# Tagged Questions

Questions about Mathematica's functional programming style, including the use of pure functions (Function[], #, &) and functions such as Map, Apply, Nest, and Through.

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### How to make a custom function as inbuilt

I have a custom function like following: ...
2answers
58 views

### How to transform the $y$ values in a list of $(x,y)$ pairs [duplicate]

How can I transform data = {{1, 0}, {0, 1}, {1, 1}} to {{1, f[0]}, {0, f[1]}, {1, f[1]}} This is similar to ...
5answers
206 views

### Transforming a list of the form {{{x, y}, z}, … } into the form {{x, y, z}, … } [duplicate]

This should be a fairly simple question, but I can't figure out how to do it. I have a list of points of the following form: ...
1answer
197 views

### Alternatives to For/Do Loop to optimize indexing Matrix

I am trying to optimize my code that searches for elements in the rows of matrix that are greater than 0. Then use that position to grab the element from other matrix. I use the do loop to iterate ...
0answers
21 views

### Express anonymous with formal parameters [duplicate]

I'd like to express the function F = Function[{#2[[1]] + #1[[2]]/#1[[1]], #2[[2]] + 1/#1[[1]]}] using explicit formal parameters. I've tried ...
1answer
39 views

### Define inverse Laplace operator as map from functions to functions

I am trying to implement the inverse Laplace operator through P[g_] := h /.NDSolve[{h''[x] == g[x], h[0] == 0, h[1] == 0}, h, {x, 0, 1}][[1]] If I now define ...
0answers
35 views

### Which the functions of parameters can use Span [closed]

As I know,ImageValue,PixelValue,ReplaceImageValue,...
2answers
45 views

### How to round all the numbers in a function?

I have a complicated function that is a combination of floating-point numbers and variables. I want all the numbers rounded off, but I have no clue how to do this. For example I would want ...
1answer
195 views

### How to construct the RHS of Wick's theorem

I've been trying this for a few days now, but I just can't seem to find an efficient (speed-wise) functional way to code the following task. Context: I would like to construct an expressions that is ...
1answer
176 views

### Core functions or operations that every aspiring Mathematica programmer should know? [duplicate]

I am aware that there are common yet very powerful operations like Map, Thread, Apply, ...
0answers
313 views

### Is there research about the Mathematica programming paradigm?

There seem to be lots of papers discussing the functional programming paradigm terminology for Haskell, such as monad, category theory, lambda calculus, *morphism, etc. People study concepts and ...
0answers
50 views

### Different ways to program a recursive algorithm

Construct f (a numeric function) which takes multiple arguments with the following property: The single argument case $f(x_1)$ is meaningless, and the two-argument ...
2answers
89 views

### Partial Function Evaluation [closed]

How can I evaluate only part of a stack of function calls? In particular, given f[x_,y_,z_]=x+y+z;, say, I'd like to define a function ...
0answers
58 views

### Strange sharp spikes causing overflow while doing gradient descent

I am trying to find a function h(r) that minimises a functional H(h) by gradient descent. The result of H(h) is a single number. (Basically, I have a field configuration in space and I am trying to ...
1answer
69 views

### How to use currying to write a tail recursive function for summing factorials given a certain bound

I am very confused about how can i use currying to write a tail recursive function for summing factorials within a certain bound or summing the bounds i.e. given [1,5] i should be getting 1!+2!+3!+4!+...
8answers
5k views

### General strategies to write big code in Mathematica?

I think after six months of exposure to Mathematica and the Wolfram Language I am fairly OK with writing short codes and snippets. However, what are some general strategies to use in order to write ...
1answer
65 views

### Pairing values with their indexes for MapThread

Several operations require you to map over a list of values and to know the index of each value as you process it. To accomplish this, my current somewhat ugly solution uses MapThread: ...
3answers
111 views

### Counting runs in bits, along with their starts and lengths, in functional style

Here is some code to visualize Project Euler Problem 502. The code scans for runs of bits in the binary representation of an integer, and outputs the beginning position of each run and the length of ...
0answers
71 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 ...
1answer
50 views

### Recognition Power Head for numeric value

We know: Map[Head, {a, a^2, a^3}] (* {Symbol, Power, Power} *) and Map[Head, {2, 2^2, 2^3}] all of them will be known as <...
0answers
142 views

### Variable naming conventions for nested pure functions [closed]

My understanding is that for nesting pure functions, one should use the explicit version of pure functions. I would like to know the best way of making it readable for people. I currently have ...
3answers
117 views

### how to map a function on a variable list

The following is just an example that captures what I want to do (more on it at the bottom). I'm trying to do something that can be paraphrased as follows: I have a global list, say ...
0answers
180 views

### How best to simulate n-body systems in a functional way

I want to simulate a N-body system in the most functional way possible. The system I'm modeling are metallic colloidal particles in a solution of peroxide water, as here http://arxiv.org/pdf/1502....
1answer
125 views

### The basic primitive recursive functions

How can the basic primitive recursive functions be expressed in the Wolfram Language? Apparently here's an example for primitive recursion: ...
0answers
86 views

### Delimited Continuations: Easy? or Fundamentally Difficult?

Apologies in advance for the length of this question, but this is as short as I have been able to make it. The Prescription I'm looking at the following tutorial on delimited (or composable) ...
4answers
927 views

### How can I avoid using a For-loop in my code?

I am trying to avoid using For because I heard that For is not cool in functional programming. Below is a problem that the first ...
3answers
95 views

### How to organize expression by symbols (like Collect), but apply different functions to each coefficient

I want to mimic the functionality of Collect[expr, {vars}, func], but with the following modification: The function f that is ...
1answer
75 views

### Defining a list of functions

I'm using polynomial mappings such as s[{x_,y_}] := {x + y^2, y -x} and playing with compositions of such mapping, e.g. ...
2answers
104 views

### Repeatedly apply a bivariate function with one argument running over a list

I'd like to know how, given symbols f and g, and a list {a,b,c,...}, to produce the ...
2answers
46 views

### Deciding whether the return value of a function is defined based on its input [duplicate]

I have been met with the following problem: I have defined the following: myFunc[e_Integer]; That means, if I call: ...
1answer
99 views

### Iterations in Mathematica [closed]

this is probably a very easy question for all of you. I have a stochastic Mathematica code (not important what it's exactly) which gives me a number at the end. Now I want Mathematica to run this ...
1answer
204 views

### How to terminate early a functional computation

Problem description: Given a list $A=\{1,2,0,7,0,-1,2,6,\ldots\}$ and a list $B=\{0,7,0\}$ write a program that determines whether $B$ appears in $A$ or not. Note: the order of $B$'s items does matter....
1answer
509 views

### Does Mathematica have a functional programming idiom to loop over a list till a condition is met? [duplicate]

The module below takes a list of integers and performs fadic addition on it (if a bit slowly). ...
2answers
122 views

### A better way than using nested For-loops to make a search list

I'm generating a List that can be up to 26 values long, a simplified example is below. Is there a better way than nested loops? ...
1answer
77 views

### How can I get all pairs of values from an association with elements key->list

I have an association of the form ds=<|key1 -> list1, key2 -> list2,... ,keyn -> listn|> I would like a simple way to map a function to all pairs <...
3answers
144 views

### List of functions to list of parameters

I am working in a Dataset and I need to create a function for a ChartStyle option of a ...
1answer
129 views

### Writing code which generates a function to append many columns to a dataset

I love datasets in Mathematica. Say I have one that looks like this: ...
3answers
200 views

### Through does not work with Subtract

Through[(Max - Min)[#]] & @ {1, 2, 3, 4, 5} gives 5 + (-Min)[{1, 2, 3, 4, 5}] Of course I can work around by ...
1answer
162 views

### The equivalent of dplyr mutate with Dataset

In R, there is a package "dplyr" that works on data.frame objects, which is one of the origins of the Mathematica Dataset construct. One of the things dplyr can do is "mutate" the columns of a data....
1answer
130 views

### functional way to identify & summarize repeated elements in List?

I have a List, for example (assume it's always ordered like this one): myList = {6, 6, 8, 10, 14} I would like to get a result like this: ...
1answer
101 views

### Using Map multiple times in one command

Is there a way to reproduce the effect of Table[i ** j, {i, list1}, {j, list2}] using Map instead of Table? Specifically, I want to write something along the ...
2answers
87 views

### Is there a way to create a table where the number of dimensions is parameterized?

I'm imagining the likes of this: ...
3answers
169 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 ...
1answer
130 views

### Unevaluated @ {args} versus Unevaluated /@ {args}

Working my way through Robby Villegas's lovely notes on withholding evaluation, I almost got Polish Notation on my first try. Here is my final solution, which seems to work well enough: ...
1answer
152 views

### Use Map with multiple arguments over a nested list

I noticed there are a few similar questions to mine on here, but I couldn't figure out how to accomplish this mapping. I have sets of data I want to plot, which represent intensity and frames, and I ...
2answers
254 views

### Multiply pure function with scalar

Somtimes I still get lost in the Hold, HoldAll etc. functions of Mathematica. I want to scale a simple PDF function with a previously calculated variable e.g. ...
1answer
57 views

### Mapping Linear Model Fit Over An Arbitrary Number of sets

I have multiple sets of data, and I want to apply Linear Model Fit sequentially to each set of data. For example, below tstlst contains 3 data sets. Right now I ...
5answers
657 views

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2answers
80 views

### How to define a function to save a list to a same-name file

I want a convenient way to save lots of intermediate data lists into files, so that next time the files can be imported automatically to homonym list variables in the notebook, without having to ...