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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60
votes
4answers
2k 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 ...
41
votes
6answers
1k 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 ...
36
votes
6answers
2k views

How can I create a function with 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 ...
35
votes
3answers
960 views

Tiling a square

I wondered if there was a way to automate the process of finding a way to tile a tile into a square. The idea is to represent the tile with a matrix of $0$s for blank space and $1$s for filled spaces ...
32
votes
9answers
7k views

Generating a Sierpinski carpet

I am trying to draw a Sierpinski_carpet. I have code that works, but I think there is a more elegant way to do than my way. Maybe I couls use Tuples or ...
29
votes
2answers
777 views

Variable naming changes everything

I am having a rather unusual problem I do not understand with Mathematica where renaming one of the variables of my function causes the function to stop "working". Here is the example of the code ...
25
votes
4answers
513 views

How to make MapAt work with Span?

Span (;;) is very useful, but doesn't work with a lot of functions. Given the following input ...
24
votes
1answer
364 views

which is better, using Assert[] or manual checks on arguments and other computations?

I never used Asserts in Mathematica, but trying to see what advantage they have over just argument check and additional definitions of the function to capture unwanted input. For example, which one ...
22
votes
6answers
1k views

Convert an expression to a Function

I need a function which can take an expression and return a pure function based on the symbols in the expression. The symbols might have values so must be protected from evaluation. It is probably ...
22
votes
6answers
414 views

Constructing symbol definitions for With

I would like to be able to define two arrays, one containing symbol names and one containing the values of those symbols, for use in constructs such as With. For ...
22
votes
1answer
471 views

How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
21
votes
3answers
1k views

Sum over n variables

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 ...
21
votes
4answers
618 views

Why is there no PositionFunction in Mathematica?

Too often I have seen the programs of inexperienced users greatly slowed by using Position in an iterative fashion, when far faster would have been to compute a ...
20
votes
4answers
368 views

Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs

Using global variables the following turns an "expression" into a Function: expr = 2 x; Function[x, Evaluate[expr]] Of course ...
19
votes
1answer
358 views

How can I make threading more flexible?

Threading automatically with Listable functions requires the argument expressions to have the same length (or for one of them to be atomic). For nested lists the ...
19
votes
3answers
343 views

Why x = x doesn't cause an infinite loop, but f[x_] := f[x] does?

If I execute: In[1] := x = x Out[1] = x and then I evaluate the symbol x: ...
18
votes
2answers
245 views

Plotting a defined function gives different results from plotting the function directly

Consider the following piece of code: function[t_]:=Exp[-9 t^2]; LogLogPlot[{function[t],Exp[-9 t^2]},{t,.01,100}] I expect the two plots to exactly overlap each ...
17
votes
3answers
310 views

Nested definition: How can I define a function with a passed-in expression?

Here's a simplified version of what I'm trying to do: ...
17
votes
2answers
278 views

Pattern that matches colors

Suppose I'm writing a function that takes a color as a parameter; for example: drawShape[color_] := Graphics[{Style[Disk[], color]}]; But if the caller inputs an ...
16
votes
12answers
1k views

Pick elements of largest absolute value

For example, given list = {{1, -3, -5}, {2, 1, 6}, {0, 2, 4}, {-9, 2, 6}} should return: {-5, 6, 4, -9} Updated I found ...
16
votes
9answers
845 views

How do you check if there are any equal arguments(even sublist) in a list?

I would like to set up a function which has to return True if at least two arguments of a given List are equal. So if I give {1,4,6,2} to the function it has to ...
16
votes
5answers
1k views

The difference between 0. and 0

I have a function for which 0 is a special case: f[A___, 0, B___] := 0 But since I am doing numerics, sometimes in the course ...
16
votes
4answers
274 views

Can I make a default for an optional argument the value of another argument?

I'd like to define a function with several optional arguments, some of which default to the value supplied for other arguments. For example, I'd like to be able to write something like ...
16
votes
3answers
617 views

Using pure functions in Table

I need a table with the elements made of pure functions and list elements. This is a simplified example: I need a list as: ...
16
votes
1answer
251 views

Kernel inexplicably hangs if I define a pure function without suppressing output

Save any unsaved work before trying as it may crash Mathematica and other programs by filling up the memory! In v9.0.1.0 on OSX 10.8.5, if I start a new session and define two functions ...
15
votes
2answers
642 views

Define parameterized function

I would like to be able to define the gain function of a system from its parameters. Specifically, I'd like to define a function that accepts two inputs, call them $b$ and $w$, and returns a function ...
15
votes
2answers
475 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, ...
15
votes
1answer
221 views

Multiple templates for a single user-defined function

How do I use the ::usage tag to allow the Mathematica v9 front end to know that there are multiple ways to call an overloaded function (a function that can have ...
14
votes
5answers
735 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. ...
14
votes
6answers
768 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 ...
14
votes
7answers
564 views

A function that accepts a pair or a list of pairs

Probably a duplicate, but it's not easy to search on "lists". I have a function that accepts a list of lists, say {{a1, b1}, {a2, b2}, {a3, b3}} and performs some ...
14
votes
4answers
482 views

Can a function be made to accept a variable amount of inputs?

I have a function that takes two inputs and processes them for a single output. What I need is one that can take a varying number of inputs. and process them to a single output. Is this possible in ...
14
votes
3answers
233 views

What's wrong with this pattern of the form Except[Repeated[…]]?

I'm trying to build a head that recognizes molecules. Here's the code ...
14
votes
2answers
339 views

Using several anonymous functions mixed together

This works: list // BarChart[#[[2]], ChartLabels -> DateString @@@ #[[1]], ChartStyle -> "Pastel"] & This doesn't: ...
14
votes
3answers
475 views

Function that counts the number of arguments of other functions

I have a newbie question: is it possible to write a function that counts the arguments (total and optionals) of a given function? Possibly it should be able to work with built-in and custom functions ...
14
votes
1answer
273 views

How to represent a continuous monotonic phase of Airy functions?

Note: In this question I am concerned only with real-valued variables and functions. DLMF, §9.8 Airy Functions, Modulus and Phase, formula $9.8.4$ defines the phase of Airy functions: ...
14
votes
1answer
229 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? ...
13
votes
2answers
345 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: ...
13
votes
3answers
445 views

Is it possible to get the order of inputs when “overloading” an orderless function?

When working with symbolic matrix operations or other objects which don't have commutative multiplication, it would be nice to not have to constantly switch out times for ...
13
votes
1answer
564 views

How to Combine Pattern Constraints and Default Values for Function Arguments

EDIT: As several respondents have noted in the answers and comments below, the original example had a default value that would never be used because of the way patterns and default values are ...
13
votes
0answers
158 views

func::usage needs to be run twice? [duplicate]

There is an annoying problem that I can't figure out why it's happening. I have defined a usage for a my function tensorA: ...
12
votes
2answers
217 views

f[arg1, arg2,…,argN] vs. f[{arg1, arg2,…,argN}]

I am trying to reproduce the API of a function (written in R) that accepts an arbitrary number of arguments and handles it the same way as it would handle a single argument that is a list of different ...
12
votes
4answers
337 views

Equivalent Nested Loop Structure

Consider the following examples: ...
12
votes
1answer
219 views

Is it possible to Clear all variables (but not functions)?

I have written a Mathematica script in which I define functions and variables. Here is a vastly simplified example: ...
12
votes
2answers
166 views

How can one write a robust ListableQ function?

I would like to have a test that determines if a particular function is Listable. In the case of Symbols this is merely a matter of checking Attributes. ...
11
votes
4answers
396 views

Assessing argument type in set delayed function definitions

I'm wondering how to properly assess the type of arguments passed to functions defined with :=. I want my functions to be the most efficient, unambiguous and clear ...
11
votes
3answers
850 views

What is Mathematica's equivalent to MATLAB's filter function?

The MATLAB code filter(0.5,[1, -0.5], [1:10]) is equivalent to Rest@FoldList[(#1 + #2)/2. &, 0, Range[10]] I don't ...
11
votes
5answers
483 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 ...
11
votes
2answers
560 views

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 ...
11
votes
1answer
255 views

Modules that initialize themselves on first call

I use a lot of functions that extract a specific data item from a file with many data items. I want these functions to load data (slow) and return the item (fast) on first call, but just return the ...