}{\sqrt {(x - x_i)^2 + c_i^2}}.$$ I would like to use something ...
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### Finding generators for a polynomial ideal given some polynomials belonging to it

Let $k$ be a finite field, $n$ a positive integer and $R := k[x_1,\ldots,x_n]$ the polynomial ring in $n$ variables. Let $f_1,\ldots,f_n\in R$ be polynomials with the following property: $f_i$ has ...
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### Counterexample 3n + 1 problem (Collatz) Exponential and linear Diophantine equation

So, I have found a sufficient condition (not necessary) for finding a counterexample to the 3n + 1 problem, namely the existence of solutions for the following two-parameter family of Diophantine ...
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### Book that helps recognizing underlying mathematical expression of numerical results

I strongly remember having seen a couple of years ago a huge book that only consisted out of an enormous table over hundreds of pages containing approx. 10⁵ numerical results in ascending order with ...
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### Is a possible use of a Mill's constant the encapsulation/encryption of messages?

I wonder if the way that Mill's constant is defined could provide a good data encapsulation and encryption method if instead of encapsulating primes, for instance a simple ASCII message is ...
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### Discrete Fourier transform - seemingly different definitions

I've noticed that in most sources the definition of the DFT is given by $$F_k = DFT\{f_n\}=\frac{1}{N}\sum\limits_{n=0}^{N-1}f_nW_N^{-kn}$$ where $W_N$ is the $N$th root of unity and $0\le k \le N-1$. ...
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### Lyapunov exponent of multiple time series

I have multiple time series data that I have generated by varying the initial conditions infinitesimally. I now want to calculate the Lyapunov exponent to identify the sensitivity to initial ...
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### Fastest point-plane distance in $R^3$

Many questions regard computing the point-plane distance, my question in borderline with computer science, though. What is the fastest way of computing in $R^3$ the point-plane distance, with ...
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### references for concrete computations in Lie groups for abstract toplogical concepts

A Lie group is a smooth manifold whose tangent space at its origin is its Lie algebra. Taking an example for lie group such as SL(2), and due to above facts we should then be able to translate the ...
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### Number of $N$ formed from the set of points

Given $k$ points on 2d plane, I need to find the number of $N$ shaped figures from these $k$ points. lets consider four different points from the set and name them $A$, $B$, $C$, and $D$ (in that ...
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### Find all vectors with magnitude between $n-\delta$ and $n+\delta$

I am working on an program to compute the structure factor of a given configuration of 3D points, and I need an efficient algorithm to generate all the possible 3D vectors with integer coordinates and ...
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### How to find a modulus equation? [closed]

Let $x$ and $q$ be an integer.Also, $a$ and $b$ are integers. We know the two modulus equations. i) $x \equiv y$ mod $p^a -1$ ii) $x \equiv z$ mod $p^b -1$ Then how to find $x$? Can we find $x$ ...
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### The eventual advantage of a primality test without known exceptions

The primality test of Fermat with base $2$ seems to be as secure as the computer hardware for testing numbers big enough. However, I think there are an infinite numbers of false primes using this ...
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### Is the cohomology ring of a CW complex computable?

There is a well-developed technology for computing the cohomology groups of a CW complex, cellular cohomology. It reduces the problem of computing cohomology to the two simpler problems of (1) ...
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### How to define a variable which is an integral involving cauchy principal value inside?

How to define a variable which is an integral involving cauchy principal value inside in any computer programming language? I want to know how to break down the procedure step by step from a ...
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### Is there an alternative way to represent the $\operatorname{diag}$ function?

In optimization, it is common to see the so called $\operatorname{diag}$ function Given a vector $x \in \mathbb{R}^n$, $\operatorname{diag}(x)$ = $n \times n$ diagonal matrix with components of $x$ ...
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### Generating all prime powers $\leq N$

Some very good algorithms exist to generate all primes $p$ up to some bound $N$, like the sieve of Erastothenes and the sieve of Atkin. However, suppose I want to generate a (sorted) list of all prime ...
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### Mysterious functions

I originally asked the following question in stackoverflow, but the question is closed because some members meant that the question is about math(see the following thread) So I will give a try here: ...
Is it true that if we are given a number system with base 3, mantissa 2, $-1 \le p \le 1$, determined by $$\pm 0.d_1 d_2 \times 3^p$$ where each number is normalized, unless it is zero, then the ...
For each odd prime $p$ there exist $n\in\mathbb{N}$ such that $p\equiv n^2 \text{ (mod }\varphi(n^2))$, where $\varphi$ is Euler's totient function. I'm developing my Forth based computational ...