245
votes
24answers
32k 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 ...
355
votes
13answers
75k 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 ...
54
votes
4answers
4k 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 ...
116
votes
3answers
18k 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 ...
95
votes
8answers
8k 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 ...
123
votes
7answers
5k 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: ...
84
votes
7answers
24k 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 ...
17
votes
2answers
3k 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 ...
72
votes
5answers
47k 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? ...
59
votes
5answers
4k views

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?
49
votes
4answers
16k 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 ...
41
votes
8answers
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]}] ...
18
votes
5answers
15k 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?
58
votes
2answers
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 ...
88
votes
7answers
4k 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 ...
55
votes
6answers
3k views

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 ...
84
votes
7answers
8k 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 ...
110
votes
2answers
5k views

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

When reading through the documentation, you often encounter the phrases DownValues, UpValues, ...
39
votes
4answers
6k 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 ...
41
votes
4answers
2k 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 ...
52
votes
2answers
2k 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 ...
121
votes
5answers
8k 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" ...
43
votes
5answers
2k 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 ...
28
votes
4answers
3k views

Why does MatrixForm affect calculations?

This is a really newbie question, but it has me confused. Why does this code work without // MatrixForm and doesn't work with ...
19
votes
4answers
12k 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 ...
85
votes
1answer
4k 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 ...
52
votes
4answers
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 ...
25
votes
2answers
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 ...
61
votes
2answers
5k views

Shaving the last 50 ms off NMinimize

The epilogue: A paper where the below answer is used was published. The answer below is cited among the references:) The background: I have to fit an objective function for ~10 000 datasets in near ...
36
votes
6answers
6k 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 ...
57
votes
11answers
11k 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 ...
48
votes
8answers
2k 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 ...
29
votes
4answers
3k 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 ...
45
votes
3answers
1k views

Replace inside Held expression

I wish to make functional replacement inside Held expression like this: ...
23
votes
3answers
1k 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: ...
73
votes
4answers
4k 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 ...
58
votes
7answers
6k views

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 ...
37
votes
8answers
6k views

How do you convert a string containing a number in C scientific notation to a Mathematica number?

Suppose I have a string containing the C-representation of a floating point number, for example s = "1.23e-5" and I want to convert this to a Mathematica number. ...
16
votes
4answers
1k views

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) ...
31
votes
7answers
5k 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 ...
20
votes
2answers
3k views

How to fit 3 data sets to a model of 4 differential equations?

I'm a biologist and a newbie in Mathematica. I want to fit three data sets to a model consisting of four differential equations and 10 parameters. I want to find the parameters best fitting to my ...
17
votes
4answers
9k views

Finding unit tangent, normal, and binormal vectors for a given r(t)

For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$. I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...
25
votes
2answers
954 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: ...
107
votes
5answers
4k views

How can one find undocumented options or option values in Mathematica?

Mathematica has a lot of undocumented or poorly documented options. How does one go about working out if there is an undocumented option that might solve a particular problem? How does one work out ...
84
votes
5answers
19k 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 ...
109
votes
3answers
6k views

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.
65
votes
6answers
13k 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 ...
38
votes
3answers
6k 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, ...
23
votes
4answers
608 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
5answers
1k views

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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