# 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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### How do #1 and #2 work in a function defined by 2 variables?

Can someone please explain the function of #1 and #2 in a pure random function of two variables? For example, if I had something ...
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201 views

### Evaluation leak in Derivative[]

Bug introduced in 4, persisting through 14.1. I usually only report bugs, but in this case, two reason prompted me to post this: Given that derivatives are computed internally by various commands, ...
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### How to call a list of pure functions/pure vector function? [closed]

In one dimension, pure functions work as usual: f = Function[{x}, 2 x] f[a] However, with a list of pure functions / a vector pure function this does not work with ...
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### Using MapThread with pure function and variable number of elements

I have a variable size array of lists and would like to set up a MapThread of the lists with a variable pure function $\{\#1,\#2,...,\#n\}\&$ with $n$ being the number of rows in the array and am ...
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### How Can I Use an Element of a Tuple as an Argument for a Pure Function?

(If I should elaborate on the circumstances, tell me.) I want to do the following: Suppose I have a tuple tuple={x,4,something,...} and I want to define a pure ...
86 views

### Same code behaves differently as a pure function and a function, and insider another function

I have a rule-transformer that takes a list of rules (and a list generator = {σ[z], σ[-1], σ[1]}) ...
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### Define equations as a pure function with list as argument

I have these set of equations. The number of equations depends on $n,$ which I want to keep control of. The code that I have generates it using Table and equations generated by this does not take an ...
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### Generalize the code to more variables

I have this code it runs and gives me the solution. How can I make it more compact and If I want it to extend(generalize) it to more variables how can I do it. I had asked a similar question here (...
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1 vote
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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 ...
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1 vote
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### 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) ...
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1 vote
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### 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". ...
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### 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....
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### 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 ...
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### 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: ...
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### Condition inside pure function

Why condition /; not work inside pure function? Suppose we have: ...
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### 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.
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### 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: ...
192 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....
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### 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?
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### 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 ...
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### Slots inside nested pure functions

I'd like /@ instead of Table or Map. But let we have it inside pure function: ...
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### 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: ...
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### 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
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### 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. ...
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### 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 ...
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### 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: ...
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### 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 ...
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1 vote
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### 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 \...
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### 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 ...
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### 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 ...
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### 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 {{$1,1,1$},{$0,0,0$},{$1,0,1$}}...
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### When is ##@@@##& more appropriate than ##@@##&?

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

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

I guessed the output for (Sequence[#, 7]&)[3] should be Sequence[3,7] But my guess was wrong. See the screenshot: And I ...
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### 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 ...
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### Splitting a list into sublists at provided markers

For a list of strings (or other elements): SeedRandom[3]; t1 = Table[RandomChoice[CharacterRange["A", "E"]], 20] ...
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### Evaluating a FittedModel over a list of values

Simplified version Using the simpler version suggested by @ulrich-neumann : ...
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### Why do these two calls to Apply return different results?

In the following example, why do these two calls to Apply return different results? ...
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### 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: ...
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### 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. ...
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### 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:...
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### 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.: ...
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### Why does this function only work with exact numbers?

First, I tried calculating A^k with this and got an error. ...
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### 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.
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### 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: ...
180 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 ...
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1 vote
116 views

### pure function assignment

I do not understand this statement from the Introduction to Dynamic tutorial: ...
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1 vote
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### Apply function using level

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