# Tagged Questions

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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### Interpreting Mathematica output or producing cleaner output [closed]

Could someone please explain what the following would look like in standard math notation (or explain to me what this means): ...
31 views

### How to use OptionValue inside a pure function [duplicate]

I want to define a function with OptionsPattern as argument which returns a pure function using OptionValue: ...
416 views

### Pure function with attributes of arbitrary number of arguments: Is it possible?

Mathematica allows to define pure function, like Function[{a, b},Length[Unevaluated@a]{b}][1+2,2+3] (* ==> {0} *) Pure functions in Mathematica can take an ...
85 views

### Optimization of the solution to an ODE

Apologies if this is obvious -- I'm very new to Mathematica. I'm trying to minimize the solution to an ODE with respect to a variable. The following code generates the solution to the ODE, ...
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### Greatest common denominator command. Can you explain why this command works?

Can you explain how this function works? mysteryFunction := Fold[#/#2 /. {n_~_~_ -> #/n, _ -> #2} &, #, {##}] &
111 views

### Evaluate pure function through round brackets

In have some matrices of pure functions or numbers which I multiply by other matrices or vectors. I would like the functions to be evaluated in the result, but all that I get is something like this: <...
1k views

### Using patterns in pure functions

Pure functions may be handy if you don't want to assign your function a name. For example I would calculate $x(x-1)$ for some numbers $x$ by ...
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### Solving pure functions

I've been trying to use Solve with pure functions to receive function efinition and then use it with Map , to obtain results from mapping function to some data. Here is example ...
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### Automatic generation of pure function

My main problem consist in the creation of a sort function which wolud be used inside SortBy. Introduction The principle of the sort to apply is the following (...
964 views

### Can you plot pure function without specifying variable?

Given a pure function, e.g. f=Sin[#]&, it is possible to plot it with introducing an arbitrary local variable, e.g., ...
80 views

### Matching All Functions [duplicate]

Is there any way to match all functions? There's an existing answer for matching functions of one parameter (_@_) but it doesn't work for trying to test if a symbol ...
68 views

### How to force evaluation inside the body of a pure function?

For example, I'm writing a function to scale my list of numbers into a specific range. It goes like ...
122 views

### Select with test function that depends on #

I'm trying to teach myself to use pure functions and slots as much as possible. Here is my problem. I have a list: ...
108 views

### How to use Select according to a list of criteria to produce a list of subsets of another list obeying those criteria [duplicate]

The code Print[Select[{1, 4, 3, 9}, Mod[#, 3] == 0 &]]; Print[Select[{1, 4, 3, 9}, Mod[#, 3] == 1 &]]; Print[Select[{1, 4, 3, 9}, Mod[#, 3] == 2 &]] ...
472 views

### Expansion in Basis Functions

I am trying to create an expansion of the form f[x,y]->Sum[Cn[x] y^n,{n,1,order}] To replace the function f by the ...
1k views

### Is there any way to define pure functions with optional arguments?

For example consider the following function: Function[{u,v},u^2+v^4] Is there anyway to define default values for the variables ...
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### 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 ...
85 views

### Creating a list of unevaluated pure functions with Apply

Suppose I have a list list with length L and a function ...
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### Deciphering Coding Shortcuts [duplicate]

I'm having trouble deciphering why the following couple of expressions evaluate the way they do. #&@@ This returns the first value of a list. Why? NaÃ¯vely I ...
981 views

### Is it possible to reference “self” from a pure function?

This would calculate the factorial of 6, if the "self" was the function itself. Is there something that could allow this? ...
103 views

### How to write this code as a pure function? [duplicate]

The code has three places with same variable ls. So I think it would be possible to write it as a pure function. ...
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### How to get the values out of Alternatitves? [closed]

Saying we have something like: SomeFunction[ ... { Alternatives[1, 2, 3] :> "something" } ... ] How can I know if ...
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### Why is g[#1, #2] & different from g[##] & for a function with two variables in this example? [duplicate]

If we only consider functions with two variables, I expect g[#1, #2] & is the same as g[##] &. But in the following ...
99 views

### Replace variable with # and pass function body as an argument to a function

I have a very simple problem, which I would like to make a bit general, but none of my naive approaches have worked yet. This is what I want to do step by step: Define a parameter: ...
54 views

### What makes items with head Function different?

I apologize beforehand for the muddleheadedness of this question. It reflects the fact that I'm trying to interpret outward "behaviors" of Mathematica expressions without having any understanding of ...
66 views

### Translating syntax of a pure function

I have a matrix in complex exponential form. I want to factor out the complex exponential form and then express the inside in the a+i*b form. For example: \begin{bmatrix} e^{i \frac{\pi}{4}} ...
320 views

### How can I create currying functions using pure function syntax?

For example how can I write In: pureFunctionSyntax[myF] /@ {7, 3} Out: {myF[7, Log[7]], myF[3, Log[3]]}
320 views

### Why does #0[[1]] &[] output 0?

When a pure function accesses the first element of itself, 0 is output. What is the logic behind this, or is there any?
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### How to use pattern matching to apply a function to specific elements of a matrix

I have a 3x3 matrix testweightedgraph = {{{}, {p, q, pq, pq}, {}}, {{p, q, pq, pq}, {q}, {}}, {{}, {}, {}}}; whose elements are (possibly empty) lists. I would ...
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### “Nonatomic expression” error when identifying certain positions in a list [duplicate]

Please can anyone help ? I have a list of sets, and I am trying to find the positions in that list of those sets which are subsets of a given set. (Here I am ignoring the distinction between lists and ...
79 views

### Working with functionals [closed]

I am trying to work with functionals in Mathematica, this means that I want to define a function of a function. I defined my function of a function as: ...
237 views

### Cases vs Select, Pattern vs Pure function [duplicate]

What is the difference between having Cases with selection condition presented by pattern and a with pure function as condition? ...
310 views

### Mma10 mystery: Failure of pure function substitution with Interpretation?

Bug introduced in 10.0.0 and fixed in 10.0.1 I had code to display with subscripts from Displaying index as subscript on output: e.g. C[i] -> C_i with Notation[...] or Interpretation[..]? which ...
1k views

### What happens when you divide by ##?

I've been playing around with sequences a bit. In particular with using ## with unary and binary operators. Let's start simple, the following all make some kind of ...
129 views

### Substitute a function's definition for its name

I'm having trouble with a function which is supposed to work on another function. Simplified version: ...
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### Pure “Select” function over matrix

I have several lists of tuples in the following shape: l1 = {{1, 134}, {2, 314}, {3, 164}} I do want to select, from each list, list elements fulfilling a ...
165 views

### Using Through with SlotSequence

I have an expression consisting of a few pure functions added together like so: f+g+h I want to add the bodies of these functions together and make that a pure ...
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 ...
279 views

### How to write an operator that acts on pure function (to give another pure function)

I would like to write an operator oper that acts on a pure function f with an undetermined number of arguments, with the syntax <...
90 views

### Pure Function that adds all arguments

the question asks to create a pure function that adds any number of arguments. Is the following acceptable? sum := Plus[##] & It does work, but can it be considered a pure function? I felt like ...
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### Sum of Integers with a Pure Function

How would I find the sum of an argument, with the constraint that they are all integers (so if the argument contains a non-integer value, the function will not evaluate). I came up with these two: ...
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### How-to implement iteration over a result of an iteration in a functional way

I have a pure function f:= #1 * #2 * #3 &; Which I can invoke in a following way: f[#,2,3]& /@ {1,2,3} Which ...
2k views

### Memoization with pure functions?

Is this possible? If I have a simple function, say: f=If[#>0,1,2]& then for each value of # this will re-evaluate f right? Is it possible to define a ...
505 views

### Using several anonymous functions mixed together

This works: list // BarChart[#[[2]], ChartLabels -> DateString @@@ #[[1]], ChartStyle -> "Pastel"] & This doesn't: ...
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### Wrong autogenerated package from notebook containing #key and Part as subscript

Bug introduced in 10.0.0 and persisting through 10.1.0 or later Mathematica v10.1.0, under Windows 8.1 x64 Mathematica v10.0.2, under Windows 1) Define a function in an initialization cell: <...
86 views

### Expressing a definite integral as pure function with the upper-bound as it argument

Suppose i have an integral which has a closed form, $\quad \quad \int_{a}^{b} f(x) dx=F(a,b)$ I want to use output function $F$ as a pure function, like ...
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### Use of parenthesis and pure function

I had read that when using a pure-function it was a good general practice to enclose the function and the associated ampersand in parenthesis. (#^2 &)[a] I ...