An algorithm is a sequence of well-defined steps that defines in abstract the solution to a problem.

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2
votes
3answers
165 views

Given a list of triangle vertices, how to find the neighbors for each vertex?

A triangle is represented by {a,b,c}, indicting that its vertex IDs are a, b, and ...
6
votes
1answer
172 views

How to do automatic differentiation?

Does Mathematica have any AD functionality or does it only support symbolic differentiation? If not, are there any packages or other third party implementations available? Edit (J. M.) Here is an ...
0
votes
1answer
53 views

A question about the syntax [closed]

I have $3$ elementary questions to ask and I thank you in advance. Question N┬░1. What is the right syntax for $$y\equiv0\pmod {2}$$ in the code below? ...
2
votes
1answer
138 views

i need a swap mutation code (genetic algorithm) in Mathematica?

I'm working on GA coding to optimize the locators position in fixturing system to minimize the error in precision manufacturing.I need a code for mutation (genetic algorithm) in Mathematica. Here, I ...
7
votes
1answer
119 views

Challenging matrix sorting request?

I have an application in mind, and I need to do the following analysis, but am having a high degree of difficulty conceptualizing it in terms of syntax. I understand what I want, but cannot seem to ...
1
vote
1answer
262 views

Efficient algorithm to generate a basis for exact diagonalization

The problem is described as follows: I need to generate a basis(matrix) in lexicographic order. For two different basis vector $\{n_1,n_2,\cdots,n_M\}$ and $\{t_1,t_2,\cdots,t_M\}$, there must exist ...
6
votes
1answer
375 views

Efficiently find all connected subgraphs

Is there a way to generate all the connected subgraphs of a graph in mathematica without going through all the subsets of the nodes and checking if the subgraph is connected (which will be ...
7
votes
5answers
1k views

Check if a matrix is Positive Semidefinite

I have a question concerning the check whether a given matrix is positive semidefinite or not. In mathematica the function PositiveDefiniteMatrixQ[m] tells me ...
2
votes
1answer
197 views

Using the Baby-Step Giant-Step algorithm

Here is a concept I am working through: As part of an attack on an El-Gamal cipher, solving the discrete logarithm problem $$10^x = 532107 \;\, {\rm mod} \;\, 1313839.$$ Using the ...
4
votes
3answers
854 views

Computing Gaussian curvature

Can Gaussian curvature $K$ be computed from WolframAlpha or any other available Mathematica program? Please indicate the program or its reference. If input ...
0
votes
0answers
69 views

3-adic FFT algorithm

I am trying to implement the FFT algorithm when $n=3^k$, but maybe my code is wrong. Are there any suggestions for improving my code? ...
0
votes
0answers
50 views

Recursive method for the SR1 correction

I am looking to program a recursive formula for implementing the Symmetric rank-one correction. I am not sure exactly where my program fails. Every value is correct except the value for ...
1
vote
0answers
237 views

Integration of graphs with datasets

Mathematica has a rich family of graph algorithms. I would like to leverage some of these for a very large tree structure. Because of the size of the structure, I would like to store it in a Dataset ...
3
votes
2answers
158 views

Replace missing data

I have vectors of equal lengths where I want to replace the zeroes (missing data) with their preceding values. So far I have written: ...
3
votes
1answer
288 views

Spectral Clustering

I am attempting to implement a spectral clustering routine using Mathematica, but I am encountering difficulties. Using the standard Gaussian similarity function found in section 2.2 of this paper ...
1
vote
0answers
147 views

How to write my own interpolation method [duplicate]

I was comparing results of spline interpolation in Mathematica and C++/gsl-library Results of interpolation are different if I use ...
2
votes
0answers
103 views

AVL binary search tree implementation

Is there any text-book implementation of self-balancing binary search trees such as AVL or red-black in Mathematica?
2
votes
1answer
131 views

Maximizing the number of zero entries in a matrix

I have a matrix with a bunch of parameters in its entries, they all come in different combinations in different places of the matrix. I can post the matrix itself if requested, but I think what I mean ...
-1
votes
1answer
46 views

Algorithm in Module behaves different [closed]

In my Notebook i wrote this algorithm: ...
5
votes
4answers
623 views

Efficient way to sum all the primes below $N$ million in Mathematica

Today, I saw a problem described as below: Sum all primes below $N$ million At the beginning, I feel it is rather simple to calculate it in Mathematica ...
26
votes
7answers
1k views

Splitting words into specific fragments

I am looking into splitting words into a succession of chemical elements symbols, where possible. For example: Titanic = Ti Ta Ni C (titanium, tantalum, nickel, carbon) A word may or may not be ...
3
votes
2answers
2k views

How to linearize an expression automatically?

I would like to automatically linearize some long equations in the scope of variational calculus. Here follows an example of what I need to do : Given two variables $a_1 = q_1 + \delta q_1$ and $a_2 ...
5
votes
4answers
722 views

A too complicated lookup

I have the following keys: nm = {"bay", "ica", "rat", "tat", "dax", "dow", "sp5", "nas", "mean", "total"}; which I want to use to find a corresponding entry in ...
5
votes
3answers
147 views

Unragging a matrix

Today I ran into matrices like this one: ...
25
votes
7answers
755 views

Faster position list construction from a “take instructions” list

Take some list, e.g., {1,2,3,4,5}, and a "take instructions" list, say {1,1,2,1,1}. The latter is read as "take the first ...
2
votes
2answers
54 views

Count elements between matching opening and closing parentheses?

Suppose I have a List of the form: lst={"(", "x1", "x2", "(", "(", "x3", ")", "x5", "(", "x6", ")", ")", ")"} For each pair ...
10
votes
5answers
781 views

Match opening and closing parentheses?

Suppose I have a List of the form: lst={"(", "(", "(", ")", "(", ")", ")", ")"} By running ...
6
votes
1answer
391 views

How can I compute the chromatic index and number of a graph?

I saw a recent question from M.R. and realized there is no function to compute the chromatic index and number of a graph, other than a really slow method in the now deprecated Combinatorica. So, how ...
3
votes
1answer
156 views

Stochastic Predator-Prey model using Gillespie's SSA

I'm trying to model the predator-prey situation using SSA. I am very new to Mathematica so my handling of matrices is probably terrible, and that's probably adding to my confusion: ...
2
votes
2answers
68 views

Efficiently or Elegantly construct linear graph list from vertex pairs

I am processing MRP data, with BOM relations as pairs of part number strings. I want to construct lists that represent the linear graphs defined by these pairs. Here is some code to generate random ...
1
vote
0answers
100 views

Implementation of Lubaehevsky-Stillinger Algorithm to pack hard spheres

To generate a model of a polycrystalline material with specified grain size distribution (e.g coming from a Monte Carlo Grain Growth simulation) the Paper "Effects of grain size distribution and ...
1
vote
1answer
420 views

Code efficiency improvement needed solving problem 499 in Project Euler

I am trying to solve https://projecteuler.net/problem=499 by constructing a transition matrix and finding its steady state. Here is my code: ...
16
votes
7answers
705 views

Enumerating tuples from a larger space such that all pairs of values are present at least once

I am trying to write a function that will accept a list of N lists and returns a list of N-tuples that represent all pairs of values from the original N lists at least once. To illustrate with an ...
1
vote
0answers
171 views

How can I detect certain letters by shape in an image? [closed]

I have a website where people can post Flipbook animations, called Flipnotes. Unfortunately, most of the Popular flipnotes are in the following categories: MV (Music Video) AV (Audio Video) AMV ...
2
votes
0answers
116 views

How to compute the longest non-contiguous common sequence?

LongestCommonSequence[] works well, but what about finding the longest common sub-sequence (not necessarily contiguous)? Is this function built in to the genome ...
15
votes
3answers
272 views

Partitioning with constraints on subsets

Given the following data: constraints = {{11, 2}, {11, 3}, {11, 4}, {11, 6}, {11, 9}, {1, 6}, {5, 6}, {2, 5}}; weights = {3, 7, 3, 2, 4, 2, 2, 2, 3, 2, 1}; I ...
4
votes
1answer
157 views

How to execute a notebook in background

I am developing an algorithm that take time to return results. I thought if I could run this notebook in background and continue to develop the rest of my work. It is possible to do that?
23
votes
7answers
830 views

Alternative ways to implement a triangular recursion

Triangular recursions are a class of algorithms that frequently turn up in computational mathematics. These recursions are expressible in the general form ...
3
votes
3answers
83 views

Generating increasingly longer lists from a single list

I start with an array such as {{1,1},{0,1},{-1,1}}. (1) I want to create an array from this which replaces each array inside the array with 3 new arrays, one ...
6
votes
2answers
417 views

Pruning elements in an array based on the existence of similar elements in adjacent arrays

Imagine I have a series of particles floating around in $\mathrm{R}^3$, where, at any given time, particles can pop into and out of existence. Here, for some number of time points, $(t_1, \dots, ...
2
votes
1answer
146 views

Neighbourhood - Calculations

SeedRandom[0]; n = 5; (m = N @ RandomInteger[{1, 3}, {n, n}]) // MatrixForm result1 = MeanFilter[m, 1] // MatrixForm ...
55
votes
3answers
28k views

How to create a new “person curve”?

Wolfram|Alpha has a whole collection┬╣ of parametric curves that create images of famous people. To see them, enter WolframAlpha["person curve"] into a Mathematica ...
11
votes
5answers
1k views

How to deal with recursion formula in Mathematica?

In engineering problems, I am always seeing many recursion formula. For instance, In the book "The NURBS book", I discovered many recursion formula Fibonacci ...
12
votes
2answers
297 views

Temporal database reconstruction in mathematica

<EDIT> after some internet research I found the database domain that deals with this kind of thing: Temporal Databases. I think my question therefore becomes how to reconstruct a temporal ...
2
votes
3answers
66 views

Reconstructing an expression [duplicate]

I have a nested expression like this one expr = Tan[Sin[Cos[x]]]; I can deconstruct it with ...
5
votes
2answers
202 views

Graph expansion on Mathematica

Is there a way by which Mathematica can be given a graph as an input and be asked to find its expansion? Note: By "expansion" I mean the quantity called "isoperimetric number" or "Cheeger constant", ...
8
votes
3answers
318 views

Random Integer Sequences

I want to construct a random square matrix in the following manner: a) Three states [0 | 1 | 2] are repeated ...
14
votes
2answers
515 views

Better way to test that a matrix is upper-triangular?

Today, I got to thinking about how to test that a matrix was upper-triangular. So I had a try at it. Algorithm $\quad \quad a_{ij}=0 $ Or $i \leq j$ $\Rightarrow$ $True$ My solution is ...