# Tagged Questions

Questions on writing non-trivial programs in Mathematica. Do not use this tag for questions on plotting/graphics or for questions on doing mathematics with Mathematica, where the focus is more on the math than the program.

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### What are the most common pitfalls awaiting new users?

As you may already know, Mathematica is a wonderful piece of software. However, it has a few characteristics that tend to confuse new (and sometimes not-so-new) users. That can be clearly seen from ...
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### Where can I find examples of good Mathematica programming practice?

I consider myself a pretty good Mathematica programmer, but I'm always looking out for ways to either improve my way of doing things in Mathematica, or to see if there's something nifty that I haven't ...
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### Alternatives to procedural loops and iterating over lists in Mathematica

While there are some cases where a For loop might be reasonable, it's a general mantra – one I subscribe to myself – that "if you are using a ...
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### What does the construct f[x_] := f[x] = … mean?

This question mentions "x := x = trickery". What does defining a function as f[x_] := f[x] = ... do and what is it good for?
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### What is a Mathematica packed array?

A simple sounding question with a few sub questions: What is the difference between unpacked vs packed array? Are packed arrays more space efficent, how much so? Are packed arrays more time ...
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### How do I evaluate only one step of an expression?

I am looking for a simple, robust way to evaluate an expression only one step, and return the result in a held form. The definition of a single step is ambiguous, and this itself is probably worthy ...
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### Updating Wagon's FindAllCrossings2D[] function

Stan Wagon's Mathematica in Action (second edition; I haven't read the third edition and I'm hoping to eventually see it), demonstrates a nifty function called ...
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### Struct equivalent in Mathematica?

I really miss having something like a struct in Mathematica. I know of (and regularly use) a couple of programming techniques which feel like a ...
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### How to check if a 2D point is in a polygon?

Background: I use code from An Efficient Test For A Point To Be In A Convex Polygon Wolfram Demonstration to check if a point ( mouse pointer ) is in a ( convex ) polygon. Clearly this code fails for ...
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### Do I have to code each case of this Grid full of plots separately?

I have written some custom functions to draw multi-panel graphs like this one: It's done by passing a matrix of (custom) plotting functions to a MultiPanelGraph ...
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### Creating Mathematica packages

I'm building a package to help me write packages and their documentation. In this post I explained how to make a package and its documentation. In the answer I provided I describe how to build a very ...
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### Elegant manipulation of the variables list

I have a list of global variables (some of them are indexed variables), for example: varsH = Hold[U0[1], U0[2], B0, V0[1], V0[2]] Or (if it is easier to handle) ...
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### How to perform a depth-first preorder traversal of an expression?

Due to confusion of terminology on my part I asked the wrong question before. Since it has already received other answers I shall not edit it, but instead ask the question I meant to in the first ...
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### when is f@g not the same as f[g]?

I have always thought that f@g will give the same result as f[g] in all cases, and it is just a matter of style which one to use ...
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### Mathematica Destructuring

Context I'm writing a function that look something like: ...
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### Performance tuning in Mathematica?

What performance tuning tricks do you use to make a Mathematica application faster? MATLAB has an amazing profiler, but from what I can tell, Mathematica has no similar functionality.
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### 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 ...
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### Programming with Dynamic

I don't understand the following: f[a_, b_] := a + b ls = {1, 2, 3}; MapThread[f, {ls, {10, 20, 30}}] This yields ( as expected ) {11,22,33} If I change ...
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### Flatten command: matrix as second argument

One thing I could never wrap my head around is how Flatten works when provided with a matrix as the second argument, and the Mathematica help isn't particularly ...
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### Fastest way to calculate matrix of pairwise distances

It is a very common problem that given a distance function $d(p_1,p_2)$ and a set of points pts, we need to construct a matrix ...
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### How can I implement dynamic programming for a function with more than one argument?

Dynamic programming is a technique for avoiding the repeated computation of the same values in a recursive program. Each value computed is immediately stored. If the value is needed again, it is not ...
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### How to modify function argument?

Usually in programming languages, function arguments are normal local variables, which can be modified. Is this not true in Mathematica? ...
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### Using a list of tuples in a pure function

I want to use a list of tuples within a function to make assignments. Say I want to make assignments of the form value[i,j] = val What I have is a list of ...
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### Programmatic formatting for Mathematica code - possible?

It seems to be both an interesting programming challenge and a very useful practical application to have a Mathematica program which would allow one to pretty-print Mathematica code, so that it is ...
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### How do you set attributes on SubValues?

SubValues, as discussed in a previous question, are declared as follows ...
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### Once more on object orientation in Mathematica: does it have to be so hard?

Recently I came across a set of problems which would be solved most easily within an object-oriented approach. I first attempted to solve them by other means, but found the complexity of the code ...
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### 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 ...
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### ListPlot with each point a different color and a legend bar

I would like to generate a ListPlot with the color for each point in the plot corresponding to a particular value (not associated with the position in the plot). I'd then like to add a legend ...
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### What can I use as the second argument to Return in my own functions?

Having found out about the second argument to Return I played a bit with it, and the following tests all resulted in ...
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### Metaprogramming in Mathematica

Being functional, and having no "quotation", i.e. essentially treating data and programs semantically same, Mathematica seems naturally capable of doing metaprogramming. But could anyone construct a ...
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### The clearest way to represent Mathematica's evaluation sequence

WReach has presented here a nice way to represent the Mathematica's evaluation sequence using OpenerView. It is much more clear way to go than using the standard <...
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### Open Excel file with Mathematica

I would like to open an Excel file and manipulate it as a COM object. While I'm able to open an instance of excel with ...
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### Reading periodic elements from a large file

I have a large binary data file (big endian) with 100+ million "rows" of 11 elements, combination of floats and integers. This is the format: ...
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### Expressions containing globally undefined symbols inside a function where they are defined

Consider the following code. f[a_,b_]:=x; Clear[a,b]; x=a+b; f[1,2] It returns a+b. However, from a certain viewpoint, one ...
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### General strategies to write big code in Mathematica?

I think after six months of exposure to Mathematica and the Wolfram Language I am fairly OK with writing short codes and snippets. However, what are some general strategies to use in order to write ...
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### How to change the default ColorData used in Mathematica's Plot?

This question leads on from the recent question What are the standard colors for plots in Mathematica? There it was determined that the default color palette used by ...
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### Are there any cases when For[] loops are reasonable?

To my mind the only reason for the existence of For[] loops in Mathematica is to allow new users with some experience in procedural programming languages to write ...
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### Debugging memory leaks

I've written my incredibly complex, incredibly elegant analysis function, that works great on small test data. But when I run it on my real (bigger) data set it keeps running out of memory. It turns ...
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### Finding all elements within a certain range in a sorted list

Suppose we have a sorted list of values. Let's use list = Sort@RandomReal[1, 1000000]; for this example. I need a fast function ...
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### How do I automatically evaluate a cell when a notebook is opened?

I'm trying to put together a GUI in Mathematica and need to evaluate one cell to kick that off. Is there a way to automatically evaluate that cell when the notebook is opened? Here is an example of ...
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### What tools can help in realizing tail recursion?

I had nice discussions with Leonid and Rojo that got me interested in tail recursion. Tail recursion is not always easy to realize with Mathematica, so it would be nice to have some tools to help with ...
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In the ideas shared in my answer to this post Struct equivalent in Mathematica? at the end I propose a solution that changes the way Set works in a particular case that can be expressed in plain words ...
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### What are the best practices / most common / idiomatic ways to report errors in Mathematica?

In particular, what are the best ways to report errors about incorrect arguments to a function? Checking for the correct arguments is relatively easy using patterns, but how to report an informative ...
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### How to use Mathematica functions in Python programs?

I'd like to know how can I call Mathematica functions from Python. I appreciate a example, for example, using the Mathematica function Prime. I had search about MathLink but how to use it in Python ...
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### Custom functions by delegating options in a specific way and using core functions

I'd like to create a custom function that does essentially the same as a core function of mathematica but uses different default settings. Example: I want a Plot function that uses Mathematica's core ...
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### How to set Block local variables by code?

I need to create a user-defined Block function where the Block variables' values are defined by code. For example, imagine I ...
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### Select/Delete with Sublist elements?

Probably easy and short question, I still didn't fully figure out how to easily select/delete sublists from a list. Example: tt = {{2, 4}, {4, 8}} I want to delete/select all the elements where ...
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### Keep function range as a variable

Plot[2*x^2 - x + 2, {x, -1, 1}] plots a function of x from -1 to 1. As far as I can see, I cannot "save" this range in a variable: ...
In MATLAB, there is a command kmeans() that divides an array into $k$ clusters and calculates the centroid of each cluster. Is there any command in Mathematica to ...