# Questions tagged [computational-complexity]

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### Simplify expression: overcome a barrier in the complexity function

I would like to simplify x=n[a] f[b, a] + f[a, b] using 2 rules ...
122 views

### Check if list is singleton in sub linear time

A singleton is a list whose elements are equal. Some ways of checking this in Mathematica: {Equal@@#&, 1==Length@Union@#&, MatchQ[#,{x_ ..}]&} I ...
2k views

### Is there a way to do Quantum Computing in Mathematica notebook?

I saw 2 efforts in that direction: WSS17 and WSS16, but I am not sure if there is something in the latest Mathematica that actually allows users to simulate quantum gates. Can anyone please point me ...
64 views

### What's the time / space complexity of pattern matching?

For example, in ReplaceAll[expression, pattern], what are the main algorithms used internally? How does the asymptotic time / space complexity scale with the length ...
171 views

### How to calculate the complexity of summation [closed]

I am trying to calculate the computation complexity of an algorithm and I have reached the following summation (that shows the number of operations) and I don't know how to find the Big O. (H is a ...
234 views

### SparseArray: accesing nonzero row and column entries

I have an enormous $m\!\times\!n$ sparse matrix $d$ with $l$ nonzero entries, stored as d=SparseArray[{{i1,j1}->w1,...,{il,jl}->wl},{m,n}];. How do I access ...
132 views

### Cutting digits of a number without approximation:

I am evaluating an exponential and I end up with the following result: $1.4497788553129478854329$ Is there a command on Mathematica that allows me to cut my result without approximating it? I would ...
40 views

### Measuring space complexity? [closed]

I like using GeneralUtilities function BenchmarkPlot for estimating time complexities, is there something similar for ...
26 views

### Is there a better way : solutions to integer equation

I have the following code which solves for Integers the equation $$a_1+a_2+a_3+a_4+b_1+b_2+b_3+b_4+c_1+c_2+c_3+c_4=tot$$ with $$-4<a_i\in \mathbb{Z}<4$$ $$-7<b_i\in \mathbb{Z}<7$$  -4&...
41 views

### Finding ponts closer to each other than a given distance

As a working example let's assume that we are given a list of points in the unit square (say by RandomVariate[UniformDistribution[{0, 1}], {20, 2}]). I want to ...
149 views

### How can one expand an arbitrary boolean combination into the $2^n$ atoms of the associated boolean algebra of size $2^{2^n}$?

The answer of user250938 to Can one usefully apply the Boolean functions of Mathematica to measurable Boolean sets? and the second comment of Monroe Eskew to the answer to https://mathoverflow.net/...
39 views

### Speed up Multidimensional numerical integration

I have the following 9-D integral, where the domain of integration is a nine-dimensional hypercube of unit length. The problem is that Mathematica takes too long to evaluate this. Is there any ...
80 views

### How maximaze very complex problem in a few hours using some server?

I need to execute a code that runs a maximize function built-in function with symbolic variables. The problem is that my computer has not enough memory (has 4 GB of ...
53 views

### How solve this system of trigonometric equations?

I have the following system of equations: (substituting any real values for a,b,c,r,Alpha,Beta will return the same answer for x) ...
76 views

### Evaluation taking extremely long

I am trying to solve the following: ...
85 views

### Computing a difficult integral which is taking too long

I am trying to solve the following code: ...
70 views

### My plotting comes out to be gray not coloured using AbsArgPlot function in Mathematica. What is the reason for not getting a coloured graph??h

My graph comes out to be gray, not coloured using AbsArgPlot function in Mathematica. What is the reason for not getting a coloured graph or what I can deduce from ...
34 views

### Handling large data generated by a script file (using parallelization in Mathematica)

I want to write a script file Script_file.m which I am going to run on a server and collect all the data in a file named ...
33 views

### Numerical errors in compiled function involving real and complex numbers as output

I am trying to use the Compile command in Mathematica to reduce the computation time because of its fast execution within Mathematica and ability to use the ...
41 views

### Diagonalization of Hermitian Matrices vs Unitary matrices

What are the differences involved in diagonalization of large Hermitian matrices and Unitary matrices? (>5000 x 5000) Mathematica seems to diagonalize Hermitian matrices almost 20 times as fast as ...
35 views

### Computation of operation count for the numerical evaluation in Mathematica

Is there any way to find the complexity of computation in Mathematica? There is a command in Maple that computes the number of multiplications, storage, and assignments. Is there any similar command ...
70 views

### Minimizing computation time

I'm having issues with reducing the computation time of a NMinimize function. I've tried setting the WorkingPrecision and N and ...
85 views

### Ways to decrease computational time

I have created a 2D axisymmetric simulation of the motion of charged particles in an electric field. The electric field is created by a needle attached to a top plate both of which are at -3800V with ...
20 views

### AsymptoticLess function confusion

I have an algorithm which complexity is: ...
I have the following code which is supposed to return me the arguments for $l1,k1$ that maximize the function $fsub$, subject to constraints. I need the answers algebraically as functions of the other ...