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# Questions tagged [functions]

Questions about the use of built-in Mathematica functions, including pure functions.

401 questions with no upvoted or accepted answers
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### Performance problems in new Sequence functions

The new-in-10.1 Sequence* family of functions should provide newly optimized methods for handling sequence problems. Happily in some cases they do! For example ...
161 views

All these functions seem capable of doing the same things: Import, URLFetch, URLSave, ...
186 views

### Is there a documentation generator for Mathematica?

I'm looking for a way to document the functions of my packages inline, preferably inside comments. There should be a Doxygen type tool for this that takes comments and that generates html from markup ...
247 views

### Performance of pure function - Best way to define a function?

In general, to define a function, we often use f[x_]. Another way is to use pure function (full form and shorthand). I want to test the performance of these ...
145 views

### Exceeding recursion limit with no obvious recursion: Optional pattern-matching causing nonlocal behavior

So, I've come across something strange, and wanted to get a deeper understanding of what was going on. Consider the following code: ...
244 views

### What is the difference between GenerateDocument and TemplateApply[NotebookTemplate[

Bug introduced in V10.0 and persisting through V10.4 Since V10.3 the bug still remains but additionally the Genarate and ...
255 views

### Finding periodic cycles of a function

Given a function f[{x,y}] it is rather simple to use, for example, NSolve to find periodic points of period $n$. We simply take ...
151 views

### A Curiosity: What is DispatchQ?

As shown below, my autofill in Mathematica showed an interesting function: DispatchQ. Yet, it does not appear in the Mathematica Documentation Center, a search for ...
637 views

### Totally Antisymmetric Function

My current implementation for a totally antisymmetric function is like this: ...
98 views

### When does Root have a third argument

In Mathematica "11.0.1 for Microsoft Windows (64-bit) (September 20, 2016)", Root[#^4 + 1 &, 2]; actually has three arguments, as can be seen from ...
122 views

### Different behavior of Power between versions 9 and 10

Rather by accident I've noticed that the following trivial code produces different output in Mathematica 9 and 10: -((-1)^n) Mathematica 9: $-(-1)^n$ ...
263 views

### Strange Integrate behavior (a bug!)

The following two calculations should give the same result. After all, integration is a linear operation. I have pasted the code below in case you want to play with it. ...
84 views

### How to specify halting states when using function TuringMachine?

The function TuringMachine generates a list that represents the evolution of a Turing Machine given a rule that specifies its behaviour (i.e. set of instructions). For example, the following rule ...
83 views

### How to know the string data/settings, of some options/functions

It is known that several functions and options take some sort of input in this form: option->"something" function["something"] The simple example for this is ...
93 views

### Is there something like MaxProcessorUsed?

For standard procedures it is easy to test if the implementation is better or worse than other by using Timing etc. It does not help us with creating ...
35 views

### Efficiently threading with a default value for missing parts / defining custom behavior for addition of expressions with a given head

In short, I would like to be able to "add" expressions with a particular head (call it h for our purposes) which will always appear with a sequence of (...
173 views

### How to perform feature selection for machine learning applications?

Feature selection is fairly easy in e.g. Python's scikit-learn which sports a module and tutorials or MATLAB. Mathematica even touts that it uses feature selection ...
67 views

### Cannot access ColorFunction in ListVectorDensityPlot

Working on a vector field, I'd like to use a ColorFunction dependent on both the vector direction and its norm. According to the documentation of ...
201 views

### FindGeometricTransform not working properly for a simple problem

I am surprised why FindGeometricTransform is failing to automatically register or align two sets of points that are drawn from a ...
95 views

### Are functions labelled "experimental" to be avoided while writing code?

A number of functions are currently labelled "experimental" on the official Wolfram Language Documentation Centre. (An example is AskFunction, which appears to be especially suited to my specific ...
114 views

### Order of evaluation of FunctionDomain, Reduce, Solve, etc

For the input (mine is much more complicated, this is a toy example): x/x /. x -> 0 the output of 1 (as opposed to ...
174 views

### RealDigits and functional style

So while thinking about Replacing numbers of which you only know certain digits I have faced, again, a problem that I find hard to extract from RealDigits' output ...
114 views

### Why does FromDigits transpose its argument (sometimes)?

a = {{1, 2}, {3, 4}, {5, 6}} ; FromDigits /@ Transpose@ a == FromDigits @ a (* True *) The only "strange" syntax I've found in the docs is But it doesn't ...
272 views

### Input List of Images into a cloud deployed API function

I'm new to APIFunction and CloudDeploy, but essentially, here's my situation: I have a function (let's call it ...
108 views

### Using an external Pattern breaks Format

I noted while writing this answer that using an external Pattern on Format doesn't work: ...
484 views

### Extracting an equation from an interpolated function

Im trying to use LibraryLink to do some calculations in C but part of the expression i want to calculate is an Interpolating Function. C cant use that obviously so I'm trying to shift it to a data ...
339 views

### Strange behaviour of MMA in derivatives of some standard functions

There are some peculiar things to be discovered in derivatives of some standard functions in MMA: Strange behaviour Example 1: Abs We have ...
157 views

### Make Mathematica show function template's arguments in different lines (i.e. in column) by default?

I feel a bit uncomfortable with Mathematica 10's layout. I mean, I'm impressed how powerful functional programming can be and so on, but it's me or those programs are often just a bunch of nested ...
103 views

I would like to obtain a "slick" implementation of A*-search algorithm on Graph objects, using the built-in BreadthFirstScan (if that is possible at all). I noticed that BreadthFirstScan is static in ...
189 views

### Gather dependency on list order?

I get intrigued about Gather behavior on this post. I thought that Gather was invariant under list order? Here is the result I ...
431 views

In order to make my computations faster I have developed a C/C++ application calling Mathematica kernel and performing many operations using Mathematica functions for equation solving. Now I want to ...
52 views

### How can one automatically arrange the connections of a circuit with as few crossings as possible, given a set of edges?

Here are two functions to create symbols of dc voltage source and a resistor. ...
190 views

### Using new FoxH function to solve a trinomial equation. Possible issue?

There is a possible issue on solving the following trinomial equation $$x^\alpha+x=y$$ for real $x,y,\alpha$. From Belkic , it is known that for $\alpha>1$ a solution is found using the ...
57 views

### Definition of large expression - makes PC freezed

In A=Range[10^4];?A Out (* definition of A*) It works for 10^4. But if I increase the number to 10^6 ...
60 views

### Differences between u[x,y,t] vs. u[x,y][t] vs. u[x][y][t]

Is there any difference between defining a variable by u[x,y,t] or u[x,y][t] or u[x][y][t] ? ...
103 views

### InverseFunction doesn't work well with ConditionalExpression

I have a polynomial constructed with InterpolatingPolynomial. It is not a one-to-one function but I want to have its inverse on some range where it is monotonously ...
182 views

### How to call an old build-in function in a new version of Mathematica?

In order to use the UnitStep of Mathematica 5.2, I have to install two different versions 5.2 and 11.3 at the same time because ...
54 views

### Conditional application of a function (looking for a built-in solution)

Is there a built-in function which will apply a function f to x when test yields true? A ...
97 views

### Applying a function along the desired dimensions of a n-dimensional array

I am trying to apply an arbitrary function f that takes several inputs and returns a scalar along some specific dimensions of an n-dimensionnal array. Here is an ...
121 views

### Monitor CUDA function

Is there a way to monitor CUDA function without bringing much performance reduction. For example, Map can be monitored by ...
223 views

### Generating function for Newton series?

The function GeneratingFunction gives generating function for Taylor series. Is there a similar function for Newton's series? $$f(x) = \sum_{k=0}^\infty \binom{x}k \Delta^k [f]\left (0\right)$$
535 views

### Speeding Up Image Processing Functions

I am working with stacks of 1024x1024 timelapse microscopy images that I am performing a series of image processing functions on to help segment each image. These functions include ...
1k views

### Slow mixture fitting when having ill-conditioned covariance matrices. How to make it faster?

I'm using Mathematica 9.0 to fit multidimensional observations with a gaussian mixture. To do so I first adapted these steps to ensure that the mixture parameters are well defined (see https://...
378 views

### Do a gauge transformation for a Chern-Simons theory?

Suppose we have the following Lagrangian density:  L=\epsilon^{\mu\nu\rho}\big(\sum_a A^a_{\mu}(x) \partial_\nu A^a_{\rho}(x)-\sum_{a,b,c}\frac{1}{3} f^{bca} A^a_{\mu}(x) A^b_{\nu}(x) A^c_{\rho}(x)...
109 views

### Finding the argument set for internal functions in Mathematica v9.0

I've recently run into a problem with importing TIF stacks in Mathematica: Slow import of multigigabyte TIF image stacks On the advice of Simon Woods and others, I've been looking into the behavior ...
144 views

### ProbabilityDistribution PDF on boundary points

I would like to evaluate the PDF of a custom ProbabilityDistribution at the min and max values. However, PDF[...] returns 0 at ...
47 views

### Mathematica Implementations of Post Quantum Cryptography Algorithms?

Mathematica supports several cryptographic commands like Encrypt, Decrypt and others. This includes support for asymmetric signature ciphers like RSA and Elliptic curves and symmetric ciphers like &...
53 views

### Is it safe to alias a ResourceFunction with a symbol of the same name?

The following will show how easy I alias Ding which is my very first ResourceFunction and it works very well. ...