# Questions tagged [pure-function]

Questions about implementing or applying functions which: (1) always yield the same result for the same input, (2) are independent of outside information, and (3) produce no side effects.

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### A way to generalize my code for this non linear ODE problem

I am trying to solve the differential equation $y''(x) = y(x)+\sin[y'(x)]$ using "Fixed Point Iteration" over the interval $[0,1].$ Now using central difference method I arrived at the ...
1 vote
65 views

### Mapping two pure functions over different lists

Say if I have two lists of vectors of the same length, for example: u = {{1,0,0},{0,1,0},{0,0,1}} v = {{1,0,1},{1,1,0},{1,1,1}} I want to add (modulo 2) ...
1 vote
71 views

### Why must the "&" symbol be placed inside function instead of outside? [closed]

The following code is taken from Wolfram Community "Quantum Error Correction: bit flip". ...
33 views

### Use FoldList to successively ImageAdd regular polygons with between 3 and 8 sides, and with opacity 0.2 [closed]

This question is from Section 29 of "An Elementary Introduction to the Wolfram Language". The objective is to successively add regular polygons with between 3 and 8 sides, and with opacity 0....
71 views

### Memory leak with pure function and in the listable option of compiled function?

I'm using 13.0.0 for Microsoft Windows (64-bit) (December 3, 2021) When I repeatedly run the command ...
228 views

### Pure functions: currying for & notation

I looked up currying in Shifrin's book. He points out that currying can be used for pure functions using nested functions as in the following example: ...
82 views

### Condition inside pure function

Why condition /; not work inside pure function? Suppose we have: ...
69 views

### Pure function with pattern test

Is it possible to achieve pattern test inside a pure function? I have tried f = Function[{x_?NumericQ}, x ] but the error Function::flpar occured.
1k views

### Pure function of lists

I need to create a function with two arguments f(s, l): s is a list of three integer like: s={1,-3,+5} and l is a list of lists of naturals of same length: ...
189 views

### Pure functions failing in algebra

f[equation_] := Module[{}, ContourPlot[equation[x, y] == 1, {x, -2, 2}, {y, -2, 2}] ] equation = (#1^2 + #2^2) &; f[equation] The above code draws a circle....
81 views

### How to define pure functions in matrix form?

I want to define pure functions x(#1,#2) and y(#1,#2) like But they aren't proper pure functions in the current form. How to modify the code?
466 views

### Pure function on pure function

Given t1 = {2, 4, 8, 16}; t2 = {1, 5, 9}; First[Select[t1, # > 1 &]] First[Select[t1, # > 5 &]] First[Select[t1, # > 9 &]] can somehow be ...
150 views

### Slots inside nested pure functions

I'd like /@ instead of Table or Map. But let we have it inside pure function: ...
72 views

### Sort a list using a scoring list with Switch [duplicate]

I have a minimal working example (MWE) list called listToSort that is a list of string triplets: ...
51 views

### Sorting a list by increasing order algorythm [closed]

Im new to loops on mathematica,was wondering how could I create a function to loop through a list which finds the index of the smallest value of that list, makes a sublist from index 1 to that ...
1 vote
80 views

### Drawing lines between coordinates in a list

Variable "l" is a list of coordinates and I am trying to draw a line from each coordinate to the next. But how? Apparently the last line isn't working. ...
81 views

### MapAt with pure functions

Consider expr = Hold[1 + a + x + b + c + y + z]; idxes = {{1, 3}, {1, 4}}; Q1. I don't understand why ...
573 views

### Can a pure function be constructed whose argument list is a matrix?

Can a pure function be constructed whose argument list is a matrix? Using Function, I know it's not possible, but I'd like to get something like: ...
1k views

### How to simplify a pure function?

I am dealing with the vibration of a multi degree of freedom system with driving force, and I need to find the relation between the amplitude and the frequency of the driving force. I hope to get an ...
1 vote
101 views

### Nested pure function argument as table

I made a nested pure function Nest[(x^2)/ ((2x+1) + #)&, x,n] I would like that for each iteration the value of x increment of 1, to have something like \...
154 views

### How to replace a multiple iterator Table to speed up computation

I need to create an array of data which resembles to something like this Table[{i, Sin[j^2*i]}, {j, 2000}, {i, 0., Pi, Pi/10000.}] where each "row" of ...
21 views

### How to select from a sum the terms containing minus? [duplicate]

In a sum y = \[Beta] x v - \[Mu] y z - \[Gamma] y; I would like to extract the terms which contain a minus, i.e. - [Mu] y z and - [Gamma] y I can test when a term ...
126 views

### Minimize Sum of Hamming Distances

Problem: Given an $n \times m$ matrix with binary values $(0,1)$, find a binary vector that minimizes the sum of Hamming Distances to the rows. Example: If the matrix is {{$1,1,1$},{$0,0,0$},{$1,0,1$}}...
937 views

### When is ##@@@##& more appropriate than ##@@##&?

When assigning attachment operators, I often run into confusing statements like ##@@##&, ##@@@##&, or even ...
449 views

### Construct a pure function containing built-in 'Sequence'

I guessed the output for (Sequence[#, 7]&) should be Sequence[3,7] But my guess was wrong. See the screenshot: And I ...
124 views

### Spurious renaming in nested Function construct

From the documentation of Function, I take this example (slightly simplified). Renaming the dummy or bound variable (y->y\$ in the inner ...
64 views

### Splitting a list into sublists at provided markers

For a list of strings (or other elements): SeedRandom; t1 = Table[RandomChoice[CharacterRange["A", "E"]], 20] ...
133 views

### Evaluating a FittedModel over a list of values

Simplified version Using the simpler version suggested by @ulrich-neumann : ...
117 views

### Why do these two calls to Apply return different results?

In the following example, why do these two calls to Apply return different results? ...
477 views

### An anonymous function with constraints [duplicate]

I'm not very good at working with anonymous functions, a fact that has now come back to bite me. Suppose I have a function defined as follows: ...
50 views

### MeshFunctions::invmeshf that resists other solutions

I'm trying to base mesh on the slope of the function. That's why there is a Cross of two partial derivatives. ...
92 views

### Apply function modification to curried function

This is based on A function that modifies functions - well-defined operation?, a previous question of mine. Lukas Lang's answer of course works very well, but now I encountered the following edge case:...
310 views

### How to supply argument to pure function when slot is already defined?

Here's an example of a pure function: 3^# > 100 & I can supply any value I please to the function, by placing that value after the prefix. E.g.: ...
47 views

### Why does this function only work with exact numbers?

First, I tried calculating A^k with this and got an error. ...
141 views

### How to use a pure function to write following sum?

How to use a pure function to write following sum? I have tried to use FoldList, but it is still not working.
56 views

### Maximize returns unevaluated even though there is a global maximum

I was trying to calculate the maximum of a gaussian plus a line, but Maximize return unevaluated: ...
161 views

### bind specific 'Slots' to specific 'Map'

Is it possible to construct a pure function using multiple slots, with the following concept :       Binding   specific slot    to    specific apply or map For example : In this example, To ...
1 vote
114 views

### pure function assignment

I do not understand this statement from the Introduction to Dynamic tutorial: ...
1 vote
61 views

### Apply function using level

The following use of Level is documented, without any example. Let's try some simple codes : ...
119 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 ...
148 views

### Reduce from two pure functions to one

Liking the headings and spacing allowed by Row[] and TableForm[] I set up the below with 3 TableForm[]'s to use as a model from which to generalize, using a pure function, to display a list of 3-ples, ...
1 vote
69 views

### Shorten Pure Function

My task is to write a pure function with 5 characters or less that can be called with a single number a or a list {a,b,c} and returns 1/a^3 or {1/a^3,1/b^3, 1/c^3,...}, depending on the input. I am ...
25 views

### Pure functions with derivatives and list elements [duplicate]

I have a list list = {x, y, z} and then the following line D[#, list[]] & gives the output ...
151 views

### Using a pure function as an option of a function

Here's my code: Options[f] = {"Func" -> Exp}; f[x_, OptionsPattern[]] := OptionValue["Func"][x] f[2, "Func" -> (# + 2) &] ...
45 views

### Function does something bizarre with formal parameters

I think this may overlap with existing questions, including one I asked years ago, but I'm not sure how, because the behavior I'm seeing is confusing enough I can't even really describe it except to ...
192 views

### Function incorrectly renaming variables in Rule Pattern

Consider the simple pure Function containing a Rule with the named pattern q. ...
70 views

### How to write a function returning Chebyshev Polynominals of the first kind using Nest[]? [duplicate]

I want to create a function returning the Chebyshev polynomials of the first kind using the in build Nest[] function, preferably with a pure function. I know there exist an in-build function for the ...
1 vote
201 views

### Pattern matching tuples as inputs to pure function

I've been having an issue with functions which are supposed to receive as input a list of tuples. My troubles are two-fold: The function doesn't properly identify the pattern test I laid out in the ...