# Questions tagged [function-construction]

For questions on writing functions (pure or using Set/SetDelayed) for any purpose, including the features that may be incorporated in those functions, such as options, patterns and conditions.

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### How to plot a barycentric line

I want to plot a barycentric function on an equilateral triangle (ternary plot). For example f1 = {Abs[Sin[x]], Mod[x, 2], Abs[Cos[x]]}; At the moment I evaluate ...
2k views

### Picking random items out of a list only once

I'm trying to create a function that randomly returns a value from a list but remembers the values that have been given before. At the end when the list is empty it should return an empty list. ...
2k views

### Force function to make assumptions about its input variables in Mathematica

I'm trying to force a Mathematica function to make an assumption about its input variables. In my case, I'm trying to define a function to return the pdf of a Gaussian. But let's use a simple toy case:...
263 views

### 3x+1 on arithmetic chains, tree pruning and NestList

Given the following function Collatz: ...
725 views

### How do I use the result of Solve in a function definition?

I'm trying to adapt the following piece to the part where PowerF is a function of amax. ...
641 views

### Using several anonymous functions mixed together

This works: list // BarChart[#[[2]], ChartLabels -> DateString @@@ #[[1]], ChartStyle -> "Pastel"] & This doesn't: ...
2k views

### Integrating with multiple indicator functions

I am trying to calculate an integral involving multiple indicator functions, such as: $$h(u,v,w) = -\int_0^1 J^{\prime\prime}(s) (I_{(0,s]}(u) - s)(I_{(0,s]}(v) - s)(I_{(0,s]}(w) - s)\, dF^{-1}(s)$$...
201 views

### Calling a function an unspecified number of times

I would like to be able to call a function an unspecified number of times. That is, I would like the generalization of something like: ...
2k 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 ...
241 views

### What's the most intelligent way to store the information of a selfmade graph?

I have a very long list of element, say $a1,a2, a3$,..., and they are all connected in that each is the child of many parents. E.g. $a74$ is associated with $a2,a55,a71$, and also contains information,...
1k views

### Composition of functions

I have a number of rotations computed by rot = RotationTransform[theta, point], and I would like to compose them to produce one function that is the composition of ...
725 views

### Can SetDelayed (:=) be compiled?

Is it possible to put an If statement as below within a compile (see below)? I received a warning about SetDelayed. ...
2k views

### Defining an integer-valued function on an integer domain

This should be an easy question! I want to define a function with domain = the 12 integers {1,12}, with the values f[1]=31, <...
489 views

### Defining a ForEach function

Consider the following function definition: ForEach[iterators__] := Table[#, iterators] &; Two questions about it: I. It works perfectly if you call it like <...
1k views

### Inverting a function in a certain region

InverseFunction works well for globally invertible functions, like f = 2*# + 2 &; InverseFunction[f] ...
458 views

### How to make a function like Set, but with a Block construct for the pattern names

How can we define a function that works like f[x_]=ComputeSomething[x] and treats x as a variable that does not have a value? ...
3k views

### Passing down arguments

In R, one can use ... to pass arguments down to another function. For example ...
2k views

### define a function from a list

I would like to create a mapping from a list and I am wondering if there is a slick way of doing it. For example, consider the list ...
5k views

### How to avoid collision between optional arguments and options

Is it possible to create a function with optional arguments that also takes options? Here is a simple example. I have a function f with option "g". It also has ...
4k views

### Functions vs. patterns

Every time I define a new function, I wonder which construct I should use: true functions obtained by using Function, or rule-based syntax. For example, these are ...
7k views

### Functions with Options

Suppose you want to create a function which has optional arguments. Maeder's book Programming in Mathematica covers the topic extensively up to version 3, but some things have changed/evolved since ...
2k views

### Constructing functions with variable number of output arguments

In Mathematica, you can construct a function f to have different definitions based on its input arguments. For example, ...
626 views

### SetAttributes[f,Flat]: Why the order dependence?

I'm experiencing a strange phenomenon. Here's a (quite artificial) test case: The following definition work just fine: ...
What is the most painless way to sum over n variables, for example, if the range of summation is $i_1 < i_2 < i_3 < \dots < i_n$, where $n$ is an argument of the function in question? Is ...