# All Questions

55k views

### 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 ...
97k views

### 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 ...
26k views

### 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 ...
6k views

### Plot draws list of curves in same color when not using Evaluate

This example comes from the Mathematica documentation for Plot under Basic Examples. Can someone please explain why these are each plotted as a different color in ...
7k views

### What are the use cases for different scoping constructs?

Mathematica includes three functions that I know of which can be used to effectively (if not actually) define a variable and give it a value within a local scope: ...
11k views

### List of compilable functions

Is there somewhere a list on the functions that Compile can compile, or the cases in which a particular function can be compiled that I haven't found? I'd be glad ...
35k views

### Elegant operations on matrix rows and columns

Question The Mathematica tutorial has a section 'Basic Matrix Operations', describing operations like transpose, inverse and determinant. These operations all work on entire matrices. I am missing a ...
5k views

### How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
6k views

### What is the distinction between DownValues, UpValues, SubValues, and OwnValues?

When reading through the documentation, you often encounter the phrases DownValues, UpValues, ...
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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 the most convenient way to read definitions of in-memory symbols when we don't have the source files? (Spelunking tools)

Note: I put Simon's implementation on GitHub. Contributions welcome! When trying to read the definition of already defined (package or built-in) symbols using ...
5k views

### Can one identify the design patterns of Mathematica?

... or are they unnecessary in such a high-level language? I've been thinking about programming style, coding standards and the like quite a bit lately, the result of my current work on a mixed .Net/...
68k views

### Get a “step-by-step” evaluation in Mathematica

Is it possible in Mathematica to get a step-by-step evaluation of some functions; that's to say, outputting not only the result but all the stages that have led to it? If so, how does one do it? ...
2k views

### Injecting a sequence of expressions into a held expression

Consider the following toy example: Hold[{1, 2, x}] /. x -> Sequence[3, 4] It will give Hold[{1, 2, Sequence[3, 4]}] ...
3k views

### 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 ...
20k views

### Creating legends for plots with multiple lines?

So I have a graph with multiple lists, for e.g. data = {{1,2}, {3,4}, {3,5}, {2,3} . . .} If I then do ...
28k views

### Assign the results from a Solve to variable(s)

I understand Mathematica can't assign the results of a Solve to the unknowns because there may be more than 1 solution. How can I assign the 4 values of following result to variables?
9k views

### How do I save a variable or function definition to a file?

Is it possible to save a function which was created via Interpolation of some data in such a way that I can use this function in a new Mathematica session without ...
3k views

### 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 ...
10k views

### Are you interested in purchasing David Wagner's “Power programming with Mathematica”?

I recently contacted McGraw-Hill to see if they have a mechanism in place for printing out-of-print books that are still of interest. Specifically, I asked about "Power programming with Mathematica" ...
3k views

### 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 ...
10k views

### 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 ...
13k views

### 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 ...
2k 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: ...
2k views

### Replacement inside held expression

I wish to make a replacement inside a held expression: f[x_Real] := x^2; Hold[{2., 3.}] /. n_Real :> f[n] The desired output is ...
3k views

### Extract values for ViewMatrix from a Graphics3D

Under More Information in the help page of ViewMatrix the following entry can be found With the setting ...
7k views

### Plotting implicitly-defined space curves

It is known that space curves can either be defined parametrically, \begin{align*}x&=f(t)\\y&=g(t)\\z&=h(t)\end{align*} or as the intersection of two surfaces, \begin{align*}F(x,y,...
3k views

### 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 ...
1k 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 ...
930 views

### Combining values in one column (or part) when values in another column (or part) match

Consider the following: ...
3k views

### Using a PatternTest versus a Condition for pattern matching

My last question to the site resulted in several answers that involve using pattern matching in Mathematica, a feature I wasn't very familiar with at the time. I am currently reading Mathematica ...
3k views

### Partitioning with varying partition size

How can I partition a list into partitions whose sizes vary? The length of the $k$'th partition is a function $f(k)$. For example: if $l = \{1, 2, 3, 4, 5, 6\}$ and $f(k) = k$. Then the partitioning ...
5k views

### File-backed lists/variables for handling large data

Background Currently I am working with some large data (most of it generated by Mathematica itself). I usually find it a hassle to do this. For example, I just exported a large amount of data to ...
7k views

### About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...
1k views

### Funny behaviour when plotting a polynomial of high degree and large coefficients

I am trying to plot a polynomial of degree $29$ on the domain $[0,1]$, with fairly large coefficients: ...
18k views

### Exporting graphics to PDF - huge file

I want to draw some basic surfaces, export them to PDF and include them in a LaTeX file. I create a simple 3D graphics object, for instance with ...
1k views

### What's inside InterpolatingFunction[{{1., 4.}}, <>]?

I'm curious what's inside the InterpolationFunction object? For example: ...
950 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 ...
18k views

### Plotting Complex Quantity Functions

Trying to plot with complex quantities seems not to work properly in what I want to accomplish. I would like to know if there is a general rule/way of plotting when you have complex counterparts in ...
6k views

### What are some useful, undocumented Mathematica functions?

There have already been some questions about some undocumented functionality in Mathematica. Such as (please add to these lists!) How can one find undocumented options or option values in ...
12k views

### How to compile effectively?

What are the best practices of compiling functions? I understand that this is a vague question, but let me list some aspects that might trigger useful answers. Some of these have already been answered ...
4k views

### Looking for “Longest Common Substring” solution

I'm looking for robust code to solve the "Longest Common Substring" problem: Find the longest string (or strings) that is a substring (or are substrings) of two or more strings. I can just code it ...
9k views

### How to avoid returning a Null if there is no “else” condition in an If contruct

I need to use If but with only one option that is if "a" then do "b", else do nothing. So I wrote If[a,b] but the problem is ...
14k views

### Mathematica 10.0.x freezes in Initializing kernels

Bug caused by paclet update and fixed by paclet update. I updated to Windows 10 and have been running Mathematica fine on it for over a month. For some reason, it has just stopped working. I don't ...
8k views

### Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)

Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematica gives the ...
1k views

### How are parameters evaluated for a Plot in Manipulate

I am trying to get my head around how Manipulate evaluates functions in a Plot. I have read the introduction to Manipulate, and introduction to Dynamic, but I still ...
26k views

### 1 Plot, 2 Scale/Axis

I would like to plot those two datasets on top of each other. But they have very different range on the $y$ axis. How can I have two different axis? I found the following on the help menu but quite ...
15k views

### How to find all the local minima/maxima in a range

I want to find : all local maxima in range all local minima in range From those points I can interpolate and combine functions upper and lower boundary. What I am really interested in, is the ...